DetNet_Soft_16QAM.py

#!/usr/bin/env python
import tensorflow as tf
import numpy as np
import time as tm
import math
import sys
import pickle as pkl

"""
This file is used to train and test the DetNet architecture in the soft decision output scenario.
The constellation used is 16PSK and the channel is complex
all parameters were optimized and trained over the 4X8 iid channel, changing the channel might require parameter tuning

Notice that the run time analysis presented in the paper was made on a numpy version of the tensorflow network.
The times presented in the paper differ from the ones obtained using this code.

writen by Neev Samuel based on the paper:
    "Learning to detect, Neev Samuel,Tzvi Diskin,Ami Wiesel"

contact by neev.samuel@gmail.com

"""

def find_nearest_np(values):
    values = values + 3
    values = values/2
    values = np.clip(values,0,3)
    values = np.round(values)
    values = values * 2
    values = values - 3
    return values

def find_nearest(values):
    values = values + 3
    values = values/2
    values = tf.clip_by_value(values,0,3)
    values = tf.round(values)
    values = values * 2
    values = values - 3
    return values

def validate2(y, SNR, H, K, N):
    final_probs_three = np.zeros((K))
    final_probs_one = np.zeros((K))
    final_probs_minus_one = np.zeros((K))
    final_probs_minus_three = np.zeros((K))
    sun_plus_three  = 0
    sum_plus = 0
    sum_minus = 0
    sum_minus_three = 0
    tmp_snr = (H.T.dot(H)).trace()/ K
    y = y/ np.sqrt(tmp_snr) * np.sqrt(SNR)
    for i in range(np.power(2, K)):
        binary1 = "{0:b}".format(i)
        binary1 = binary1.zfill(K)
        binary1 = [int(d) for d in binary1]
        binary1 = np.array(binary1)

        x1 = (binary1 * 2) - 1
        for j in range(np.power(2, K)):
            binary2 = "{0:b}".format(j)
            binary2 = binary2.zfill(K)
            binary2 = [int(d1) for d1 in binary2]
            binary2 = np.array(binary2)

            x2 = (binary2 * 2) - 1
            
            x = np.zeros((K))
            for jj in range(K):
                if x1[jj] == -1 and x2[jj] == -1:
                      x[jj] = -3
                if x1[jj] == -1 and x2[jj] ==  1:
                      x[jj] = -1
                if x1[jj] == 1 and x2[jj] == -1:
                      x[jj] = 1
                if x1[jj] == 1 and x2[jj] == 1:
                      x[jj] = 3

            H_tmp = H / np.sqrt(tmp_snr) * np.sqrt(SNR)
            y_temp = H_tmp.dot(x)

            prob = np.exp(-0.5 * (np.sum(np.power(y_temp[jj] - y[jj], 2) for jj in range(N))))

            for ii in range(K):
                if x[ii] == 3:
                    final_probs_three[ii] = final_probs_three[ii] + ((1.0 / np.power(2, K)) * prob)
                    sun_plus_three = sun_plus_three + 1
                if x[ii] == 1:
                    final_probs_one[ii] = final_probs_one[ii] + ((1.0 / np.power(2, K)) * prob)
                    sum_plus = sum_plus + 1
                if x[ii] == -1:
                    final_probs_minus_one[ii] = final_probs_minus_one[ii] + ((1.0 / np.power(2, K)) * prob)
                    sum_minus = sum_minus + 1
                if x[ii] == -3:
                    final_probs_minus_three[ii] = final_probs_minus_three[ii] + ((1.0 / np.power(2, K)) * prob)
                    sum_minus_three = sum_minus_three + 1
    for ii in range(K):
        norm = final_probs_one[ii] + final_probs_minus_one[ii] + final_probs_minus_three[ii] + final_probs_three[ii]
        final_probs_one[ii] = final_probs_one[ii] / norm
        final_probs_minus_one[ii] = final_probs_minus_one[ii] / norm
        final_probs_minus_three[ii] = final_probs_minus_three[ii]/norm
        final_probs_three[ii] = final_probs_three[ii]/norm                      

    return final_probs_one, final_probs_minus_one,final_probs_minus_three,final_probs_three


###start here
"""
Parameters
K - size of x
N - size of y
snrdb_low - the lower bound of noise db used during training
snr_high - the higher bound of noise db used during training
L - number of layers in DetNet
v_size = size of auxiliary variable at each layer
hl_size - size of hidden layer at each DetNet layer (the dimention the layers input are increased to
startingLearningRate - the initial step size of the gradient descent algorithm
decay_factor & decay_step_size - each decay_step_size steps the learning rate decay by decay_factor
train_iter - number of train iterations
train_batch_size - batch size during training phase
test_iter - number of test iterations
test_batch_size  - batch size during testing phase
LOG_LOSS - equal 1 if loss of each layer should be sumed in proportion to the layer depth, otherwise all losses have the same weight 
res_alpha- the proportion of the previuos layer output to be added to the current layers output (view ResNet article)
snrdb_low_test & snrdb_high_test & num_snr - when testing, num_snr different SNR values will be tested, uniformly spread between snrdb_low_test and snrdb_high_test 
"""
sess = tf.InteractiveSession()

#parameters
K = 4
N = 8
snrdb_low = 7.0
snrdb_high = 14.0
snr_low = 10.0 ** (snrdb_low/10.0)
snr_high = 10.0 ** (snrdb_high/10.0)
L=30
v_size = 4*(2*K)
hl_size = 12*(2*K)
startingLearningRate1 = 0.0005
startingLearningRate2 = 0.0005
decay_factor1 = 0.97
decay_factor2 = 0.97
decay_step_size1 = 1000
decay_step_size2 = 1000
train_iter = 80000
train_iter_no_noise = 10000

train_batch_size = 5000
test_iter= 20
test_batch_size = 50
LOG_LOSS = 1
res_alpha=0.9
num_snr = 6
snrdb_low_test=8.0
snrdb_high_test=13.0
symbols = np.array([-3,-1,1,3])
normalize_dist = 1

print('16QAM soft with validation')
print(K)
print(N)
print(snrdb_low)
print(snrdb_high)
print(snr_low)
print(snr_high)
print(L)
print(v_size)
print(hl_size)
print(startingLearningRate1)
print(startingLearningRate2)
print(decay_factor1)
print(decay_factor2)
print(decay_step_size1)
print(decay_step_size2)
print(train_iter)
print(train_batch_size)
print(test_iter)
print(test_batch_size)
print(res_alpha)
print(num_snr)
print(snrdb_low_test)
print(snrdb_high_test)
print(normalize_dist)

"""Data generation for train and test phases
In this example, both functions are the same.
This duplication is in order to easily allow testing cases where the test is over different distributions of data than in the training phase.
e.g. training over gaussian i.i.d. channels and testing over a specific constant channel.
currently both test and train are over i.i.d gaussian channel.
"""
def generate_data(B,K,N,snr_low,snr_high,noise):
    x_R = np.random.randint(4, size=(B, K))
    x_R = x_R * 2
    x_R = x_R - 3

    x_I = np.random.randint(4, size=(B, K))
    x_I = x_I * 2
    x_I = x_I - 3
    
    x_ind = np.zeros([B,K,16])
    for i in range(B):
        for ii in range(K):
            if x_R[i,ii]==-3 and x_I[i,ii] == -3:
                x_ind[i,ii,0] =  1
            if x_R[i,ii]==-3 and x_I[i,ii] == -1:
                x_ind[i,ii,1] =  1
            if x_R[i,ii]==-3 and x_I[i,ii] == 1:
                x_ind[i,ii,2] =  1
            if x_R[i,ii]==-3 and x_I[i,ii] == 3:
                x_ind[i,ii,3] =  1
            if x_R[i,ii]==-1 and x_I[i,ii] == -3:
                x_ind[i,ii,4] =  1
            if x_R[i,ii]==-1 and x_I[i,ii] == -1:
                x_ind[i,ii,5] =  1
            if x_R[i,ii]==-1 and x_I[i,ii] == 1:
                x_ind[i,ii,6] =  1
            if x_R[i,ii]==-1 and x_I[i,ii] == 3:
                x_ind[i,ii,7] =  1
            if x_R[i,ii]==1 and x_I[i,ii] == -3:
                x_ind[i,ii,8] =  1
            if x_R[i,ii]==1 and x_I[i,ii] == -1:
                x_ind[i,ii,9] =  1
            if x_R[i,ii]==1 and x_I[i,ii] == 1:
                x_ind[i,ii,10] =  1
            if x_R[i,ii]==1 and x_I[i,ii] == 3:
                x_ind[i,ii,11] =  1
            if x_R[i,ii]==3 and x_I[i,ii] == -3:
                x_ind[i,ii,12] =  1
            if x_R[i,ii]==3 and x_I[i,ii] == -1:
                x_ind[i,ii,13] =  1
            if x_R[i,ii]==3 and x_I[i,ii] == 1:
                x_ind[i,ii,14] =  1
            if x_R[i,ii]==3 and x_I[i,ii] == 3:
                x_ind[i,ii,15] =  1
                     
    x_ = np.concatenate((x_R, x_I), axis=1)

    H_R = np.random.randn(B, N, K)
    H_I = np.random.randn(B, N, K)
    H_ = np.zeros([B, 2 * N, 2 * K])

    y_ = np.zeros([B, 2 * N])

    w_R = np.random.randn(B, N)
    w_I = np.random.randn(B, N)
    w = np.concatenate((w_R, w_I), axis=1)

    Hy_ = x_ * 0
    HH_ = np.zeros([B, 2 * K, 2 * K])
    SNR_ = np.zeros([B])
    for i in range(B):
        # print i
        SNR = np.random.uniform(low=snr_low, high=snr_high)
        H = np.concatenate((np.concatenate((H_R[i, :, :], -1 * H_I[i, :, :]), axis=1),
                            np.concatenate((H_I[i, :, :], H_R[i, :, :]), axis=1)), axis=0)
        tmp_snr = (H.T.dot(H)).trace() / (2 * K)
        H_[i, :, :] = H
        y_[i, :] = H.dot(x_[i, :])   + noise*w[i,:]*np.sqrt(tmp_snr) / np.sqrt(SNR)
        Hy_[i, :] = H.T.dot(y_[i, :])
        HH_[i, :, :] = H.T.dot(H_[i, :, :])
        SNR_[i] = SNR
    return y_,H_,Hy_,HH_,x_,SNR_,x_ind



def piecewise_linear_soft_sign(x):
    t = tf.Variable(0.1)
    y = -1+tf.nn.relu(x+t)/(tf.abs(t)+0.00001)-tf.nn.relu(x-t)/(tf.abs(t)+0.00001)
    return y

def affine_layer(x,input_size,output_size,Layer_num):
    W = tf.Variable(tf.random_normal([input_size, output_size], stddev=0.01))
    w = tf.Variable(tf.random_normal([1, output_size], stddev=0.01))
    y = tf.matmul(x, W)+w
    return y

def relu_layer(x,input_size,output_size,Layer_num):
    y = tf.nn.relu(affine_layer(x,input_size,output_size,Layer_num))
    return y

def sign_layer(x,input_size,output_size,Layer_num):
    y = affine_layer(x,input_size,output_size,Layer_num)
    return y

#tensorflow placeholders, the input given to the model in order to train and test the network
HY = tf.placeholder(tf.float32,shape=[None,2*K])
X = tf.placeholder(tf.float32,shape=[None,2*K])
X_IND = tf.placeholder(tf.float32,shape=[None,K,16])
HH = tf.placeholder(tf.float32,shape=[None, 2*K , 2*K])

batch_size = tf.shape(HY)[0]

S1=[]
S1.append(tf.zeros([batch_size,2*K]))
S2=[]
S2.append(tf.zeros([batch_size,16*K]))
S4 = []
S4.append(tf.zeros([batch_size,K,4,2]))
V=[]
V.append(tf.zeros([batch_size,v_size]))
LOSS=[]
LOSS.append(tf.zeros([]))
BER=[]
BER.append(tf.zeros([]))
delta = tf.Variable(tf.zeros(L*2,1))
Z1 = []
ZZ1 = []
W11 = []
w11 = []
W22 = []
w22 = []
W33 = []
w33 = []
Z1_1 = []
temp1 = []
Z = []
first = []
second = []
#The architecture of DetNet
for i in range(1,L):
    print('i')
    print(i)
    temp11 = tf.matmul(tf.expand_dims(S1[-1],1),HH)
    temp1.append(tf.squeeze(temp11,1))
    first.append(delta[(i-1) * 2]*HY)
    second.append(delta[(i-1) * 2 + 1]*temp1[-1])
    Z1.append(S1[-1] - (delta[(i-1) * 2]*HY) + (delta[(i-1) * 2 + 1]*temp1[-1]))
    Z.append(tf.concat([Z1[-1], V[-1]], 1))
    ZZ = relu_layer(Z[-1],(2*K) + v_size , hl_size,'relu'+str(i))

    
    S2_temp = sign_layer(ZZ , hl_size , 16*K,'sign'+str(i))
    S2.append(S2_temp)
    S2[i]=(1-res_alpha)*S2[i]+res_alpha*S2[i-1]
    S2[i] =    tf.clip_by_value(S2[i],0,1)

    V_temp = affine_layer(ZZ , hl_size , v_size,'aff'+str(i))
    V.append(V_temp)
    V[i]=(1-res_alpha)*V[i]+res_alpha*V[i-1] 
    
    S3 = tf.reshape(S2[i],[batch_size,K,16])

    temp_0 = S3[:,:,0]
    temp_1 = S3[:,:,1]
    temp_2 = S3[:,:,2]
    temp_3 = S3[:,:,3]
    temp_4 = S3[:,:,4]
    temp_5 = S3[:,:,5]
    temp_6 = S3[:,:,6]
    temp_7 = S3[:,:,7]
    temp_8 = S3[:,:,8]
    temp_9 = S3[:,:,9]
    temp_10 = S3[:,:,10]
    temp_11 = S3[:,:,11]
    temp_12 = S3[:,:,12]
    temp_13 = S3[:,:,13]
    temp_14 = S3[:,:,14]    
    temp_15 = S3[:,:,15]
    
    S1_real = -3.0*temp_0  +\
              -3.0*temp_1  +\
              -3.0*temp_2  +\
              -3.0*temp_3  +\
              -1.0*temp_4  +\
              -1.0*temp_5  +\
              -1.0*temp_6  +\
              -1.0*temp_7  +\
               1.0*temp_8  +\
               1.0*temp_9  +\
               1.0*temp_10 +\
               1.0*temp_11 +\
               3.0*temp_12 +\
               3.0*temp_13 +\
               3.0*temp_14 +\
               3.0*temp_15

    S1_im =   -3.0*temp_0  +\
              -1.0*temp_1  +\
               1.0*temp_2  +\
               3.0*temp_3  +\
              -3.0*temp_4  +\
              -1.0*temp_5  +\
               1.0*temp_6  +\
               3.0*temp_7  +\
              -3.0*temp_8  +\
              -1.0*temp_9  +\
               1.0*temp_10 +\
               3.0*temp_11 +\
              -3.0*temp_12 +\
              -1.0*temp_13 +\
               1.0*temp_14 +\
               3.0*temp_15
               
    S1.append(tf.concat([S1_real, S1_im], 1))
    
    S4_temp =  tf.zeros([batch_size,K, 4, 2])  

    temp_0 = tf.expand_dims(temp_0,2)
    temp_1 = tf.expand_dims(temp_1,2)
    temp_2 = tf.expand_dims(temp_2,2)
    temp_3 = tf.expand_dims(temp_3,2)
    temp_4 = tf.expand_dims(temp_4,2)
    temp_5 = tf.expand_dims(temp_5,2)
    temp_6 = tf.expand_dims(temp_6,2)
    temp_7 = tf.expand_dims(temp_7,2)
    temp_8 = tf.expand_dims(temp_8,2)
    temp_9 = tf.expand_dims(temp_9,2)
    temp_10 = tf.expand_dims(temp_10,2)
    temp_11 = tf.expand_dims(temp_11,2)
    temp_12 = tf.expand_dims(temp_12,2)
    temp_13 = tf.expand_dims(temp_13,2)
    temp_14 = tf.expand_dims(temp_14,2)
    temp_15 = tf.expand_dims(temp_15,2)

    S4_temp1 = tf.concat([temp_0 + temp_1 + temp_2 + temp_3,temp_4 + temp_5 + temp_6 + temp_7,temp_8 + temp_9 + temp_10 + temp_11,temp_12 + temp_13 + temp_14 + temp_15],2)
    S4_temp2 = tf.concat([temp_0 + temp_4 +  temp_8 + temp_12,temp_1 + temp_5 +  temp_9 + temp_13,temp_2 + temp_6 +  temp_10 + temp_14,temp_3 + temp_7 +  temp_11 + temp_15],2)
    S4_temp1 = tf.expand_dims(S4_temp1,3)
    S4_temp2 = tf.expand_dims(S4_temp2,3)
    
    S4_temp3 = tf.concat([S4_temp1,S4_temp2],3)
    
    S4.append(S4_temp3)
    X_IND_reshaped = tf.reshape(X_IND,[batch_size,16*K])
    if LOG_LOSS == 1:
        LOSS.append(np.log(i)*tf.reduce_mean(tf.reduce_mean(tf.square(X_IND_reshaped - S2[-1]),1)))
    else:
        LOSS.append(tf.reduce_mean(tf.reduce_mean(tf.square(X_IND_reshaped - S2[-1]),1)))
    BER.append(tf.reduce_mean(tf.cast(tf.not_equal(X_IND, tf.round(S3)), tf.float32)))
Max_Val = tf.reduce_max(S3,axis=2, keep_dims=True)
Greater = tf.greater_equal(S3,Max_Val)
BER2 = tf.round(tf.cast(Greater,tf.float32))
BER3 = tf.not_equal(BER2, X_IND)
BER4 = tf.reduce_sum(tf.cast(BER3,tf.float32),2)
BER5 = tf.cast(tf.greater(BER4,0),tf.float32)
SER =  tf.reduce_mean(BER5)     

TOTAL_LOSS=tf.add_n(LOSS)

saver = tf.train.Saver()


global_step1 = tf.Variable(0, trainable=False)
learning_rate1 = tf.train.exponential_decay(startingLearningRate1, global_step1, decay_step_size1, decay_factor1, staircase=True)
train_step1 = tf.train.AdamOptimizer(learning_rate1).minimize(TOTAL_LOSS)

global_step2 = tf.Variable(0, trainable=False)
learning_rate2 = tf.train.exponential_decay(startingLearningRate2, global_step2, decay_step_size2, decay_factor2, staircase=True)
train_step2 = tf.train.AdamOptimizer(learning_rate2).minimize(TOTAL_LOSS)

init_op=tf.initialize_all_variables()

sess.run(init_op)
for i in range(train_iter_no_noise): #num of train iter
    batch_Y, batch_H, batch_HY, batch_HH, batch_X , SNR1, x_ind= generate_data(train_batch_size,K,N,snr_low,snr_high,0)
    train_step1.run(feed_dict={HY: batch_HY, HH: batch_HH, X: batch_X ,X_IND: x_ind})
    if i % 100== 0 :
        sys.stderr.write(str(i)+' ')
        batch_Y, batch_H, batch_HY, batch_HH, batch_X ,SNR1,x_ind= generate_data(train_batch_size,K,N,snr_low,snr_high,0)
        results = sess.run([LOSS[L-1],SER], {HY: batch_HY, HH: batch_HH, X: batch_X,X_IND: x_ind})
        print_string = [i]+results
        print ' '.join('%s' % x for x in print_string)

for i in range(train_iter): #num of train iter
    batch_Y, batch_H, batch_HY, batch_HH, batch_X , SNR1,x_ind= generate_data(train_batch_size,K,N,snr_low,snr_high,1)
    train_step2.run(feed_dict={HY: batch_HY, HH: batch_HH, X: batch_X,X_IND: x_ind})
    if i % 1000 == 0 :
	sys.stderr.write(str(i)+ ' ')
        batch_Y, batch_H, batch_HY, batch_HH, batch_X ,SNR1,x_ind= generate_data(train_batch_size,K,N,snr_low,snr_high,1)
        results = sess.run([LOSS[L-1],SER], {HY: batch_HY, HH: batch_HH, X: batch_X,X_IND: x_ind})
        print_string = [i]+results
        print ' '.join('%s' % x for x in print_string)
          

#Testing the trained model

avg_val_error_last_layer = np.zeros((num_snr))

snrdb_list = np.linspace(snrdb_low_test,snrdb_high_test,num_snr)
snr_list = 10.0 ** (snrdb_list/10.0)
bers = np.zeros((1,num_snr))
times = np.zeros((1,num_snr))
tmp_bers = np.zeros((1,test_iter))
tmp_times = np.zeros((1,test_iter))

stat_distance = np.zeros((num_snr,2*K))

for j in range(num_snr):
    new_dist_temp = np.zeros((2*K))
    print('snr:')
    print(snrdb_list[j])
    for jj in range(test_iter):
        if jj%100 == 0:
            print('test iteration:')
            print(jj)
        batch_Y, batch_H, batch_HY, batch_HH, batch_X ,SNR1, BATCH_X_IND= generate_data(test_batch_size , K,N,snr_list[j],snr_list[j],1)

        tic = tm.time()
        tmp_bers[0,jj] = np.array(sess.run(SER, {HY: batch_HY, HH: batch_HH, X: batch_X, X_IND:BATCH_X_IND}))
        toc = tm.time()
        tmp_times[0][jj] =  toc - tic

        last_layer = np.array(sess.run(S4[-1], {HY: batch_HY, HH: batch_HH, X: batch_X, X_IND:BATCH_X_IND}))

        last_layer = np.clip(last_layer, 0, 1)
        
        for jjj in range(test_batch_size):
            real_prob_one, real_prob_min_one ,real_prob_min_three,real_prob_three = validate2(batch_Y[jjj], SNR1[jjj], batch_H[jjj], 2*K, 2*N)

            NN_lastLayer_minus3_Re = last_layer[jjj,:,0,0]
            NN_lastLayer_minus3_Im = last_layer[jjj,:,0,1]
            
            NN_lastLayer_minus1_Re = last_layer[jjj,:,1,0]
            NN_lastLayer_minus1_Im = last_layer[jjj,:,1,1]
            
            NN_lastLayer_1_Re = last_layer[jjj,:,2,0]
            NN_lastLayer_1_Im = last_layer[jjj,:,2,1]

            NN_lastLayer_3_Re = last_layer[jjj,:,3,0]
            NN_lastLayer_3_Im = last_layer[jjj,:,3,1]
            
            if normalize_dist:
                Sum_Re = NN_lastLayer_minus3_Re + NN_lastLayer_minus1_Re + NN_lastLayer_1_Re + NN_lastLayer_3_Re
                Sum_Im = NN_lastLayer_minus3_Im + NN_lastLayer_minus1_Im + NN_lastLayer_1_Im + NN_lastLayer_3_Im
            
                NN_lastLayer_minus3_Re = NN_lastLayer_minus3_Re/Sum_Re
                NN_lastLayer_minus1_Re = NN_lastLayer_minus1_Re/Sum_Re
                NN_lastLayer_1_Re      = NN_lastLayer_1_Re/Sum_Re
                NN_lastLayer_3_Re      = NN_lastLayer_3_Re/Sum_Re
                
                NN_lastLayer_minus3_Im = NN_lastLayer_minus3_Im/Sum_Im
                NN_lastLayer_minus1_Im = NN_lastLayer_minus1_Im/Sum_Im
                NN_lastLayer_1_Im = NN_lastLayer_1_Im/Sum_Im
                NN_lastLayer_3_Im = NN_lastLayer_3_Im/Sum_Im
            
            NN_lastLayer_3 = np.concatenate([NN_lastLayer_3_Re,NN_lastLayer_3_Im],0)
            NN_lastLayer_1 = np.concatenate([NN_lastLayer_1_Re,NN_lastLayer_1_Im],0)
            NN_lastLayer_minus3 = np.concatenate([NN_lastLayer_minus3_Re,NN_lastLayer_minus3_Im],0)
            NN_lastLayer_minus1 = np.concatenate([NN_lastLayer_minus1_Re,NN_lastLayer_minus1_Im],0)
               
            new_dist_temp = new_dist_temp + np.absolute(NN_lastLayer_3 - real_prob_three) +  np.absolute(NN_lastLayer_1 - real_prob_one) +  np.absolute(NN_lastLayer_minus3 - real_prob_min_three) +  np.absolute(NN_lastLayer_minus1 - real_prob_min_one) 

    stat_distance[j] = new_dist_temp/(test_batch_size*test_iter)
    bers[:,j] = np.mean(tmp_bers,1)
    times[:,j] = np.mean(tmp_times[0])/test_batch_size

print('snrdb_list')
print(snrdb_list)
print('bers')
print(bers)
print('times')
print(times)
print('stat_distance')
print(stat_distance)

save_path = saver.save(sess, "./DetNet_Soft_16QAM/16QAM_Soft_model.ckpt")