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Journal of Signal Processing Systems

A Stage-Combined Belief Propagation Decoder for Polar Codes

Jin Sha, Jingbo Liu, Jun Ting Lin, Zhongfeng Wang

Published Oct 7, 2016• 8 citations
Publisher
DOI
10.1007/s11265-016-1181-y

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The error correction performance of Belief Propagation (BP) decoding for polar codes is satisfactory compared with the Successive Cancellation (SC) decoding. Nevertheless, it has to complete a fixed number of iterations, which results in high computational complexity. This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding. This paper proposes a hybrid technique that combines the “parity-check” with the “G-matrix” to reduce the computational complexity of BP decoder for polar codes. The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process, which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding. We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance. Moreover, mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated. The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding. Simulation results show that the proposed hybrid technique reduces the iterations by about 90% of BP decoding in a high Signal-to-Noise Ratio (SNR) (i.e., 3.5 ∼ 4 ​dB), and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.

Digital Communications and Networks•Dec 15, 2022•1 citation
Polar Codes are a new class of capacity-reaching codes that have low decoding complexity and excessive reliability. They are primarily based on the concept of channel polarization, which makes a few bits inside the codeword more reliable and a few much less reliable because the code duration increases. This examination comprehensively evaluates how effective Belief Propagation (BP) and Belief Propagation with List (BPL) Decoding algorithms are in the Binary Erasure Channel (BEC) setup. The fundamental purpose is to recognize how nicely these algorithms deal with errors and enhance the reliability of verbal exchange structures. Different code lengths and list sizes are examined to see how they affect the Block Error Rate (BLER). This paper considers 4 codes studied and carried out in the usage of MATLAB lengths: N=256, 512, 1024, and 2048, and varies the Energy per bit to Noise power (Eb/No) from 1 dB to a 3.5 dB with list sizes eight and sixteen. The experiments show how the BP and BPL algorithms perform in coping with erasure errors and ensuring reliable deciphering. The BLER figures provide an in-depth description and comparison of the BP and BPL interpreting algorithms. The analysis highlights the promising blunder-correction talents of each BP and BPL algorithm in the BEC context. As the code length increases, the capability to correct errors also improves, showing that these algorithms can scale effectively. The addition of list decoding in BPL similarly enhances blunder correction by offering multiple possible answers. These examine the effect of Eb/No stages on the performance of BP and BPL deciphering, displaying that better Eb/No stages enhance accuracy but also increase the erasure chance. This paper discusses the trade-offs between accuracy and complexity for BP and BPL deciphering, presenting insights into their performance traits and optimization.
The error correction performance of Belief Propagation (BP) decoding for polar codes is satisfactory compared with the Successive Cancellation (SC) decoding. Nevertheless, it has to complete a fixed number of iterations, which results in high computational complexity. This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding. This paper proposes a hybrid technique that combines the “parity-check” with the “G-matrix” to reduce the computational complexity of BP decoder for polar codes. The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process, which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding. We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance. Moreover, mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated. The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding. Simulation results show that the proposed hybrid technique reduces the iterations by about 90% of BP decoding in a high Signal-to-Noise Ratio (SNR) (i.e., 3.5 ∼ 4 ​dB), and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.