├── .gitignore ├── LICENSE ├── README.md ├── bcjr_decoder.m ├── convolutional_encoder.m ├── display_llr_histograms.m ├── generate_llrs.m ├── jac.m ├── main_capacity.m ├── main_inner.m ├── main_mod.m ├── main_outer.m ├── measure_mutual_information_averaging.m ├── measure_mutual_information_histogram.m ├── modulate.m └── soft_demodulate.m /.gitignore: -------------------------------------------------------------------------------- 1 | *.m~ 2 | .DS_Store 3 | 4 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # exit-matlab 2 | Tools for plotting Extrinsic Information Transfer (EXIT) charts in Matlab 3 | -------------------------------------------------------------------------------- /bcjr_decoder.m: -------------------------------------------------------------------------------- 1 | % BCJR algorithm for a half-rate systematic recursive convolutional code 2 | % having 1 memory element, a generator polynomial of [1,0] and a feedback 3 | % polynomial of [1,1]. For more information, see Section 1.3.2.2 of Rob's 4 | % thesis (http://eprints.ecs.soton.ac.uk/14980) or the BCJR paper 5 | % (http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1055186). 6 | % Copyright (C) 2008 Robert G. Maunder 7 | 8 | % This program is free software: you can redistribute it and/or modify it 9 | % under the terms of the GNU General Public License as published by the 10 | % Free Software Foundation, either version 3 of the License, or (at your 11 | % option) any later version. 12 | 13 | % This program is distributed in the hope that it will be useful, but 14 | % WITHOUT ANY WARRANTY; without even the implied warranty of 15 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 16 | % Public License for more details. 17 | 18 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 19 | 20 | 21 | 22 | function [aposteriori_uncoded_llrs, aposteriori_encoded1_llrs, aposteriori_encoded2_llrs] = bcjr_decoder(apriori_uncoded_llrs, apriori_encoded1_llrs, apriori_encoded2_llrs) 23 | 24 | if(length(apriori_uncoded_llrs) ~= length(apriori_encoded1_llrs) || length(apriori_encoded1_llrs) ~= length(apriori_encoded2_llrs)) 25 | error('LLR sequences must have the same length'); 26 | end 27 | 28 | 29 | % All calculations are performed in the logarithmic domain in order to 30 | % avoid numerical issues. These occur in the normal domain, because some of 31 | % the confidences can get smaller than the smallest number the computer can 32 | % store. See Section 1.3.2.4 of Rob's thesis for more information on this. 33 | % 34 | % A multiplication of two confidences is achieved using the addition of the 35 | % corresponding log-confidences. If A = log(a) and B = log(b), then 36 | % log(a*b) = A+B (Equation 1.17 in Rob's thesis). 37 | % 38 | % An addition of two confidences is achieved using the Jacobian logarithm 39 | % of the corresponding log-confidences. The Jacobian logarithm is defined 40 | % in the jac.m file. If A = log(a) and B = log(b), then 41 | % log(a+b) = max(A,B) + log(1+exp(-abs(A-B))) (Equation 1.19 in Rob's 42 | % thesis). 43 | 44 | % Matrix to describe the trellis 45 | % Each row describes one transition in the trellis 46 | % Each state is allocated an index 1,2,3,... Note that this list starts 47 | % from 1 rather than 0. 48 | % FromState, ToState, UncodedBit, Encoded1Bit, Encoded2Bit 49 | transitions = [1, 1, 0, 0, 0; 50 | 1, 2, 1, 1, 1; 51 | 2, 1, 1, 1, 0; 52 | 2, 2, 0, 0, 1]; 53 | 54 | % Find the largest state index in the transitions matrix 55 | % In this example, we have two states since the code has one memory element 56 | state_count = max(max(transitions(:,1)),max(transitions(:,2))); 57 | 58 | % Calculate the a priori transition log-confidences by adding the 59 | % log-confidences associated with each corresponding bit value. This is 60 | % similar to Equation 1.12 in Rob's thesis or Equation 9 in the BCJR paper. 61 | gammas=zeros(size(transitions,1),length(apriori_uncoded_llrs)); 62 | for bit_index = 1:length(apriori_uncoded_llrs) 63 | for transition_index = 1:size(transitions,1) 64 | if transitions(transition_index, 3)==0 65 | gammas(transition_index, bit_index) = gammas(transition_index, bit_index) + apriori_uncoded_llrs(bit_index)/2; 66 | % Dividing the LLR by 2 gives a value that is log-proportional to 67 | % the actual log-confidence it instills. Log-proportional is fine 68 | % for us though, because we're after the log-ratio of 69 | % confidences. Don't worry too much about this confusing 70 | % feature. 71 | else 72 | gammas(transition_index, bit_index) = gammas(transition_index, bit_index) - apriori_uncoded_llrs(bit_index)/2; 73 | end 74 | 75 | if transitions(transition_index, 4)==0 76 | gammas(transition_index, bit_index) = gammas(transition_index, bit_index) + apriori_encoded1_llrs(bit_index)/2; 77 | else 78 | gammas(transition_index, bit_index) = gammas(transition_index, bit_index) - apriori_encoded1_llrs(bit_index)/2; 79 | end 80 | 81 | if transitions(transition_index, 5)==0 82 | gammas(transition_index, bit_index) = gammas(transition_index, bit_index) + apriori_encoded2_llrs(bit_index)/2; 83 | else 84 | gammas(transition_index, bit_index) = gammas(transition_index, bit_index) - apriori_encoded2_llrs(bit_index)/2; 85 | end 86 | end 87 | end 88 | 89 | % Forward recursion to calculate state log-confidences. This is similar to 90 | % Equation 1.13 in Rob's thesis or Equations 5 and 6 in the BCJR paper. 91 | alphas=zeros(state_count,length(apriori_uncoded_llrs)); 92 | alphas=alphas-inf; 93 | alphas(1,1)=0; % We know that this is the first state 94 | for state_index = 2:state_count 95 | alphas(state_index,1)=-inf; % We know that this is *not* the first state (a log-confidence of minus infinity is equivalent to a confidence of 0) 96 | end 97 | for bit_index = 2:length(apriori_uncoded_llrs) 98 | for transition_index = 1:size(transitions,1) 99 | alphas(transitions(transition_index,2),bit_index) = jac(alphas(transitions(transition_index,2),bit_index),alphas(transitions(transition_index,1),bit_index-1) + gammas(transition_index, bit_index-1)); 100 | end 101 | end 102 | 103 | % Backwards recursion to calculate state log-confidences. This is similar 104 | % to Equation 1.14 in Rob's thesis or Equations 7 and 8 in the BCJR paper. 105 | betas=zeros(state_count,length(apriori_uncoded_llrs)); 106 | betas=betas-inf; 107 | for state_index = 1:state_count 108 | betas(state_index,length(apriori_uncoded_llrs))=0; % The final state could be any one of these 109 | end 110 | for bit_index = length(apriori_uncoded_llrs)-1:-1:1 111 | for transition_index = 1:size(transitions,1) 112 | betas(transitions(transition_index,1),bit_index) = jac(betas(transitions(transition_index,1),bit_index),betas(transitions(transition_index,2),bit_index+1) + gammas(transition_index, bit_index+1)); 113 | end 114 | end 115 | 116 | % Calculate a posteriori transition log-confidences. This is similar to 117 | % Equation 1.15 in Rob's thesis or Equation 4 in the BCJR paper. 118 | deltas=zeros(size(transitions,1),length(apriori_uncoded_llrs)); 119 | for bit_index = 1:length(apriori_uncoded_llrs) 120 | for transition_index = 1:size(transitions,1) 121 | deltas(transition_index, bit_index) = alphas(transitions(transition_index,1),bit_index) + gammas(transition_index, bit_index) + betas(transitions(transition_index,2),bit_index); 122 | end 123 | end 124 | 125 | % Calculate the a posteriori LLRs. This is similar to Equation 1.16 in 126 | % Rob's thesis. 127 | aposteriori_uncoded_llrs = zeros(1,length(apriori_uncoded_llrs)); 128 | for bit_index = 1:length(apriori_uncoded_llrs) 129 | prob0=-inf; 130 | prob1=-inf; 131 | for transition_index = 1:size(transitions,1) 132 | if transitions(transition_index,3)==0 133 | prob0 = jac(prob0, deltas(transition_index,bit_index)); 134 | else 135 | prob1 = jac(prob1, deltas(transition_index,bit_index)); 136 | end 137 | end 138 | aposteriori_uncoded_llrs(bit_index) = prob0-prob1; 139 | end 140 | 141 | aposteriori_encoded1_llrs = zeros(1,length(apriori_uncoded_llrs)); 142 | for bit_index = 1:length(apriori_uncoded_llrs) 143 | prob0=-inf; 144 | prob1=-inf; 145 | for transition_index = 1:size(transitions,1) 146 | if transitions(transition_index,4)==0 147 | prob0 = jac(prob0, deltas(transition_index,bit_index)); 148 | else 149 | prob1 = jac(prob1, deltas(transition_index,bit_index)); 150 | end 151 | end 152 | aposteriori_encoded1_llrs(bit_index) = prob0-prob1; 153 | end 154 | 155 | aposteriori_encoded2_llrs = zeros(1,length(apriori_uncoded_llrs)); 156 | for bit_index = 1:length(apriori_uncoded_llrs) 157 | prob0=-inf; 158 | prob1=-inf; 159 | for transition_index = 1:size(transitions,1) 160 | if transitions(transition_index,5)==0 161 | prob0 = jac(prob0, deltas(transition_index,bit_index)); 162 | else 163 | prob1 = jac(prob1, deltas(transition_index,bit_index)); 164 | end 165 | end 166 | aposteriori_encoded2_llrs(bit_index) = prob0-prob1; 167 | end 168 | 169 | end -------------------------------------------------------------------------------- /convolutional_encoder.m: -------------------------------------------------------------------------------- 1 | % Encoder for a half-rate systematic recursive convolutional code 2 | % having 1 memory element, a generator polynomial of [1,0] and a feedback 3 | % polynomial of [1,1]. 4 | % Copyright (C) 2008 Robert G. Maunder 5 | 6 | % This program is free software: you can redistribute it and/or modify it 7 | % under the terms of the GNU General Public License as published by the 8 | % Free Software Foundation, either version 3 of the License, or (at your 9 | % option) any later version. 10 | 11 | % This program is distributed in the hope that it will be useful, but 12 | % WITHOUT ANY WARRANTY; without even the implied warranty of 13 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 14 | % Public License for more details. 15 | 16 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 17 | 18 | 19 | 20 | function [encoded1_bits, encoded2_bits] = convolutional_encoder(uncoded_bits) 21 | 22 | % Systematic bits 23 | encoded1_bits = uncoded_bits; 24 | 25 | % Parity bits 26 | encoded2_bits=zeros(1,length(uncoded_bits)); 27 | encoded2_bits(1) = uncoded_bits(1); 28 | for i = 2:length(uncoded_bits) 29 | encoded2_bits(i) = mod(encoded2_bits(i-1)+uncoded_bits(i),2); 30 | end 31 | 32 | end -------------------------------------------------------------------------------- /display_llr_histograms.m: -------------------------------------------------------------------------------- 1 | % Display the histograms of LLRs. This can be used to check that the LLRs 2 | % are self-consistent and well-conditioned. 3 | % Copyright (C) 2009 Robert G. Maunder 4 | 5 | % This program is free software: you can redistribute it and/or modify it 6 | % under the terms of the GNU General Public License as published by the 7 | % Free Software Foundation, either version 3 of the License, or (at your 8 | % option) any later version. 9 | 10 | % This program is distributed in the hope that it will be useful, but 11 | % WITHOUT ANY WARRANTY; without even the implied warranty of 12 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 13 | % Public License for more details. 14 | 15 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 16 | 17 | 18 | 19 | % llrs is a 1xK vector of LLRs 20 | % bits is a 1xK vector of the correct bit values 21 | % bin_width is an optional input, which can be set to the difference 22 | % between consecutive LLR values in the case of fixed-point LLRs. If 23 | % bit_width is omitted, then an appropriate value is calculated 24 | % automatically. 25 | function display_llr_histograms(llrs, bits, bin_width) 26 | 27 | 28 | if(length(llrs) ~= length(bits)) 29 | error('Must have same number of llrs and bits!'); 30 | end 31 | 32 | 33 | bit_1_count = sum(bits); 34 | bit_0_count = length(bits) - bit_1_count; 35 | if(bit_0_count == 0 || bit_1_count == 0) 36 | error('All bits have the same value'); 37 | end 38 | 39 | llr_0_noninfinite_count = 0; 40 | llr_1_noninfinite_count = 0; 41 | llr_0_max = -Inf; 42 | llr_0_min = Inf; 43 | llr_1_max = -Inf; 44 | llr_1_min = Inf; 45 | for bit_index = 1:length(bits) 46 | if(llrs(bit_index) ~= -Inf && llrs(bit_index) ~= Inf) 47 | if(bits(bit_index) == 0) 48 | llr_0_noninfinite_count = llr_0_noninfinite_count+1; 49 | 50 | if(llrs(bit_index) > llr_0_max) 51 | llr_0_max = llrs(bit_index); 52 | end 53 | if(llrs(bit_index) < llr_0_min) 54 | llr_0_min = llrs(bit_index); 55 | end 56 | else 57 | llr_1_noninfinite_count = llr_1_noninfinite_count+1; 58 | 59 | if(llrs(bit_index) > llr_1_max) 60 | llr_1_max = llrs(bit_index); 61 | end 62 | if(llrs(bit_index) < llr_1_min) 63 | llr_1_min = llrs(bit_index); 64 | end 65 | end 66 | end 67 | end 68 | 69 | if(llr_0_noninfinite_count > 0 && llr_1_noninfinite_count > 0) 70 | if ~exist('bin_width','var') 71 | llr_0_mean = 0.0; 72 | llr_1_mean = 0.0; 73 | for bit_index = 1:length(bits) 74 | if(llrs(bit_index) ~= -Inf && llrs(bit_index) ~= Inf) 75 | if(bits(bit_index) == 0) 76 | llr_0_mean = llr_0_mean+llrs(bit_index); 77 | else 78 | llr_1_mean = llr_1_mean+llrs(bit_index); 79 | end 80 | end 81 | 82 | end 83 | llr_0_mean = llr_0_mean/llr_0_noninfinite_count; 84 | llr_1_mean = llr_1_mean/llr_1_noninfinite_count; 85 | 86 | llr_0_variance = 0.0; 87 | llr_1_variance = 0.0; 88 | for bit_index = 1:length(bits) 89 | if(llrs(bit_index) ~= -Inf && llrs(bit_index) ~= Inf) 90 | 91 | if(bits(bit_index) == 0) 92 | 93 | llr_0_variance = llr_0_variance + (llrs(bit_index) - llr_0_mean)^2; 94 | else 95 | 96 | llr_1_variance = llr_1_variance + (llrs(bit_index) - llr_1_mean)^2; 97 | end 98 | end 99 | end 100 | llr_0_variance = llr_0_variance/llr_0_noninfinite_count; 101 | llr_1_variance = llr_1_variance/llr_1_noninfinite_count; 102 | 103 | bin_width = 0.5*(3.49*sqrt(llr_0_variance)*(llr_0_noninfinite_count^(-1.0/3.0)) + 3.49*sqrt(llr_1_variance)*(llr_1_noninfinite_count^(-1.0/3.0))); 104 | end 105 | if(bin_width > 0.0) 106 | 107 | bin_offset = floor(min(llr_0_min, llr_1_min)/bin_width)-1; 108 | temp = max(llr_0_max, llr_1_max)/bin_width-bin_offset+1; 109 | bin_count = ceil(temp); 110 | if(bin_count == temp) 111 | bin_count = bin_count+1; 112 | end 113 | 114 | else 115 | 116 | bin_offset = -1; 117 | bin_count = 3; 118 | end 119 | lots_of_bins = true; 120 | 121 | else 122 | lots_of_bins = false; 123 | bin_count = 4; 124 | end 125 | 126 | histogram = zeros(2,bin_count); 127 | 128 | for bit_index = 1:length(bits) 129 | if(llrs(bit_index) == -Inf) 130 | histogram(bits(bit_index)+1,1) = histogram(bits(bit_index)+1,1)+1; 131 | elseif(llrs(bit_index) == Inf) 132 | histogram(bits(bit_index)+1,bin_count) = histogram(bits(bit_index)+1,bin_count)+1; 133 | else 134 | if(lots_of_bins == true) 135 | if(bin_width > 0.0) 136 | histogram(bits(bit_index)+1,floor(llrs(bit_index)/bin_width)-bin_offset+1) = histogram(bits(bit_index)+1,floor(llrs(bit_index)/bin_width)-bin_offset+1)+1; 137 | else 138 | histogram(bits(bit_index)+1,2) = histogram(bits(bit_index)+1,2)+1; 139 | end 140 | else 141 | histogram(bits(bit_index)+1,bits(bit_index)+2) = histogram(bits(bit_index)+1,bits(bit_index)+2)+1; 142 | end 143 | end 144 | end 145 | 146 | results = zeros(4, bin_count); 147 | 148 | 149 | for bin_index=1:bin_count 150 | % if(histogram(1,bin_index) > 0 || histogram(2,bin_index) > 0) 151 | if(bin_index == 1) 152 | results(1,bin_index) = -inf; 153 | % fprintf(' -inf '); 154 | elseif(bin_index == bin_count) 155 | results(1,bin_index) = inf; 156 | % fprintf(' inf '); 157 | else 158 | if(lots_of_bins == true) 159 | if(bin_width > 0.0) 160 | results(1,bin_index) = (bin_index+bin_offset-1)*bin_width+bin_width/2.0; 161 | % fprintf('%14.6f ', (bin_index+bin_offset-1)*bin_width+bin_width/2.0); 162 | else 163 | results(1,bin_index) = 0.0; 164 | % fprintf('%14.6f ', 0.0); 165 | end 166 | else 167 | if(bin_index == 2) 168 | results(1,bin_index) = -1; 169 | % fprintf(' neg '); 170 | else 171 | results(1,bin_index) = -2; 172 | % fprintf(' pos '); 173 | end 174 | end 175 | end 176 | p0 = histogram(1,bin_index)/bit_0_count; 177 | p1 = histogram(2,bin_index)/bit_1_count; 178 | 179 | results(2,bin_index) = p0; 180 | % fprintf('%14.6f ', p0); 181 | results(3,bin_index) = p1; 182 | % fprintf('%14.6f ', p1); 183 | 184 | 185 | if(p0 == 0.0) 186 | results(4,bin_index) = -inf; 187 | % fprintf(' -inf \n'); 188 | elseif(p1 == 0.0) 189 | results(4,bin_index) = inf; 190 | % fprintf(' inf \n'); 191 | else 192 | results(4,bin_index) = log(p0/p1); 193 | % fprintf('%14.6f \n', log(p0/p1)); 194 | end 195 | % end 196 | end 197 | 198 | 199 | figure; 200 | plot(results(1,:),results(2,:),results(1,:),results(3,:)) 201 | xlabel('The values that the LLRs have'); 202 | ylabel('Histogram'); 203 | legend({'LLRs of 0-valued bits','LLRs of 1-valued bits'},'Location','northwest') 204 | hold on 205 | 206 | figure; 207 | plot(results(1,:),results(4,:),'-'); 208 | axis equal 209 | axis manual 210 | hold on 211 | plot([-1000,1000],[-1000,1000],'--'); 212 | xlabel('The values that the LLRs have'); 213 | ylabel('The values that the LLRs should have'); 214 | 215 | end 216 | -------------------------------------------------------------------------------- /generate_llrs.m: -------------------------------------------------------------------------------- 1 | % Generate Gaussian distributed a priori LLRs 2 | % Copyright (C) 2008 Robert G. Maunder 3 | 4 | % This program is free software: you can redistribute it and/or modify it 5 | % under the terms of the GNU General Public License as published by the 6 | % Free Software Foundation, either version 3 of the License, or (at your 7 | % option) any later version. 8 | 9 | % This program is distributed in the hope that it will be useful, but 10 | % WITHOUT ANY WARRANTY; without even the implied warranty of 11 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 12 | % Public License for more details. 13 | 14 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 15 | 16 | 17 | 18 | function llrs = generate_llrs(bits, mutual_information) 19 | if(mutual_information < 0 || mutual_information >= 1) 20 | error('mutual_information must be in the range [0,1)'); 21 | end 22 | sigma = (-1.0/0.3073*log(1.0-mutual_information^(1.0/1.1064))/log(2.0))^(1.0/(2.0*0.8935)); 23 | llrs = randn(1,length(bits))*sigma - (bits-0.5)*sigma^2; 24 | end -------------------------------------------------------------------------------- /jac.m: -------------------------------------------------------------------------------- 1 | % Jacobian logarithm 2 | % If A = log(a) and B = log(b), then log(a+b) = max(A,B) + log(1+exp(-abs(A-B))) 3 | % Copyright (C) 2008 Robert G. Maunder 4 | 5 | % This program is free software: you can redistribute it and/or modify it 6 | % under the terms of the GNU General Public License as published by the 7 | % Free Software Foundation, either version 3 of the License, or (at your 8 | % option) any later version. 9 | 10 | % This program is distributed in the hope that it will be useful, but 11 | % WITHOUT ANY WARRANTY; without even the implied warranty of 12 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 13 | % Public License for more details. 14 | 15 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 16 | 17 | 18 | 19 | function C = jac(A,B) 20 | 21 | C = max(A,B) + log(1+exp(-abs(A-B))); 22 | % C = max(A,B); 23 | 24 | 25 | 26 | end 27 | -------------------------------------------------------------------------------- /main_capacity.m: -------------------------------------------------------------------------------- 1 | % Plots the Continuous-input Continuous-output Memoryless Channel (CCMC) 2 | % and Discrete-input Continuous-output Memoryless Channel (DCMC) capacity 3 | % of AWGN and uncorrelated Rayleigh fading channels for BPSK, QPSK, 8PSK 4 | % and 16QAM. 5 | % Copyright (C) 2011 Robert G. Maunder 6 | 7 | % This program is free software: you can redistribute it and/or modify it 8 | % under the terms of the GNU General Public License as published by the 9 | % Free Software Foundation, either version 3 of the License, or (at your 10 | % option) any later version. 11 | 12 | % This program is distributed in the hope that it will be useful, but 13 | % WITHOUT ANY WARRANTY; without even the implied warranty of 14 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 15 | % Public License for more details. 16 | 17 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 18 | 19 | clear all; 20 | close all; 21 | 22 | % Control the accuracy and duration of the simulation 23 | symbol_count = 10000; 24 | 25 | % Set range of channel SNRs 26 | snr = -10:0.1:30; % dB 27 | 28 | % Select channel 29 | channel = 'AWGN'; 30 | % channel = 'Rayleigh'; 31 | 32 | % Setup modulation schemes 33 | modulation_name{1} = 'BPSK'; 34 | modulation{1} = [+1, -1]; 35 | 36 | modulation_name{2} = 'QPSK'; 37 | modulation{2} = [+1, +1i, -1, -1i]; 38 | 39 | modulation_name{3} = '8PSK'; 40 | modulation{3} = [+1, sqrt(1/2)*(+1+1i), +1i, sqrt(1/2)*(-1+1i), -1, sqrt(1/2)*(-1-1i), -1i, sqrt(1/2)*(+1-1i)]; 41 | 42 | modulation_name{4} = '16QAM'; 43 | modulation{4} = sqrt(1/10)*[-3+3*1i, -1+3*1i, +1+3*1i, +3+3*1i, -3+1*1i, -1+1*1i, +1+1*1i, +3+1*1i, -3-1*1i, -1-1*1i, +1-1*1i, +3-1*1i, -3-3*1i, -1-3*1i, +1-3*1i, +3-3*1i]; 44 | 45 | % If you add more modulation schemes here, make sure their average transmit power is normalised to unity 46 | 47 | 48 | 49 | % Calculate the CCMC capacity 50 | CCMC_capacity = nan(size(snr)); 51 | for snr_index = 1:length(snr) 52 | Gamma = 10^(snr(snr_index)/10); 53 | if strcmp(channel, 'AWGN') 54 | CCMC_capacity(snr_index)=log2(1+Gamma); 55 | elseif strcmp(channel, 'Rayleigh') 56 | % Refer to the following paper for CCMC capacity of Rayleigh fading 57 | % channel 58 | % https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=130999 59 | else 60 | error('Unsupported channel'); 61 | end 62 | end 63 | 64 | % Plot vs SNR 65 | my_legend = {'CCMC'}; 66 | figure(1); 67 | plot(snr,CCMC_capacity); 68 | xlabel('SNR [dB]'); 69 | ylabel('Capacity [bit/s/Hz]') 70 | legend(my_legend); 71 | title(channel); 72 | hold on 73 | 74 | % Plot vs Eb/N0 75 | figure(2); 76 | plot(snr-10*log10(CCMC_capacity),CCMC_capacity); 77 | xlabel('E_b/N_0 [dB]'); 78 | ylabel('Capacity [bit/s/Hz]') 79 | legend(my_legend); 80 | title(channel); 81 | hold on 82 | 83 | % DCMC simulation 84 | for modulation_index = 1:length(modulation) 85 | DCMC_capacity = nan(size(snr)); 86 | for snr_index = 1:length(snr) 87 | 88 | % Generate some random symbols 89 | symbols = ceil(length(modulation{modulation_index})*rand(1,symbol_count)); 90 | 91 | % Generate the transmitted signal 92 | x = modulation{modulation_index}(symbols); 93 | 94 | % Generate the channel gains 95 | if strcmp(channel, 'AWGN') 96 | h = ones(1,symbol_count); 97 | elseif strcmp(channel, 'Rayleigh') 98 | % Uncorrelated narrowband Rayleigh fading channel 99 | h = sqrt(1/2)*(randn(1,symbol_count)+1i*randn(1,symbol_count)); 100 | else 101 | error('Unsupported channel'); 102 | end 103 | 104 | % Generate some noise 105 | N0 = 1/(10^(snr(snr_index)/10)); 106 | n = sqrt(N0/2)*(randn(1,symbol_count)+1i*randn(1,symbol_count)); 107 | 108 | % Generate the received signal 109 | y = x.*h+n; 110 | 111 | % Calculate the symbol probabilities 112 | probabilities = max(exp(-(abs(ones(length(modulation{modulation_index}),1)*y - modulation{modulation_index}.'*h).^2)/N0),realmin); 113 | 114 | % Normalise the symbol probabilities 115 | probabilities = probabilities ./ (ones(length(modulation{modulation_index}),1)*sum(probabilities)); 116 | 117 | % Calculate the DCMC capacity 118 | DCMC_capacity(snr_index) = log2(length(modulation{modulation_index}))+mean(sum(probabilities.*log2(probabilities))); 119 | end 120 | 121 | % Plot vs SNR 122 | my_legend{end+1} = modulation_name{modulation_index}; 123 | figure(1) 124 | plot(snr,DCMC_capacity); 125 | legend(my_legend); 126 | 127 | % Plot vs Eb/N0 128 | figure(2) 129 | plot(snr-10*log10(DCMC_capacity),DCMC_capacity); 130 | legend(my_legend); 131 | 132 | end -------------------------------------------------------------------------------- /main_inner.m: -------------------------------------------------------------------------------- 1 | % EXIT function for a convolutional code used as an inner code 2 | % Copyright (C) 2008 Robert G. Maunder 3 | 4 | % This program is free software: you can redistribute it and/or modify it 5 | % under the terms of the GNU General Public License as published by the 6 | % Free Software Foundation, either version 3 of the License, or (at your 7 | % option) any later version. 8 | 9 | % This program is distributed in the hope that it will be useful, but 10 | % WITHOUT ANY WARRANTY; without even the implied warranty of 11 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 12 | % Public License for more details. 13 | 14 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 15 | 16 | 17 | 18 | % Number of bits to encode 19 | bit_count=100000; 20 | 21 | % Number of a priori mutual informations to consider 22 | IA_count=11; 23 | 24 | % Channel SNR in dB 25 | SNR = -4; 26 | 27 | % Noise variance 28 | N0 = 1/10^(SNR/10); 29 | 30 | % Generate some random bits 31 | uncoded_bits = round(rand(1,bit_count)); 32 | 33 | % Encode using a half-rate systematic recursive convolutional code having a single memory element 34 | [encoded1_bits, encoded2_bits] = convolutional_encoder(uncoded_bits); 35 | 36 | % BPSK modulator 37 | tx1 = -2*(encoded1_bits-0.5); 38 | tx2 = -2*(encoded2_bits-0.5); 39 | 40 | % Send the two BPSK signals one at a time over an AWGN channel 41 | rx1 = tx1 + sqrt(N0/2)*(randn(1,length(tx1))+1i*randn(1,length(tx1))); 42 | rx2 = tx2 + sqrt(N0/2)*(randn(1,length(tx2))+1i*randn(1,length(tx2))); 43 | 44 | % BPSK demodulator 45 | apriori_encoded1_llrs = (abs(rx1+1).^2-abs(rx1-1).^2)/N0; 46 | apriori_encoded2_llrs = (abs(rx2+1).^2-abs(rx2-1).^2)/N0; 47 | 48 | % Plot the LLR histograms 49 | display_llr_histograms([apriori_encoded1_llrs,apriori_encoded2_llrs],[encoded1_bits,encoded2_bits]); 50 | 51 | % A priori mutual informations to consider 52 | IA = 0.999*(0:1/(IA_count-1):1); 53 | 54 | % Initialise results 55 | IE_av=zeros(1,IA_count); 56 | IE_hist=zeros(1,IA_count); 57 | area=0.0; 58 | 59 | % Consider each a priori mutual information 60 | for IA_index = 1:IA_count 61 | 62 | % Generate the a priori LLRs having the a priori mutual information considered 63 | apriori_uncoded_llrs = generate_llrs(uncoded_bits, IA(IA_index)); 64 | 65 | % Do the BCJR 66 | [aposteriori_uncoded_llrs, aposteriori_encoded1_llrs, aposteriori_encoded2_llrs] = bcjr_decoder(apriori_uncoded_llrs, apriori_encoded1_llrs, apriori_encoded2_llrs); 67 | 68 | % Calculate the new information 69 | extrinsic_uncoded_llrs = aposteriori_uncoded_llrs-apriori_uncoded_llrs; 70 | 71 | % Measure the mutual information of the extrinsic LLRs 72 | IE_hist(IA_index) = measure_mutual_information_histogram(extrinsic_uncoded_llrs, uncoded_bits); 73 | IE_av(IA_index) = measure_mutual_information_averaging(extrinsic_uncoded_llrs); 74 | 75 | % Update the area beneath the EXIT function 76 | if(IA_index > 1) 77 | area = area + (IE_av(IA_index)+IE_av(IA_index-1))*(IA(IA_index)-IA(IA_index-1))/2; 78 | end 79 | end 80 | 81 | 82 | % Plot EXIT function 83 | figure 84 | xlim([0 1]); 85 | ylim([0 1]); 86 | xlabel('Quality of input LLRs (a priori mutual information I_A)'); 87 | ylabel('Quality of output LLRs (extrinsic mutual information I_E)'); 88 | title(['EXIT function for SNR = ', num2str(SNR), ' dB']); 89 | hold on 90 | plot(IA,IE_hist,'r'); 91 | plot(IA,IE_av,'b'); 92 | legend({'True quality','Claimed quality'},'Location','northwest'); 93 | 94 | % Display the area beneath the EXIT function 95 | annotation('textbox','String',{['Area = ', num2str(area)]},'LineStyle','none','Position',[0.7 0.1 0.2 0.1]); 96 | 97 | -------------------------------------------------------------------------------- /main_mod.m: -------------------------------------------------------------------------------- 1 | % EXIT function for a soft-input soft-output demodulator 2 | % Copyright (C) 2008 Robert G. Maunder 3 | 4 | % This program is free software: you can redistribute it and/or modify it 5 | % under the terms of the GNU General Public License as published by the 6 | % Free Software Foundation, either version 3 of the License, or (at your 7 | % option) any later version. 8 | 9 | % This program is distributed in the hope that it will be useful, but 10 | % WITHOUT ANY WARRANTY; without even the implied warranty of 11 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 12 | % Public License for more details. 13 | 14 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 15 | 16 | 17 | 18 | % Number of bits to encode 19 | bit_count=100000; 20 | 21 | % Number of a priori mutual informations to consider 22 | IA_count=11; 23 | 24 | % Channel SNR in dB 25 | SNR = 0; 26 | 27 | % Noise variance 28 | N0 = 1/10^(SNR/10); 29 | 30 | % A priori mutual informations to consider 31 | IA = 0.999*(0:1/(IA_count-1):1); 32 | 33 | % Initialise results 34 | IE_av=zeros(1,IA_count); 35 | IE_hist=zeros(1,IA_count); 36 | area=0.0; 37 | 38 | % Consider each a priori mutual information 39 | for IA_index = 1:IA_count 40 | 41 | % Generate some random bits 42 | bits = round(rand(1,bit_count)); 43 | 44 | % Encode using a half-rate systematic recursive convolutional code having a single memory element 45 | tx = modulate(bits); 46 | 47 | % Rayleigh fading 48 | h = sqrt(1/2)*(randn(size(tx))+1i*randn(size(tx))); 49 | 50 | % Noise 51 | n = sqrt(N0/2)*(randn(size(tx))+1i*randn(size(tx))); 52 | 53 | % Uncorrelated narrowband Rayleigh fading channel 54 | rx = h.*tx + n; 55 | 56 | 57 | % Generate the a priori LLRs having the a priori mutual information considered 58 | apriori_llrs = generate_llrs(bits, IA(IA_index)); 59 | 60 | % Do the BCJR 61 | extrinsic_llrs = soft_demodulate(rx, h, N0, apriori_llrs); 62 | 63 | % Measure the mutual information of the extrinsic LLRs 64 | IE_hist(IA_index) = measure_mutual_information_histogram(extrinsic_llrs, bits); 65 | IE_av(IA_index) = measure_mutual_information_averaging(extrinsic_llrs); 66 | 67 | % Update the area beneath the EXIT function 68 | if(IA_index > 1) 69 | area = area + (IE_av(IA_index)+IE_av(IA_index-1))*(IA(IA_index)-IA(IA_index-1))/2; 70 | end 71 | end 72 | 73 | 74 | % Plot EXIT function 75 | figure 76 | xlim([0 1]); 77 | ylim([0 1]); 78 | xlabel('Quality of input LLRs (a priori mutual information I_A)'); 79 | ylabel('Quality of output LLRs (extrinsic mutual information I_E)'); 80 | title(['EXIT function for SNR = ', num2str(SNR), ' dB']); 81 | hold on 82 | plot(IA,IE_hist,'r'); 83 | plot(IA,IE_av,'b'); 84 | legend({'True quality','Claimed quality'},'Location','northwest'); 85 | 86 | % Display the area beneath the EXIT function 87 | annotation('textbox','String',{['Area = ', num2str(area)]},'LineStyle','none','Position',[0.7 0.1 0.2 0.1]); 88 | 89 | -------------------------------------------------------------------------------- /main_outer.m: -------------------------------------------------------------------------------- 1 | % EXIT function for a convolutional code used as an outer code 2 | % Copyright (C) 2008 Robert G. Maunder 3 | 4 | % This program is free software: you can redistribute it and/or modify it 5 | % under the terms of the GNU General Public License as published by the 6 | % Free Software Foundation, either version 3 of the License, or (at your 7 | % option) any later version. 8 | 9 | % This program is distributed in the hope that it will be useful, but 10 | % WITHOUT ANY WARRANTY; without even the implied warranty of 11 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 12 | % Public License for more details. 13 | 14 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 15 | 16 | 17 | 18 | % Number of bits to encode 19 | bit_count=100000; 20 | 21 | % Number of a priori mutual informations to consider 22 | IA_count=11; 23 | 24 | % Generate some random bits 25 | uncoded_bits = round(rand(1,bit_count)); 26 | 27 | % Encode using a half-rate systematic recursive convolutional code having a single memory element 28 | [encoded1_bits, encoded2_bits] = convolutional_encoder(uncoded_bits); 29 | 30 | % A priori mutual informations to consider 31 | IA = 0.999*(0:1/(IA_count-1):1); 32 | 33 | % Initialise results 34 | IE_hist=zeros(1,IA_count); 35 | IE_av=zeros(1,IA_count); 36 | BER=zeros(1,IA_count); 37 | area=0.0; 38 | 39 | % Consider each a priori mutual information 40 | for IA_index = 1:IA_count 41 | 42 | % Generate the a priori LLRs having the a priori mutual information considered 43 | apriori_encoded1_llrs = generate_llrs(encoded1_bits, IA(IA_index)); 44 | apriori_encoded2_llrs = generate_llrs(encoded2_bits, IA(IA_index)); 45 | 46 | % No a priori information for the uncoded bits when operating as an outer code 47 | apriori_uncoded_llrs = zeros(1,length(uncoded_bits)); 48 | 49 | % Do the BCJR 50 | [aposteriori_uncoded_llrs, aposteriori_encoded1_llrs, aposteriori_encoded2_llrs] = bcjr_decoder(apriori_uncoded_llrs, apriori_encoded1_llrs, apriori_encoded2_llrs); 51 | 52 | % Calculate the new information 53 | extrinsic_encoded1_llrs = aposteriori_encoded1_llrs-apriori_encoded1_llrs; 54 | extrinsic_encoded2_llrs = aposteriori_encoded2_llrs-apriori_encoded2_llrs; 55 | 56 | % Measure the mutual information of the extrinsic LLRs 57 | IE_hist(IA_index) = (measure_mutual_information_histogram(extrinsic_encoded1_llrs, encoded1_bits) + measure_mutual_information_histogram(extrinsic_encoded2_llrs, encoded2_bits))/2; 58 | IE_av(IA_index) = (measure_mutual_information_averaging(extrinsic_encoded1_llrs) + measure_mutual_information_averaging(extrinsic_encoded2_llrs))/2; 59 | 60 | % Calculate the BER 61 | decoded_bits = aposteriori_uncoded_llrs < 0; 62 | BER(IA_index) = sum(uncoded_bits ~= decoded_bits)/length(uncoded_bits); 63 | 64 | % Update the area beneath the EXIT function 65 | if(IA_index > 1) 66 | area = area + (IE_av(IA_index)+IE_av(IA_index-1))*(IA(IA_index)-IA(IA_index-1))/2; 67 | end 68 | 69 | end 70 | 71 | % Plot BER 72 | figure 73 | semilogy(IA,BER); 74 | xlim([0 1]); 75 | ylim([min(100/bit_count,0.1) 1]); 76 | xlabel('Quality of input LLRs (a priori mutual information I_A)'); 77 | ylabel('BER'); 78 | 79 | % Plot inverted EXIT function 80 | figure 81 | xlim([0 1]); 82 | ylim([0 1]); 83 | xlabel('Quality of output LLRs (extrinsic mutual information I_E)'); 84 | ylabel('Quality of input LLRs (a priori mutual information I_A)'); 85 | title('Inverted EXIT function'); 86 | hold on 87 | plot(IE_hist,IA,'r'); 88 | plot(IE_av,IA,'b'); 89 | legend({'True quality','Claimed quality'},'Location','northwest'); 90 | 91 | % Display the area beneath the inverted EXIT function 92 | annotation('textbox','String',{['Area = ', num2str(1-area)]},'LineStyle','none','Position',[0.7 0.1 0.2 0.1]); 93 | 94 | -------------------------------------------------------------------------------- /measure_mutual_information_averaging.m: -------------------------------------------------------------------------------- 1 | % Measure the mutual information of some LLRs using the averaging method. 2 | % This method assumes that the LLRs are self-consistent and 3 | % well-conditioned. 4 | % Copyright (C) 2008 Robert G. Maunder 5 | 6 | % This program is free software: you can redistribute it and/or modify it 7 | % under the terms of the GNU General Public License as published by the 8 | % Free Software Foundation, either version 3 of the License, or (at your 9 | % option) any later version. 10 | 11 | % This program is distributed in the hope that it will be useful, but 12 | % WITHOUT ANY WARRANTY; without even the implied warranty of 13 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 14 | % Public License for more details. 15 | 16 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 17 | 18 | 19 | 20 | % llrs is a 1xK vector of LLRs 21 | % mutual_information is a scalar in the range 0 to 1 22 | function mutual_information = measure_mutual_information_averaging(llrs) 23 | P0 = exp(llrs)./(1+exp(llrs)); 24 | P1 = 1-P0; 25 | entropies = -P0.*log2(P0)-P1.*log2(P1); 26 | mutual_information = 1-sum(entropies(~isnan(entropies)))/length(entropies); 27 | end -------------------------------------------------------------------------------- /measure_mutual_information_histogram.m: -------------------------------------------------------------------------------- 1 | % Measure the mutual information of some LLRs using the histogram method. 2 | % This method works best when the vector of LLRs is as long as possible. 3 | % It does not assume that the LLRs are self-consistent and 4 | % well-conditioned. 5 | % Copyright (C) 2010 Robert G. Maunder 6 | 7 | % This program is free software: you can redistribute it and/or modify it 8 | % under the terms of the GNU General Public License as published by the 9 | % Free Software Foundation, either version 3 of the License, or (at your 10 | % option) any later version. 11 | 12 | % This program is distributed in the hope that it will be useful, but 13 | % WITHOUT ANY WARRANTY; without even the implied warranty of 14 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 15 | % Public License for more details. 16 | 17 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 18 | 19 | 20 | 21 | % llrs is a 1xK vector of LLRs 22 | % bits is a 1xK vector of the correct bit values 23 | % bin_width is an optional input, which can be set to the difference 24 | % between consecutive LLR values in the case of fixed-point LLRs. If 25 | % bit_width is omitted, then an appropriate value is calculated 26 | % automatically. 27 | % mutual_information is a scalar in the range 0 to 1 28 | function mutual_information = measure_mutual_information_histogram(llrs, bits, bin_width) 29 | 30 | 31 | if(length(llrs) ~= length(bits)) 32 | error('Must have same number of llrs and bits!'); 33 | end 34 | 35 | 36 | bit_1_count = sum(bits); 37 | bit_0_count = length(bits) - bit_1_count; 38 | if(bit_0_count == 0 || bit_1_count == 0) 39 | mutual_information = 0.0; 40 | else 41 | 42 | llr_0_noninfinite_count = 0; 43 | llr_1_noninfinite_count = 0; 44 | llr_0_max = -Inf; 45 | llr_0_min = Inf; 46 | llr_1_max = -Inf; 47 | llr_1_min = Inf; 48 | for bit_index = 1:length(bits) 49 | if(llrs(bit_index) ~= -Inf && llrs(bit_index) ~= Inf) 50 | if(bits(bit_index) == 0) 51 | llr_0_noninfinite_count = llr_0_noninfinite_count+1; 52 | 53 | if(llrs(bit_index) > llr_0_max) 54 | llr_0_max = llrs(bit_index); 55 | end 56 | if(llrs(bit_index) < llr_0_min) 57 | llr_0_min = llrs(bit_index); 58 | end 59 | else 60 | llr_1_noninfinite_count = llr_1_noninfinite_count+1; 61 | 62 | if(llrs(bit_index) > llr_1_max) 63 | llr_1_max = llrs(bit_index); 64 | end 65 | if(llrs(bit_index) < llr_1_min) 66 | llr_1_min = llrs(bit_index); 67 | end 68 | end 69 | end 70 | end 71 | 72 | if(llr_0_noninfinite_count > 0 && llr_1_noninfinite_count > 0 && llr_0_min <= llr_1_max && llr_1_min <= llr_0_max) 73 | 74 | if ~exist('bin_width','var') 75 | 76 | llr_0_mean = 0.0; 77 | llr_1_mean = 0.0; 78 | for bit_index = 1:length(bits) 79 | if(llrs(bit_index) ~= -Inf && llrs(bit_index) ~= Inf) 80 | if(bits(bit_index) == 0) 81 | llr_0_mean = llr_0_mean+llrs(bit_index); 82 | else 83 | llr_1_mean = llr_1_mean+llrs(bit_index); 84 | end 85 | end 86 | 87 | end 88 | llr_0_mean = llr_0_mean/llr_0_noninfinite_count; 89 | llr_1_mean = llr_1_mean/llr_1_noninfinite_count; 90 | 91 | llr_0_variance = 0.0; 92 | llr_1_variance = 0.0; 93 | for bit_index = 1:length(bits) 94 | if(llrs(bit_index) ~= -Inf && llrs(bit_index) ~= Inf) 95 | 96 | if(bits(bit_index) == 0) 97 | 98 | llr_0_variance = llr_0_variance + (llrs(bit_index) - llr_0_mean)^2; 99 | else 100 | 101 | llr_1_variance = llr_1_variance + (llrs(bit_index) - llr_1_mean)^2; 102 | end 103 | end 104 | end 105 | llr_0_variance = llr_0_variance/llr_0_noninfinite_count; 106 | llr_1_variance = llr_1_variance/llr_1_noninfinite_count; 107 | 108 | bin_width = 0.5*(3.49*sqrt(llr_0_variance)*(llr_0_noninfinite_count^(-1.0/3.0)) + 3.49*sqrt(llr_1_variance)*(llr_1_noninfinite_count^(-1.0/3.0))); 109 | end 110 | if(bin_width > 0.0) 111 | 112 | bin_offset = floor(min(llr_0_min, llr_1_min)/bin_width)-1; 113 | temp = max(llr_0_max, llr_1_max)/bin_width-bin_offset+1; 114 | bin_count = ceil(temp); 115 | if(bin_count == temp) 116 | bin_count = bin_count+1; 117 | end 118 | 119 | else 120 | 121 | bin_offset = -1; 122 | bin_count = 3; 123 | end 124 | lots_of_bins = true; 125 | 126 | else 127 | lots_of_bins = false; 128 | bin_count = 4; 129 | end 130 | 131 | histogram = zeros(2,bin_count); 132 | 133 | for bit_index = 1:length(bits) 134 | if(llrs(bit_index) == -Inf) 135 | histogram(bits(bit_index)+1,1) = histogram(bits(bit_index)+1,1)+1; 136 | elseif(llrs(bit_index) == Inf) 137 | histogram(bits(bit_index)+1,bin_count) = histogram(bits(bit_index)+1,bin_count)+1; 138 | else 139 | if(lots_of_bins == true) 140 | if(bin_width > 0.0) 141 | histogram(bits(bit_index)+1,floor(llrs(bit_index)/bin_width)-bin_offset+1) = histogram(bits(bit_index)+1,floor(llrs(bit_index)/bin_width)-bin_offset+1)+1; 142 | else 143 | histogram(bits(bit_index)+1,2) = histogram(bits(bit_index)+1,2)+1; 144 | end 145 | else 146 | histogram(bits(bit_index)+1,bits(bit_index)+2) = histogram(bits(bit_index)+1,bits(bit_index)+2)+1; 147 | end 148 | end 149 | end 150 | 151 | pdf = zeros(2,bin_count); 152 | pdf(1,:) = histogram(1,:)/bit_0_count; 153 | pdf(2,:) = histogram(2,:)/bit_1_count; 154 | 155 | mutual_information = 0.0; 156 | for bit_value = 0:1 157 | for bin_index = 1:bin_count 158 | if(pdf(bit_value+1,bin_index) > 0.0) 159 | mutual_information = mutual_information + 0.5*pdf(bit_value+1,bin_index)*log2(2.0*pdf(bit_value+1,bin_index)/(pdf(1,bin_index) + pdf(2,bin_index))); 160 | end 161 | end 162 | end 163 | end 164 | end 165 | -------------------------------------------------------------------------------- /modulate.m: -------------------------------------------------------------------------------- 1 | % QPSK modulator using natural mapping 2 | % Copyright (C) 2010 Robert G. Maunder 3 | 4 | % This program is free software: you can redistribute it and/or modify it 5 | % under the terms of the GNU General Public License as published by the 6 | % Free Software Foundation, either version 3 of the License, or (at your 7 | % option) any later version. 8 | 9 | % This program is distributed in the hope that it will be useful, but 10 | % WITHOUT ANY WARRANTY; without even the implied warranty of 11 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 12 | % Public License for more details. 13 | 14 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 15 | 16 | % bits is a k*n vector of bits 17 | % tx is a vector of complex symbols 18 | function tx = modulate(bits) 19 | 20 | % Specify the constellation points and the bit mapping here 21 | constellation_points = [+1+1i; -1+1i; -1-1i; +1-1i]/sqrt(2); 22 | bit_labels = [0,0; 0,1; 1,1; 1,0]; 23 | 24 | % Determine the number of bits per symbol and the number of constellation points here 25 | k = size(bit_labels,2); 26 | M = 2^k; 27 | N = length(bits)/k; 28 | 29 | 30 | % Check that all the vectors and matrices have the correct dimensions 31 | if ~isequal(size(constellation_points),[M,1]) || ~isequal(size(bit_labels),[M,k]) 32 | error('wrong dimensions'); 33 | end 34 | 35 | symbols = bin2dec(num2str(reshape(bits,[k,N])'))'+1; 36 | tx = constellation_points(symbols); 37 | 38 | 39 | end 40 | 41 | -------------------------------------------------------------------------------- /soft_demodulate.m: -------------------------------------------------------------------------------- 1 | % Soft QPSK demodulator using natural mapping 2 | % Copyright (C) 2010 Robert G. Maunder 3 | 4 | % This program is free software: you can redistribute it and/or modify it 5 | % under the terms of the GNU General Public License as published by the 6 | % Free Software Foundation, either version 3 of the License, or (at your 7 | % option) any later version. 8 | 9 | % This program is distributed in the hope that it will be useful, but 10 | % WITHOUT ANY WARRANTY; without even the implied warranty of 11 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General 12 | % Public License for more details. 13 | 14 | % The GNU General Public License can be seen at http://www.gnu.org/licenses/. 15 | 16 | % apriori_llrs is a 1xk vector of a priori LLRs 17 | % rx is a complex symbol 18 | % channel is a complex channel coefficient 19 | % N0 is the noise power spectral density 20 | % extrinsic_llrs is a 1xk vector of extrinsic LLRs 21 | function extrinsic_llrs = soft_demodulate(rx, channel, N0, apriori_llrs) 22 | 23 | % Specify the constellation points and the bit mapping here 24 | constellation_points = [+1+1i; -1+1i; -1-1i; +1-1i]/sqrt(2); 25 | bit_labels = [0,0; 0,1; 1,0; 1,1]; 26 | 27 | % Determine the number of bits per symbol and the number of constellation points here 28 | k = size(bit_labels,2); 29 | M = 2^k; 30 | N = length(rx); 31 | 32 | % Check that all the vectors and matrices have the correct dimensions 33 | if ~isequal(size(constellation_points),[M,1]) || ~isequal(size(bit_labels),[M,k]) 34 | error('wrong dimensions'); 35 | end 36 | 37 | if length(channel) ~= length(rx) && length(channel) ~= 1 38 | error('wrong dimensions'); 39 | end 40 | 41 | 42 | 43 | aposteriori_symbol_LLRs = zeros(M,N); 44 | 45 | % Put the influence of the received signals into the symbol LLRs 46 | for perm_index = 1:M 47 | aposteriori_symbol_LLRs(perm_index,:) = -abs(rx-channel*constellation_points(perm_index)).^2./N0; 48 | end 49 | 50 | if exist('apriori_llrs','var') 51 | % Put the influence of the apriori LLRs into the symbol LLRs 52 | for bit_index = 1:k 53 | % aposteriori_symbol_LLRs(:,bit_permutations(bit_index,:) == 0) = aposteriori_symbol_LLRs(:,bit_permutations(bit_index,:) == 0) + repmat(apriori_llrs(bit_index:bits_per_symbol:end),[1,permutations/2]); 54 | 55 | for perm_index = 1:M 56 | if bit_labels(perm_index,bit_index) == 0 57 | aposteriori_symbol_LLRs(perm_index,:) = aposteriori_symbol_LLRs(perm_index,:) + apriori_llrs(bit_index:k:end); 58 | end 59 | end 60 | end 61 | end 62 | 63 | % Extract the aposteriori LLRs from the symbol LLRs 64 | aposteriori_llrs = zeros(1,N*k); 65 | for bit_index = 1:k 66 | p0 = -inf(1,N); 67 | p1 = -inf(1,N); 68 | 69 | for perm_index = 1:M 70 | if bit_labels(perm_index,bit_index) == 0 71 | p0 = jac(p0, aposteriori_symbol_LLRs(perm_index,:)); 72 | else 73 | p1 = jac(p1, aposteriori_symbol_LLRs(perm_index,:)); 74 | end 75 | end 76 | 77 | aposteriori_llrs(bit_index:k:end) = p0-p1; 78 | end 79 | 80 | if exist('apriori_llrs','var') 81 | % Remove the apriori from the aposteriori to get the extrinsic 82 | extrinsic_llrs = aposteriori_llrs - apriori_llrs; 83 | else 84 | extrinsic_llrs = aposteriori_llrs; 85 | end 86 | 87 | 88 | 89 | 90 | end 91 | --------------------------------------------------------------------------------