├── BaseGraph ├── BaseGraph1_Set0.txt ├── BaseGraph1_Set1.txt ├── BaseGraph1_Set2.txt ├── BaseGraph1_Set3.txt ├── BaseGraph1_Set4.txt ├── BaseGraph1_Set5.txt ├── BaseGraph1_Set6.txt ├── BaseGraph1_Set7.txt ├── BaseGraph2_Set0.txt ├── BaseGraph2_Set1.txt ├── BaseGraph2_Set2.txt ├── BaseGraph2_Set3.txt ├── BaseGraph2_Set4.txt ├── BaseGraph2_Set5.txt ├── BaseGraph2_Set6.txt └── BaseGraph2_Set7.txt ├── BaseGraph_GM ├── LDPC_GM_BG1_3.txt ├── LDPC_GM_BG2_10.txt ├── LDPC_GM_BG2_16.txt ├── LDPC_GM_BG2_2.txt ├── LDPC_GM_BG2_3.txt ├── LDPC_GM_BG2_5.txt └── LDPC_GM_BG2_6.txt ├── Biases_Var └── Biases_Var0.txt ├── GeneratorMatrix.py ├── Neural_MS.py ├── Neural_MS_damping.py ├── Neural_MS_multiloss.py ├── Neural_SP.py ├── Neural_simplified_MS.py ├── README.md └── Weights_Var └── Weights_Var0.txt /BaseGraph/BaseGraph1_Set0.txt: -------------------------------------------------------------------------------- 1 | 250 69 226 159 -1 100 10 -1 -1 59 229 110 191 9 -1 195 23 -1 190 35 239 31 1 0 -1 -1 -1 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-0.0063283043 133 | 0.113015376 134 | 0.2346033 135 | -0.043193035 136 | -0.11187369 137 | -0.15975088 138 | -0.031722296 139 | 0.04233382 140 | -0.03060595 141 | 0.14143538 142 | 0.03264099 143 | -0.034595177 144 | 0.07851754 145 | -0.008446274 146 | -0.07251844 147 | -0.035989948 148 | 0.05398303 149 | -0.02528952 150 | -0.022793386 151 | -0.2141342 152 | -0.044201747 153 | -0.11335754 154 | -0.12653308 155 | -0.035213947 156 | 0.09899772 157 | 0.10883272 158 | -0.03336991 159 | 0.057951014 160 | 0.14332551 161 | -0.0066785254 162 | -0.007733984 163 | 0.059412315 164 | 0.10624055 165 | -0.0706507 166 | -0.02707252 167 | 0.11537261 168 | -0.070532635 169 | 0.033413947 170 | -0.0341323 171 | 0.0059093917 172 | 0.031915903 173 | -0.027187746 174 | -0.047771208 175 | 0.06079971 176 | 0.047437765 177 | -0.12014758 178 | -0.01880217 179 | -0.05623773 180 | 0.12315829 181 | -0.0009401468 182 | -0.08998101 183 | 0.012640342 184 | -0.08946823 185 | -0.031650934 186 | 0.057702925 187 | -0.03876956 188 | -0.027534112 189 | -0.052504618 190 | -0.0725603 191 | -0.022331608 192 | 0.14436 193 | -0.017293952 194 | 0.15104696 195 | 0.085953556 196 | -0.14137693 197 | -0.012234991 198 | -------------------------------------------------------------------------------- /GeneratorMatrix.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | # get the generator matrix of LDPC code 4 | BaseGraph = 1 5 | Z = 5 # lifting factor 6 | ldpc_i_ls = 2 # index of base graph 7 | code_BG = np.loadtxt("./BaseGraph/BaseGraph{0}_Set{1}.txt".format(BaseGraph, ldpc_i_ls), int, delimiter=' ') # the matrix form of base graph 8 | code_N = code_BG.shape[1] 9 | code_m = code_BG.shape[0] 10 | code_k = code_N - code_m 11 | PCM = np.zeros([code_m * Z, code_N * Z], dtype=int) # parity check matrix 12 | for i in range(code_m): 13 | for j in range(code_N): 14 | if code_BG[i, j] != -1: 15 | a = code_BG[i, j] % Z 16 | for k in range(Z): 17 | PCM[i * Z + k, j * Z + (k + a) % Z] = 1 18 | 19 | def roll_left(vec, L, Z): 20 | vec1 = np.zeros([Z], dtype=int) 21 | vec1[0:Z - L] = vec[L:Z] 22 | if L != 0: 23 | vec1[Z - L:] = vec[0:L] 24 | return vec1 25 | 26 | def roll_right(vec, L, Z): 27 | vec1 = np.zeros([Z], dtype=int) 28 | vec1[0:L] = vec[Z-L:Z] 29 | vec1[L:Z] = vec[0:Z - L] 30 | if L != 0: 31 | vec1[0:L] = vec[Z-L:Z] 32 | return vec1 33 | 34 | # 5G LDPC encoder 35 | def LDPC_encoder(infoWord, code_PCM, code_n, code_m, Z): 36 | code_k = code_N - code_m 37 | infoWord = np.reshape(infoWord, [code_k, Z]) 38 | encodeWord = np.zeros((code_n, Z), dtype=int) 39 | shift = np.zeros((code_m, code_N, Z), dtype=int) 40 | encodeWord[:code_k, :] = infoWord[:, :] 41 | for i in range(0, code_m, 1): 42 | for j in range(0, code_k, 1): 43 | if(code_PCM[i, j] != -1): 44 | shift[i, j, :] = roll_left(infoWord[j, :], code_PCM[i, j] % Z, Z) 45 | check_vec = np.sum(shift, axis=1) % 2 46 | encodeWord[code_k, :] = np.sum(check_vec[0:4, :], axis=0) % 2 47 | if(BaseGraph == 1 and ldpc_i_ls == 2): 48 | encodeWord[code_k, :] = roll_right(encodeWord[code_k, :], 105, Z) 49 | if(BaseGraph == 2 and ldpc_i_ls != 3 and ldpc_i_ls != 7): 50 | encodeWord[code_k, :] = roll_right(encodeWord[code_k, :], 1, Z) 51 | for i in range(0, code_m, 1): 52 | if (code_PCM[i, code_k] != -1): 53 | shift[i, code_k, :] = roll_left(encodeWord[code_k, :], code_PCM[i, code_k] % Z, Z) 54 | check_vec = np.add(check_vec, shift[:, code_k, :]) % 2 55 | for j in range(1, 4, 1): 56 | encodeWord[code_k + j, :] = check_vec[j - 1, :] 57 | for i in range(0, code_m, 1): 58 | if (code_PCM[i, code_k + j] != -1): 59 | shift[i, code_k + j, :] = roll_left(encodeWord[code_k + j, :], code_PCM[i, code_k + j] % Z, Z) 60 | check_vec = np.add(check_vec, shift[:, code_k + j, :]) % 2 61 | encodeWord[code_k + 4:code_n, :] = check_vec[4:code_m, :] 62 | encodeWord = np.reshape(encodeWord, [code_n * Z]) 63 | return encodeWord 64 | 65 | LDPC_G = np.zeros([code_k * Z, code_N * Z], dtype=int) 66 | for i in range(0, code_k * Z, 1): 67 | infoWord = np.zeros(code_k * Z, dtype=int) 68 | infoWord[i] = 1 69 | LDPC_G[i, :] = LDPC_encoder(infoWord, code_BG, code_N, code_m, Z) 70 | 71 | np.savetxt('./BaseGraph_GM/LDPC_GM_BG{0}_{1}.txt'.format(BaseGraph, Z), LDPC_G, fmt='%s', delimiter=',') 72 | -------------------------------------------------------------------------------- /Neural_MS_damping.py: -------------------------------------------------------------------------------- 1 | from __future__ import print_function, division 2 | import os 3 | import tensorflow.compat.v1 as tf 4 | tf.disable_v2_behavior() 5 | import numpy as np 6 | import datetime 7 | 8 | # GPU settings 9 | os.environ["CUDA_VISIBLE_DEVICES"] = "0" 10 | config = tf.ConfigProto() 11 | config.gpu_options.allow_growth = True 12 | sess = tf.Session(config=config) 13 | 14 | # get the base graph and generator matrix 15 | code_PCM0 = np.loadtxt("./BaseGraph/BaseGraph2_Set0.txt", int, delimiter=' ') 16 | code_PCM1 = np.loadtxt("./BaseGraph/BaseGraph2_Set1.txt", int, delimiter=' ') 17 | code_PCM2 = np.loadtxt("./BaseGraph/BaseGraph2_Set2.txt", int, delimiter=' ') 18 | code_GM_16 = np.loadtxt("./BaseGraph_GM/LDPC_GM_BG2_16.txt", int, delimiter=',') 19 | code_GM_3 = np.loadtxt("./BaseGraph_GM/LDPC_GM_BG2_3.txt", int, delimiter=',') 20 | code_GM_10 = np.loadtxt("./BaseGraph_GM/LDPC_GM_BG2_10.txt", int, delimiter=',') 21 | 22 | code_PCM = code_PCM0.copy() 23 | Ldpc_PCM = [code_PCM0, code_PCM1, code_PCM2]# three LDPC codes with different code lengths 24 | Ldpc_GM = [code_GM_16, code_GM_3, code_GM_10] 25 | Z_array = np.array([16, 3, 10]) 26 | 27 | N = 52 28 | m = 42 29 | code_n = N 30 | code_k = N - m 31 | for i in range(0, code_PCM.shape[0]): 32 | for j in range(0, code_PCM.shape[1]): 33 | if (code_PCM[i, j] == -1): 34 | code_PCM[i, j] = 0 35 | else: 36 | code_PCM[i, j] = 1 37 | 38 | # network hyper-parameters 39 | iters_max = 5 # number of iterations 40 | sum_edge_c = np.sum(code_PCM, axis=1) 41 | sum_edge_v = np.sum(code_PCM, axis=0) 42 | sum_edge = np.sum(sum_edge_v) 43 | neurons_per_even_layer = neurons_per_odd_layer = np.sum(sum_edge_v) 44 | input_output_layer_size = N 45 | 46 | # init the AWGN # 47 | code_rate = 1.0 * (N - m) / (N-2) 48 | # train SNR 49 | SNR_Matrix = np.array([[9.0,6.05,4.1,2.95,2.25,1.8,1.55,1.3,1.15,1.05,0.94,0.85,0.83,0.81,0.8,0.8,0.8,0.75,0.75,0.7,0.7,0.7,0.7,0.7,0.7], 50 | [9.1,6.2,4.6,3.7,3.2,3.0,2.8,2.7,2.6,2.55,2.5,2.45,2.4,2.4,2.4,2.35,2.35,2.3,2.3,2.3,2.25,2.25,2.25,2.25,2.25], 51 | [9,6.05,4.1,3,2.4,2,1.7,1.5,1.4,1.4,1.3,1.3,1.2,1.2,1.2,1.2,1.1,1.1,1.1,1.1,1.1,1.1,1.1,1,1]]) 52 | SNR_lin = 10.0 ** (SNR_Matrix / 10.0) 53 | SNR_sigma = np.sqrt(1.0 / (2.0 * SNR_lin * code_rate)) 54 | # ramdom seed 55 | word_seed = 2042 56 | noise_seed = 1074 57 | wordRandom = np.random.RandomState(word_seed) # word seed 58 | noiseRandom = np.random.RandomState(noise_seed) # noise seed 59 | 60 | # train settings 61 | single_damping = False 62 | learning_rate = 0.001 63 | train_on_zero_word = True 64 | numOfWordSim_train = 30 65 | batch_size = numOfWordSim_train 66 | num_of_batch = 10000 67 | 68 | #get train samples 69 | def create_mix_epoch(scaling_factor, wordRandom, noiseRandom, numOfWordSim, code_n, code_k, Z, code_GM, is_zeros_word): 70 | X = np.zeros([1, code_n * Z], dtype=np.float32) 71 | Y = np.zeros([1, code_n * Z], dtype=np.int64) 72 | 73 | # build set for epoch 74 | for sf_i in scaling_factor: 75 | if is_zeros_word: 76 | infoWord_i = 0 * wordRandom.randint(0, 2, size=(numOfWordSim, code_k * Z)) 77 | else: 78 | infoWord_i = wordRandom.randint(0, 2, size=(numOfWordSim, code_k * Z)) 79 | 80 | Y_i = np.dot(infoWord_i, code_GM) % 2 81 | X_p_i = noiseRandom.normal(0.0, 1.0, Y_i.shape) * sf_i + (-1) ** (1 - Y_i) # pay attention to this 1->1 0->-1 82 | x_llr_i = 2 * X_p_i / ((sf_i) ** 2) # defined as p1/p0 83 | X = np.vstack((X, x_llr_i)) 84 | Y = np.vstack((Y, Y_i)) 85 | X = X[1:] 86 | Y = Y[1:] 87 | X = np.reshape(X, [batch_size, code_n, Z]) 88 | return X, Y 89 | 90 | # calculate ber and fer 91 | def calc_ber_fer(snr_db, Y_test_pred, Y_test, numOfWordSim): 92 | ber_test = np.zeros(snr_db.shape[0]) 93 | fer_test = np.zeros(snr_db.shape[0]) 94 | for i in range(0, snr_db.shape[0]): 95 | Y_test_pred_i = Y_test_pred[i * numOfWordSim:(i + 1) * numOfWordSim, :] 96 | Y_test_i = Y_test[i * numOfWordSim:(i + 1) * numOfWordSim, :] 97 | ber_test[i] = np.abs(((Y_test_pred_i > 0) - Y_test_i)).sum() / (Y_test_i.shape[0] * Y_test_i.shape[1]) 98 | fer_test[i] = (np.abs(((Y_test_pred_i > 0) - Y_test_i)).sum(axis=1) > 0).sum() * 1.0 / Y_test_i.shape[0] 99 | return ber_test, fer_test 100 | 101 | 102 | ############################ init the connecting matrix between network layers ################################# 103 | Lift_Matrix1 = [] 104 | Lift_Matrix2 = [] 105 | W_odd2even = np.zeros((sum_edge, sum_edge), dtype=np.float32) 106 | W_skipconn2even = np.zeros((N, sum_edge), dtype=np.float32) 107 | W_even2odd = np.zeros((sum_edge, sum_edge), dtype=np.float32) 108 | W_output = np.zeros((sum_edge, N), dtype=np.float32) 109 | 110 | # init lifting matrix for cyclic shift 111 | for t in range(0, 3, 1): 112 | Lift_M1 = np.zeros((neurons_per_odd_layer * Z_array[t], neurons_per_odd_layer * Z_array[t]), np.float32) 113 | Lift_M2 = np.zeros((neurons_per_odd_layer * Z_array[t], neurons_per_odd_layer * Z_array[t]), np.float32) 114 | code_PCM1 = Ldpc_PCM[t] 115 | k = 0 116 | for j in range(0, code_PCM1.shape[1]): 117 | for i in range(0, code_PCM1.shape[0]): 118 | if (code_PCM1[i, j] != -1): 119 | Lift_num = code_PCM1[i, j] % Z_array[t] 120 | for h in range(0, Z_array[t], 1): 121 | Lift_M1[k * Z_array[t] + h, k * Z_array[t] + (h + Lift_num) % Z_array[t]] = 1 122 | k = k + 1 123 | k = 0 124 | for i in range(0, code_PCM1.shape[0]): 125 | for j in range(0, code_PCM1.shape[1]): 126 | if (code_PCM1[i, j] != -1): 127 | Lift_num = code_PCM1[i, j] % Z_array[t] 128 | for h in range(0, Z_array[t], 1): 129 | Lift_M2[k * Z_array[t] + h, k * Z_array[t] + (h + Lift_num) % Z_array[t]] = 1 130 | k = k + 1 131 | Lift_Matrix1.append(Lift_M1) 132 | Lift_Matrix2.append(Lift_M2) 133 | 134 | # init W_odd2even variable node updating 135 | k = 0 136 | vec_tmp = np.zeros((sum_edge), dtype=np.float32) # even layer index read with column 137 | for j in range(0, code_PCM.shape[1], 1): # run over the columns 138 | for i in range(0, code_PCM.shape[0], 1): # break after the first one 139 | if (code_PCM[i, j] == 1): # finding the first one is ok 140 | num_of_conn = int(np.sum(code_PCM[:, j])) # get the number of connection of the variable node 141 | idx = np.argwhere(code_PCM[:, j] == 1) # get the indexes 142 | for l in range(0, num_of_conn, 1): # adding num_of_conn columns to W 143 | vec_tmp = np.zeros((sum_edge), dtype=np.float32) 144 | for r in range(0, code_PCM.shape[0], 1): # adding one to the right place 145 | if (code_PCM[r, j] == 1 and idx[l][0] != r): 146 | idx_row = np.cumsum(code_PCM[r, 0:j + 1])[-1] - 1 147 | odd_layer_node_count = 0 148 | if r > 0: 149 | odd_layer_node_count = np.cumsum(sum_edge_c[0:r])[-1] 150 | vec_tmp[idx_row + odd_layer_node_count] = 1 # offset index adding 151 | W_odd2even[:, k] = vec_tmp.transpose() 152 | k += 1 153 | break 154 | 155 | # init W_even2odd parity check node updating 156 | k = 0 157 | for j in range(0, code_PCM.shape[1], 1): 158 | for i in range(0, code_PCM.shape[0], 1): 159 | if (code_PCM[i, j] == 1): 160 | idx_row = np.cumsum(code_PCM[i, 0:j + 1])[-1] - 1 161 | idx_col = np.cumsum(code_PCM[0: i + 1, j])[-1] - 1 162 | odd_layer_node_count_1 = 0 163 | odd_layer_node_count_2 = np.cumsum(sum_edge_c[0:i + 1])[-1] 164 | if i > 0: 165 | odd_layer_node_count_1 = np.cumsum(sum_edge_c[0:i])[-1] 166 | W_even2odd[k, odd_layer_node_count_1:odd_layer_node_count_2] = 1.0 167 | W_even2odd[k, odd_layer_node_count_1 + idx_row] = 0.0 168 | k += 1 # k is counted in column direction 169 | 170 | # init W_output odd to output 171 | k = 0 172 | for j in range(0, code_PCM.shape[1], 1): 173 | for i in range(0, code_PCM.shape[0], 1): 174 | if (code_PCM[i, j] == 1): 175 | idx_row = np.cumsum(code_PCM[i, 0:j + 1])[-1] - 1 176 | idx_col = np.cumsum(code_PCM[0: i + 1, j])[-1] - 1 177 | odd_layer_node_count = 0 178 | if i > 0: 179 | odd_layer_node_count = np.cumsum(sum_edge_c[0:i])[-1] 180 | W_output[odd_layer_node_count + idx_row, k] = 1.0 181 | k += 1 182 | 183 | # init W_skipconn2even channel input 184 | k = 0 185 | for j in range(0, code_PCM.shape[1], 1): 186 | for i in range(0, code_PCM.shape[0], 1): 187 | if (code_PCM[i, j] == 1): 188 | W_skipconn2even[j, k] = 1.0 189 | k += 1 190 | 191 | 192 | ############################## bulid four neural networks(Z = 16,3, 10, 6) ############################ 193 | net_dict = {} 194 | # init the learnable network parameters 195 | Weights_Var = np.ones(sum_edge, dtype=np.float32) 196 | Biases_Var = -0.5 * np.ones(sum_edge, dtype=np.float32) 197 | for i in range(0, iters_max, 1): 198 | net_dict["Weights_Var{0}".format(i)] = tf.Variable(Weights_Var.copy(), name="Weights_Var".format(i)) 199 | net_dict["Biases_Var{0}".format(i)] = tf.Variable(Biases_Var.copy(), name="Biases_Var".format(i)) 200 | if single_damping: 201 | damping_factor = 0.5 * np.ones(1, dtype=np.float32) 202 | net_dict["damping_factor{0}".format(i)] = tf.Variable(damping_factor.copy(), name="damping_factor".format(i)) 203 | else: 204 | damping_factor = 0.5 * np.ones(sum_edge, dtype=np.float32) 205 | net_dict["damping_factor{0}".format(i)] = tf.Variable(damping_factor.copy(), name="damping_factor".format(i)) 206 | 207 | # the decoding neural network of Z=16 208 | Z = 16 209 | xa = tf.placeholder(tf.float32, shape=[batch_size, N, Z], name='xa') 210 | ya = tf.placeholder(tf.float32, shape=[batch_size, N * Z], name='ya') 211 | xa_input = tf.transpose(xa, [0, 2, 1]) 212 | net_dict["LLRa{0}".format(0)] = tf.zeros((batch_size, Z, sum_edge), dtype=tf.float32) 213 | net_dict["infoM_lastlayera{0}".format(0)] = tf.zeros((batch_size, Z, sum_edge), dtype=tf.float32) 214 | for i in range(0, iters_max, 1): 215 | #variable node update 216 | x0 = tf.matmul(xa_input, W_skipconn2even) 217 | x1 = tf.matmul(net_dict["LLRa{0}".format(i)], W_odd2even) 218 | x2_3 = tf.add(x0, x1) 219 | x2 = tf.add(tf.multiply(x2_3, 1 - net_dict["damping_factor{0}".format(i)]), 220 | tf.multiply(net_dict["infoM_lastlayera{0}".format(i)], net_dict["damping_factor{0}".format(i)])) 221 | net_dict["infoM_lastlayera{0}".format(i + 1)] = x2 222 | x2 = tf.transpose(x2, [0, 2, 1]) 223 | x2 = tf.reshape(x2, [batch_size, neurons_per_odd_layer * Z]) 224 | x2 = tf.matmul(x2, Lift_Matrix1[0].transpose()) 225 | x2 = tf.reshape(x2, [batch_size, neurons_per_odd_layer, Z]) 226 | x2 = tf.transpose(x2, [0, 2, 1]) 227 | x_tile = tf.tile(x2, multiples=[1, 1, neurons_per_odd_layer]) 228 | W_input_reshape = tf.reshape(W_even2odd.transpose(), [-1]) 229 | #check node update 230 | x_tile_mul = tf.multiply(x_tile, W_input_reshape) 231 | x2_1 = tf.reshape(x_tile_mul, [batch_size, Z, neurons_per_odd_layer, neurons_per_odd_layer]) 232 | x2_abs = tf.add(tf.abs(x2_1), 10000 * (1 - tf.to_float(tf.abs(x2_1) > 0))) 233 | x3 = tf.reduce_min(x2_abs, axis=3) 234 | x2_2 = -x2_1 235 | x4 = tf.add(tf.zeros((batch_size, Z, neurons_per_odd_layer, neurons_per_odd_layer)), 1 - 2 * tf.to_float(x2_2 < 0)) 236 | x4_prod = -tf.reduce_prod(x4, axis=3) 237 | x_output_0 = tf.multiply(x3, tf.sign(x4_prod)) 238 | x_output_0 = tf.transpose(x_output_0, [0, 2, 1]) 239 | x_output_0 = tf.reshape(x_output_0, [batch_size, Z * neurons_per_odd_layer]) 240 | x_output_0 = tf.matmul(x_output_0, Lift_Matrix2[0]) 241 | x_output_0 = tf.reshape(x_output_0, [batch_size, neurons_per_odd_layer, Z]) 242 | x_output_0 = tf.transpose(x_output_0, [0, 2, 1]) 243 | # add learnable parameters 244 | x_output_1 = tf.add(tf.multiply(tf.abs(x_output_0),net_dict["Weights_Var{0}".format(i)]), net_dict["Biases_Var{0}".format(i)]) 245 | x_output_1 = tf.multiply(x_output_1, tf.to_float(x_output_1 > 0)) 246 | net_dict["LLRa{0}".format(i+1)] = tf.multiply(x_output_1, tf.sign(x_output_0)) # update the LLR 247 | # output 248 | y_output_2 = tf.matmul(net_dict["LLRa{0}".format(i+1)], W_output) 249 | y_output_3 = tf.transpose(y_output_2, [0, 2, 1]) 250 | y_output_4 = tf.add(xa, y_output_3) 251 | net_dict["ya_output{0}".format(i)] = tf.reshape(y_output_4, [batch_size, N * Z], name='ya_output'.format(i)) 252 | # calculate loss 253 | net_dict["lossa{0}".format(i)] = 1.0 * tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(labels=ya, 254 | logits=net_dict["ya_output{0}".format(i)]), name='lossa'.format(i)) 255 | # AdamOptimizer 256 | net_dict["train_stepa{0}".format(i)] = tf.train.AdamOptimizer(learning_rate= 257 | learning_rate).minimize(net_dict["lossa{0}".format(i)], 258 | var_list = [net_dict["Weights_Var{0}".format(i)], net_dict["Biases_Var{0}".format(i)], net_dict["damping_factor{0}".format(i)]]) 259 | 260 | 261 | ################################## Train #################################### 262 | sess.run(tf.global_variables_initializer()) 263 | saver = tf.train.Saver() 264 | for iter in range(0, iters_max, 1): 265 | for i in range(0, num_of_batch, 1): 266 | Z = 16 267 | SNR_set = np.array([SNR_sigma[0, iter]]) 268 | training_received_data, training_coded_bits = create_mix_epoch(SNR_set, wordRandom, noiseRandom, numOfWordSim_train, 269 | code_n, code_k, Z, 270 | Ldpc_GM[0], 271 | train_on_zero_word) 272 | training_labels_for_mse = training_coded_bits 273 | y_pred, train_loss, _ = sess.run(fetches=[net_dict["ya_output{0}".format(iter)], net_dict["lossa{0}".format(iter)], 274 | net_dict["train_stepa{0}".format(iter)]], 275 | feed_dict={xa: training_received_data, ya: training_labels_for_mse}) 276 | if i % 200 == 0: 277 | print('iteration: [{0}/{1}]\t' 278 | 'epoch: [{2}/{3}]\t' 279 | 'loss: {4}\t'.format( 280 | iter + 1, iters_max, i, num_of_batch, train_loss)) 281 | 282 | 283 | 284 | 285 | ################################## save weights and biases #################################### 286 | a, b = sess.run(fetches=[net_dict["Weights_Var{0}".format(iter)], net_dict["Biases_Var{0}".format(iter)]]) 287 | np.savetxt('./Weights_Var/Weights_Var{0}.txt'.format(iter), a, fmt='%s', delimiter=',') 288 | np.savetxt('./Biases_Var/Biases_Var{0}.txt'.format(iter), b, fmt='%s', delimiter=',') 289 | c = sess.run(fetches=[net_dict["damping_factor{0}".format(iter)]]) 290 | np.savetxt('./damping_factor/damping_factor{0}.txt'.format(iter), c, fmt='%s', delimiter='\n') 291 | 292 | -------------------------------------------------------------------------------- /Neural_simplified_MS.py: -------------------------------------------------------------------------------- 1 | from __future__ import print_function, division 2 | import os 3 | import tensorflow.compat.v1 as tf 4 | tf.disable_v2_behavior() 5 | import numpy as np 6 | import datetime 7 | 8 | # GPU settings 9 | os.environ["CUDA_VISIBLE_DEVICES"] = "0" 10 | config = tf.ConfigProto() 11 | config.gpu_options.allow_growth = True 12 | sess = tf.Session(config=config) 13 | 14 | # get the base graph and generator matrix 15 | code_PCM0 = np.loadtxt("./BaseGraph/BaseGraph2_Set0.txt", int, delimiter=' ') 16 | code_PCM1 = np.loadtxt("./BaseGraph/BaseGraph2_Set1.txt", int, delimiter=' ') 17 | code_PCM2 = np.loadtxt("./BaseGraph/BaseGraph2_Set2.txt", int, delimiter=' ') 18 | code_GM_16 = np.loadtxt("./BaseGraph_GM/LDPC_GM_BG2_16.txt", int, delimiter=',') 19 | code_GM_3 = np.loadtxt("./BaseGraph_GM/LDPC_GM_BG2_3.txt", int, delimiter=',') 20 | code_GM_10 = np.loadtxt("./BaseGraph_GM/LDPC_GM_BG2_10.txt", int, delimiter=',') 21 | code_PCM = code_PCM0.copy() 22 | Ldpc_PCM = [code_PCM0, code_PCM1, code_PCM2]# four LDPC codes with different code lengths 23 | Ldpc_GM = [code_GM_16, code_GM_3, code_GM_10] 24 | Z_array = np.array([16, 3, 10]) 25 | 26 | N = 52 27 | m = 42 28 | code_n = N 29 | code_k = N - m 30 | for i in range(0, code_PCM.shape[0]): 31 | for j in range(0, code_PCM.shape[1]): 32 | if (code_PCM[i, j] == -1): 33 | code_PCM[i, j] = 0 34 | else: 35 | code_PCM[i, j] = 1 36 | 37 | # network hyper-parameters 38 | iters_max = 25 # number of iterations 39 | sum_edge_c = np.sum(code_PCM, axis=1) 40 | sum_edge_v = np.sum(code_PCM, axis=0) 41 | sum_edge = np.sum(sum_edge_v) 42 | neurons_per_even_layer = neurons_per_odd_layer = np.sum(sum_edge_v) 43 | input_output_layer_size = N 44 | 45 | # init the AWGN # 46 | code_rate = 1.0 * (N - m) / (N-2) 47 | # train SNR 48 | SNR_Matrix = np.array([[9.0,6.05,4.1,2.95,2.25,1.8,1.55,1.3,1.15,1.05,0.94,0.85,0.83,0.81,0.8,0.8,0.8,0.75,0.75,0.7,0.7,0.7,0.7,0.7,0.7], 49 | [9.1,6.2,4.6,3.7,3.2,3.0,2.8,2.7,2.6,2.55,2.5,2.45,2.4,2.4,2.4,2.35,2.35,2.3,2.3,2.3,2.25,2.25,2.25,2.25,2.25], 50 | [9,6.05,4.1,3,2.4,2,1.7,1.5,1.4,1.4,1.3,1.3,1.2,1.2,1.2,1.2,1.1,1.1,1.1,1.1,1.1,1.1,1.1,1,1], 51 | [9.0,6.1,4.25,3.2,2.6,2.25,2,1.9,1.8,1.7,1.7,1.65,1.6,1.6,1.55,1.55,1.5,1.5,1.5,1.45,1.45,1.4,1.4,1.4,1.4]]) 52 | SNR_lin = 10.0 ** (SNR_Matrix / 10.0) 53 | SNR_sigma = np.sqrt(1.0 / (2.0 * SNR_lin * code_rate)) 54 | # ramdom seed 55 | word_seed = 2042 56 | noise_seed = 1074 57 | wordRandom = np.random.RandomState(word_seed) # word seed 58 | noiseRandom = np.random.RandomState(noise_seed) # noise seed 59 | 60 | # train settings 61 | single_parmeter_type = 2 # 2 means simplified neural NOMS, 3 means simplified neural NMS, 4 means simplified neural OMS 62 | learning_rate = 0.001 63 | train_on_zero_word = True 64 | numOfWordSim_train = 50 65 | batch_size = numOfWordSim_train 66 | num_of_batch = 50000 67 | 68 | #get train samples 69 | def create_mix_epoch(scaling_factor, wordRandom, noiseRandom, numOfWordSim, code_n, code_k, Z, code_GM, is_zeros_word): 70 | X = np.zeros([1, code_n * Z], dtype=np.float32) 71 | Y = np.zeros([1, code_n * Z], dtype=np.int64) 72 | 73 | # build set for epoch 74 | for sf_i in scaling_factor: 75 | if is_zeros_word: 76 | infoWord_i = 0 * wordRandom.randint(0, 2, size=(numOfWordSim, code_k * Z)) 77 | else: 78 | infoWord_i = wordRandom.randint(0, 2, size=(numOfWordSim, code_k * Z)) 79 | 80 | Y_i = np.dot(infoWord_i, code_GM) % 2 81 | X_p_i = noiseRandom.normal(0.0, 1.0, Y_i.shape) * sf_i + (-1) ** (1 - Y_i) # pay attention to this 1->1 0->-1 82 | x_llr_i = 2 * X_p_i / ((sf_i) ** 2) # defined as p1/p0 83 | X = np.vstack((X, x_llr_i)) 84 | Y = np.vstack((Y, Y_i)) 85 | X = X[1:] 86 | Y = Y[1:] 87 | X = np.reshape(X, [batch_size, code_n, Z]) 88 | return X, Y 89 | 90 | # calculate ber and fer 91 | def calc_ber_fer(snr_db, Y_test_pred, Y_test, numOfWordSim): 92 | ber_test = np.zeros(snr_db.shape[0]) 93 | fer_test = np.zeros(snr_db.shape[0]) 94 | for i in range(0, snr_db.shape[0]): 95 | Y_test_pred_i = Y_test_pred[i * numOfWordSim:(i + 1) * numOfWordSim, :] 96 | Y_test_i = Y_test[i * numOfWordSim:(i + 1) * numOfWordSim, :] 97 | ber_test[i] = np.abs(((Y_test_pred_i > 0) - Y_test_i)).sum() / (Y_test_i.shape[0] * Y_test_i.shape[1]) 98 | fer_test[i] = (np.abs(((Y_test_pred_i > 0) - Y_test_i)).sum(axis=1) > 0).sum() * 1.0 / Y_test_i.shape[0] 99 | return ber_test, fer_test 100 | 101 | 102 | ############################ init the connecting matrix between network layers ################################# 103 | Lift_Matrix1 = [] 104 | Lift_Matrix2 = [] 105 | W_odd2even = np.zeros((sum_edge, sum_edge), dtype=np.float32) 106 | W_skipconn2even = np.zeros((N, sum_edge), dtype=np.float32) 107 | W_even2odd = np.zeros((sum_edge, sum_edge), dtype=np.float32) 108 | W_output = np.zeros((sum_edge, N), dtype=np.float32) 109 | 110 | # init lifting matrix for cyclic shift 111 | for t in range(0, 3, 1): 112 | Lift_M1 = np.zeros((neurons_per_odd_layer * Z_array[t], neurons_per_odd_layer * Z_array[t]), np.float32) 113 | Lift_M2 = np.zeros((neurons_per_odd_layer * Z_array[t], neurons_per_odd_layer * Z_array[t]), np.float32) 114 | code_PCM1 = Ldpc_PCM[t] 115 | k = 0 116 | for j in range(0, code_PCM1.shape[1]): 117 | for i in range(0, code_PCM1.shape[0]): 118 | if (code_PCM1[i, j] != -1): 119 | Lift_num = code_PCM1[i, j] % Z_array[t] 120 | for h in range(0, Z_array[t], 1): 121 | Lift_M1[k * Z_array[t] + h, k * Z_array[t] + (h + Lift_num) % Z_array[t]] = 1 122 | k = k + 1 123 | k = 0 124 | for i in range(0, code_PCM1.shape[0]): 125 | for j in range(0, code_PCM1.shape[1]): 126 | if (code_PCM1[i, j] != -1): 127 | Lift_num = code_PCM1[i, j] % Z_array[t] 128 | for h in range(0, Z_array[t], 1): 129 | Lift_M2[k * Z_array[t] + h, k * Z_array[t] + (h + Lift_num) % Z_array[t]] = 1 130 | k = k + 1 131 | Lift_Matrix1.append(Lift_M1) 132 | Lift_Matrix2.append(Lift_M2) 133 | 134 | # init W_odd2even variable node updating 135 | k = 0 136 | vec_tmp = np.zeros((sum_edge), dtype=np.float32) # even layer index read with column 137 | for j in range(0, code_PCM.shape[1], 1): # run over the columns 138 | for i in range(0, code_PCM.shape[0], 1): # break after the first one 139 | if (code_PCM[i, j] == 1): # finding the first one is ok 140 | num_of_conn = int(np.sum(code_PCM[:, j])) # get the number of connection of the variable node 141 | idx = np.argwhere(code_PCM[:, j] == 1) # get the indexes 142 | for l in range(0, num_of_conn, 1): # adding num_of_conn columns to W 143 | vec_tmp = np.zeros((sum_edge), dtype=np.float32) 144 | for r in range(0, code_PCM.shape[0], 1): # adding one to the right place 145 | if (code_PCM[r, j] == 1 and idx[l][0] != r): 146 | idx_row = np.cumsum(code_PCM[r, 0:j + 1])[-1] - 1 147 | odd_layer_node_count = 0 148 | if r > 0: 149 | odd_layer_node_count = np.cumsum(sum_edge_c[0:r])[-1] 150 | vec_tmp[idx_row + odd_layer_node_count] = 1 # offset index adding 151 | W_odd2even[:, k] = vec_tmp.transpose() 152 | k += 1 153 | break 154 | 155 | # init W_even2odd parity check node updating 156 | k = 0 157 | for j in range(0, code_PCM.shape[1], 1): 158 | for i in range(0, code_PCM.shape[0], 1): 159 | if (code_PCM[i, j] == 1): 160 | idx_row = np.cumsum(code_PCM[i, 0:j + 1])[-1] - 1 161 | idx_col = np.cumsum(code_PCM[0: i + 1, j])[-1] - 1 162 | odd_layer_node_count_1 = 0 163 | odd_layer_node_count_2 = np.cumsum(sum_edge_c[0:i + 1])[-1] 164 | if i > 0: 165 | odd_layer_node_count_1 = np.cumsum(sum_edge_c[0:i])[-1] 166 | W_even2odd[k, odd_layer_node_count_1:odd_layer_node_count_2] = 1.0 167 | W_even2odd[k, odd_layer_node_count_1 + idx_row] = 0.0 168 | k += 1 # k is counted in column direction 169 | 170 | # init W_output odd to output 171 | k = 0 172 | for j in range(0, code_PCM.shape[1], 1): 173 | for i in range(0, code_PCM.shape[0], 1): 174 | if (code_PCM[i, j] == 1): 175 | idx_row = np.cumsum(code_PCM[i, 0:j + 1])[-1] - 1 176 | idx_col = np.cumsum(code_PCM[0: i + 1, j])[-1] - 1 177 | odd_layer_node_count = 0 178 | if i > 0: 179 | odd_layer_node_count = np.cumsum(sum_edge_c[0:i])[-1] 180 | W_output[odd_layer_node_count + idx_row, k] = 1.0 181 | k += 1 182 | 183 | # init W_skipconn2even channel input 184 | k = 0 185 | for j in range(0, code_PCM.shape[1], 1): 186 | for i in range(0, code_PCM.shape[0], 1): 187 | if (code_PCM[i, j] == 1): 188 | W_skipconn2even[j, k] = 1.0 189 | k += 1 190 | 191 | 192 | ############################## bulid four neural networks(Z = 16,3, 10, 6) ############################ 193 | net_dict = {} 194 | # init the learnable network parameters 195 | Weights_Var = np.ones(1, dtype=np.float32) 196 | Biases_Var = np.zeros(1, dtype=np.float32) 197 | for i in range(0, iters_max, 1): 198 | net_dict["Weights_Var{0}".format(i)] = tf.Variable(Weights_Var.copy(), name="Weights_Var".format(i)) 199 | net_dict["Biases_Var{0}".format(i)] = tf.Variable(Biases_Var.copy(), name="Biases_Var".format(i)) 200 | 201 | # the decoding neural network of Z=16 202 | Z = 16 203 | xa = tf.placeholder(tf.float32, shape=[batch_size, N, Z], name='xa') 204 | ya = tf.placeholder(tf.float32, shape=[batch_size, N * Z], name='ya') 205 | xa_input = tf.transpose(xa, [0, 2, 1]) 206 | net_dict["LLRa{0}".format(0)] = tf.zeros((batch_size, Z, sum_edge), dtype=tf.float32) 207 | for i in range(0, iters_max, 1): 208 | #variable node update 209 | x0 = tf.matmul(xa_input, W_skipconn2even) 210 | x1 = tf.matmul(net_dict["LLRa{0}".format(i)], W_odd2even) 211 | x2 = tf.add(x0, x1) 212 | x2 = tf.transpose(x2, [0, 2, 1]) 213 | x2 = tf.reshape(x2, [batch_size, neurons_per_odd_layer * Z]) 214 | x2 = tf.matmul(x2, Lift_Matrix1[0].transpose()) 215 | x2 = tf.reshape(x2, [batch_size, neurons_per_odd_layer, Z]) 216 | x2 = tf.transpose(x2, [0, 2, 1]) 217 | x_tile = tf.tile(x2, multiples=[1, 1, neurons_per_odd_layer]) 218 | W_input_reshape = tf.reshape(W_even2odd.transpose(), [-1]) 219 | #check node update 220 | x_tile_mul = tf.multiply(x_tile, W_input_reshape) 221 | x2_1 = tf.reshape(x_tile_mul, [batch_size, Z, neurons_per_odd_layer, neurons_per_odd_layer]) 222 | x2_abs = tf.add(tf.abs(x2_1), 10000 * (1 - tf.to_float(tf.abs(x2_1) > 0))) 223 | x3 = tf.reduce_min(x2_abs, axis=3) 224 | x2_2 = -x2_1 225 | x4 = tf.add(tf.zeros((batch_size, Z, neurons_per_odd_layer, neurons_per_odd_layer)), 1 - 2 * tf.to_float(x2_2 < 0)) 226 | x4_prod = -tf.reduce_prod(x4, axis=3) 227 | x_output_0 = tf.multiply(x3, tf.sign(x4_prod)) 228 | x_output_0 = tf.transpose(x_output_0, [0, 2, 1]) 229 | x_output_0 = tf.reshape(x_output_0, [batch_size, Z * neurons_per_odd_layer]) 230 | x_output_0 = tf.matmul(x_output_0, Lift_Matrix2[0]) 231 | x_output_0 = tf.reshape(x_output_0, [batch_size, neurons_per_odd_layer, Z]) 232 | x_output_0 = tf.transpose(x_output_0, [0, 2, 1]) 233 | # add learnable parameters 234 | x_output_1 = tf.add(tf.multiply(tf.abs(x_output_0),net_dict["Weights_Var{0}".format(i)]), net_dict["Biases_Var{0}".format(i)]) 235 | x_output_1 = tf.multiply(x_output_1, tf.to_float(x_output_1 > 0)) 236 | net_dict["LLRa{0}".format(i+1)] = tf.multiply(x_output_1, tf.sign(x_output_0)) # update the LLR 237 | # output 238 | y_output_2 = tf.matmul(net_dict["LLRa{0}".format(i+1)], W_output) 239 | y_output_3 = tf.transpose(y_output_2, [0, 2, 1]) 240 | y_output_4 = tf.add(xa, y_output_3) 241 | net_dict["ya_output{0}".format(i)] = tf.reshape(y_output_4, [batch_size, N * Z], name='ya_output'.format(i)) 242 | # calculate loss 243 | net_dict["lossa{0}".format(i)] = 1.0 * tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(labels=ya, 244 | logits=net_dict["ya_output{0}".format(i)]), name='lossa'.format(i)) 245 | # AdamOptimizer 246 | if single_parmeter_type == 2: 247 | var_list = [net_dict["Weights_Var{0}".format(i)], net_dict["Biases_Var{0}".format(i)]] 248 | elif single_parmeter_type == 3: 249 | var_list = [net_dict["Weights_Var{0}".format(i)]] 250 | elif single_parmeter_type == 4: 251 | var_list = [net_dict["Biases_Var{0}".format(i)]] 252 | 253 | net_dict["train_stepa{0}".format(i)] = tf.train.AdamOptimizer(learning_rate= 254 | learning_rate).minimize(net_dict["lossa{0}".format(i)], 255 | var_list = var_list) 256 | 257 | 258 | ################################## Train #################################### 259 | sess.run(tf.global_variables_initializer()) 260 | saver = tf.train.Saver() 261 | for iter in range(0, iters_max, 1): 262 | for i in range(0, num_of_batch, 1): 263 | Z = 16 264 | SNR_set = np.array([SNR_sigma[0, iter]]) 265 | training_received_data, training_coded_bits = create_mix_epoch(SNR_set, wordRandom, noiseRandom, numOfWordSim_train, 266 | code_n, code_k, Z, 267 | Ldpc_GM[0], 268 | train_on_zero_word) 269 | training_labels_for_mse = training_coded_bits 270 | y_pred, train_loss, _ = sess.run(fetches=[net_dict["ya_output{0}".format(iter)], net_dict["lossa{0}".format(iter)], 271 | net_dict["train_stepa{0}".format(iter)]], 272 | feed_dict={xa: training_received_data, ya: training_labels_for_mse}) 273 | if i % 200 == 0: 274 | print('iteration: [{0}/{1}]\t' 275 | 'epoch: [{2}/{3}]\t' 276 | 'loss: {4}\t'.format( 277 | iter + 1, iters_max, i, num_of_batch, train_loss)) 278 | 279 | ################################## save weights and biases #################################### 280 | a, b = sess.run(fetches=[net_dict["Weights_Var{0}".format(iter)], net_dict["Biases_Var{0}".format(iter)]]) 281 | np.savetxt('./Weights_Var/Weights_Var{0}.txt'.format(iter), a, fmt='%s', delimiter=',') 282 | np.savetxt('./Biases_Var/Biases_Var{0}.txt'.format(iter), b, fmt='%s', delimiter=',') 283 | 284 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Learning to decode Protograph LDPC Codes 2 | #Code used in paper [Learning to decode Protograph LDPC Codes] 3 | 4 | **Python environment:** 5 | python = 3.6 6 | tensorflow = 2.0.0(use GPU for training) 7 | numpy =1.19.1 8 | (the versions are not too strict) 9 | 10 | **The file 'GeneratorMatrix.py' can get generator matrixs for every lifting factor by change the value of parmeter 'Z'.** 11 | 12 | 13 | **The project contains five files which can train eight different neural LDPC algorithms in our paper.** 14 | 15 | file | algorithm | hyperparmeter 16 | ---- | ----- | ------ 17 | Neural_MS.py | neural NOMS(type1) | default 18 | Neural_SP.py | neural SP | default 19 | Neural_simplified_MS.py | simplified neural NOMS(type2) | is_weight=True, is_bias=True, others default 20 | Neural_simplified_MS.py | simplifeid neural NMS(type3) | is_weight=True, is_bias=False, others default 21 | Neural_simplified_MS.py | simplified neural OMS(type4) | is_weight=False, is_bias=True, others default 22 | Neural_MS_damping.py | neural NOMS with damping(type5) | single_damping=False, others default 23 | Neural_MS_damping.py | simplified neural NOMS with damping(type6) | single_damping=True, others default 24 | Neural_MS_multiloss.py | neural NOMS but not iteration-by-iteration | default 25 | -------------------------------------------------------------------------------- /Weights_Var/Weights_Var0.txt: -------------------------------------------------------------------------------- 1 | 0.5579404 2 | 0.4654242 3 | 0.898409 4 | 0.87073904 5 | 0.84667593 6 | 0.7635876 7 | 0.77773684 8 | 0.74884963 9 | 0.45068887 10 | 0.82474124 11 | 0.78954405 12 | 0.61951935 13 | 0.7505797 14 | 0.5493394 15 | 0.77835876 16 | 0.67497975 17 | 0.78875446 18 | 0.7224291 19 | 0.54962194 20 | 0.52159625 21 | 0.8199204 22 | 0.85396117 23 | 0.77863663 24 | 0.7853113 25 | 0.7201377 26 | 0.71464694 27 | 0.49917793 28 | 0.80369884 29 | 0.81453574 30 | 0.5602301 31 | 0.7201377 32 | 0.5999132 33 | 0.75502443 34 | 0.7002187 35 | 0.7827739 36 | 0.6678143 37 | 0.6225176 38 | 0.4949287 39 | 0.70432943 40 | 0.9459003 41 | 0.59111893 42 | 0.42753214 43 | 0.6624949 44 | 0.68291974 45 | 0.49759325 46 | 0.9140939 47 | 0.45741493 48 | 0.61352366 49 | 0.5495649 50 | 0.80129975 51 | 0.7037777 52 | 0.89837074 53 | 0.44835335 54 | 0.52338266 55 | 0.73096335 56 | 0.6488715 57 | 0.7478213 58 | 0.9138693 59 | 0.6420265 60 | 0.5812775 61 | 0.8313111 62 | 0.93141866 63 | 0.5842224 64 | 0.9253081 65 | 0.9038721 66 | 0.6097392 67 | 0.9131407 68 | 0.6514575 69 | 0.59146565 70 | 0.86759025 71 | 0.9097624 72 | 0.9275885 73 | 0.535086 74 | 0.76280224 75 | 0.89747226 76 | 0.80643135 77 | 0.9272076 78 | 0.5488366 79 | 0.9484529 80 | 0.68483424 81 | 0.95647097 82 | 0.59496355 83 | 0.50915617 84 | 0.77454966 85 | 0.62378865 86 | 0.91331 87 | 0.64298904 88 | 0.92853194 89 | 0.67555684 90 | 0.91123587 91 | 0.91971904 92 | 0.5846077 93 | 0.9005582 94 | 0.92503744 95 | 0.9542265 96 | 0.49949768 97 | 0.9091561 98 | 0.5934471 99 | 0.830801 100 | 0.94258726 101 | 0.36831796 102 | 0.8298174 103 | 0.69292825 104 | 0.8164849 105 | 0.91008633 106 | 0.3935531 107 | 0.94920504 108 | 0.80657476 109 | 0.9421076 110 | 0.6805011 111 | 0.7427661 112 | 0.9944008 113 | 0.9601113 114 | 0.61085796 115 | 0.9597327 116 | 0.78816986 117 | 0.9453477 118 | 0.60447264 119 | 0.8280537 120 | 0.85209274 121 | 0.9255214 122 | 0.7674361 123 | 0.8923394 124 | 0.97105527 125 | 0.6610071 126 | 0.93092525 127 | 0.976665 128 | 0.9454832 129 | 0.75844437 130 | 0.9107317 131 | 0.8422074 132 | 0.94112366 133 | 0.65957713 134 | 0.9477307 135 | 0.96467686 136 | 0.7992836 137 | 0.7706582 138 | 0.9112347 139 | 0.7372281 140 | 0.9285214 141 | 0.68045056 142 | 0.9602649 143 | 0.9800582 144 | 0.66065574 145 | 0.7960957 146 | 0.8028022 147 | 0.94831324 148 | 0.6181496 149 | 0.94673645 150 | 0.9697174 151 | 0.64743686 152 | 0.7253332 153 | 0.63824356 154 | 0.77786887 155 | 0.9220449 156 | 0.5803243 157 | 0.8538244 158 | 0.9699867 159 | 0.66087687 160 | 0.95997757 161 | 0.96610343 162 | 0.94132483 163 | 0.8037749 164 | 0.95592296 165 | 0.91356623 166 | 0.9447116 167 | 0.71330506 168 | 0.8089769 169 | 0.9317044 170 | 0.9377292 171 | 0.5628547 172 | 0.7193232 173 | 0.7305934 174 | 0.93130374 175 | 0.5783448 176 | 0.89507264 177 | 0.77336544 178 | 0.9355774 179 | 0.9243153 180 | 0.9047856 181 | 0.9769699 182 | 0.44700444 183 | 0.76071495 184 | 0.6776439 185 | 0.9578961 186 | 0.61958665 187 | 0.94953424 188 | 0.9153797 189 | 0.9648136 190 | 0.8561055 191 | 0.9334624 192 | 0.84508324 193 | 0.9243504 194 | 0.70547444 195 | 0.73652977 196 | 0.65348935 197 | 0.95882046 198 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