DLSTMBased Successive Cancellation Flipping Decoder for Short Polar Codes
Abstract
:1. Introduction
 A DLSTMbased SC flipping decoder is proposed. In addition, all frozen bits are clipping in the output layer to enhance accuracy. We construct the flipping set of the first error bit according to the probability of the network output in descending order, and attempt onebit flipping.
 By exploring the reliability of bit channel, we propose a novel multibit flipping scheme for sequences that reach the maximum number of onebit flipping and still fail the CRC detector. The candidate bits are sorted in ascending order in terms of the reliability, and the unreliable bits are selected in priority to multibit flipping.
 In order to make the proposed algorithm robust, we design the DLSTM network architecture to be compatible with multiple block lengths. We adopt a padding strategy to maintain data integrity, so that the training is not limited by the block length. A masking method is taken to skip the timestep and eliminate the effect of padded invalid data. Simulation results show that the proposed decoding scheme has better errorcorrection performance than the MLMSCF decoding and DSCF decoding for short block lengths. It can approach the performance of CASCL (L = 8).
2. Preliminary
2.1. Polar Codes
2.2. SC Flipping Decoder
Algorithm 1 The SC flipping algorithm. 
Input:${y}_{1}^{N}$, $\mathcal{A}$, T Output:${\widehat{u}}_{1}^{N}$

2.3. LSTM Network
3. The Proposed SC Flipping Algorithm
3.1. Analysis of Error Propagation
3.2. DLSTM Network Structure
 Input: The absolute value of the LLR sequence (both the information bits and the frozen bits) that fails CRC detector in the SC decoding.
 Output: A Kdimensional vector, the element of which corresponds to the probability of error occurrence for each information bit.
3.3. Training Process of the DLSTM Network
3.4. DLSTMBased SC Flipping Algorithm
Algorithm 2 Twobit flipping algorithm based on the DLSTM. 
Input:${y}_{1}^{N}$, ${\mathcal{W}}_{1}^{T}$, ${\mathcal{W}}_{2}^{T}$, ${T}_{1}$, ${T}_{2}$ Output:${\widehat{u}}_{1}^{N}$

3.5. DLSTMBased Robustness Mechanism
4. Performance Analysis
4.1. DLSTM Network Training Results
4.2. Decoding Complexity and Latency Analysis
4.3. BER and BLER Analysis
4.4. BLER Analysis of the Algorithm with Robustness Mechanism
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
5G  Fifth generation 
SC  Successive cancellation 
DLSTM  Double long short term memory 
CRC  Cyclic redundancy check 
LLR  Loglikelihood ratio 
CS  Critical set 
BER  Bit error rate 
BLER  Block error rate 
BPSK  Binary phase shift keying 
AWGN  Additive white Gaussian noise 
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Index  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 

Location  0  0  0  0  0  0  0  1  0  1  1  1  1  1  1  1 
Index of information bit  0  1  2  3  4  5  6  7 
Name  Parameter 

Polar codes  (64,32) 
Frame number  2,000,000 
Rate R  1/2 
CRC generator polynomial  ${x}^{8}+{x}^{7}+{x}^{5}+{x}^{4}+{x}^{1}+1$ 
Batch size  1000 
Number of epoch  30 
Regularization L2  0.008 
DLSTM  66,048 
Dense  2080 
Optimizer  Adam 
Polar Codes  Layer  Accuracy  Total Param  

$P(64,32)$  2  57.2%  77.45%  87.4%  92.84%  68,128 
3  57.12%  77.32%  87.43%  92.94%  101,152  
$P(16,8)$  2  68.63%  91.8%  98.48%  99.86%  4360 
3  68.46%  91.81%  98.44%  99.85%  6472 
Algorithm  ${\mathit{E}}_{\mathit{b}}/{\mathit{N}}_{0}$  Gain (dB)  Reduce Latency 

proposed  3.25     
MLMSCF [17]  3.53  0.28  −5.77% 
DSCF [9]  3.74  0.49  −1.16% 
CASCL (L = 2) [4]  3.91  0.66  15.73% 
CASCL (L = 4) [4]  3.44  0.19  31.22% 
CASCL (L = 8) [4]  3.23  −0.02  51.46% 
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Cui, J.; Kong, W.; Zhang, X.; Chen, D.; Zeng, Q. DLSTMBased Successive Cancellation Flipping Decoder for Short Polar Codes. Entropy 2021, 23, 863. https://doi.org/10.3390/e23070863
Cui J, Kong W, Zhang X, Chen D, Zeng Q. DLSTMBased Successive Cancellation Flipping Decoder for Short Polar Codes. Entropy. 2021; 23(7):863. https://doi.org/10.3390/e23070863
Chicago/Turabian StyleCui, Jianming, Wenxiu Kong, Xiaojun Zhang, Da Chen, and Qingtian Zeng. 2021. "DLSTMBased Successive Cancellation Flipping Decoder for Short Polar Codes" Entropy 23, no. 7: 863. https://doi.org/10.3390/e23070863