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Digital Signal Processing and Artificial Intelligence for Automatic Learning

Reliability Ratio Weighted Bit Flipping– Sum Product Algorithm for Regular LDPC Codes

Chakir Aqil, Abdelaziz Ahaitouf, Ismail Akharraz

Published Jun 1, 2022• 0 citations
Publisher

Abstract

In this paper, a new algorithm called Reliability Ratio Weighted Bit Flipping-Sum Product (RRWBFSP) decoding is proposed for low-density parity-check codes.The new algorithm combines two different algorithms, Sum Product [4] and Reliability Ratio Weighted Bit Flipping [6].The results of the simulation show that the new algorithm achieves a 0.34 dB performance gain over of the standard Sum-Product decoding algorithms.Furthermore, RRWBFSP algorithm has almost the same computational complexity compared to the standard Sum-Product algorithm.

DOI
10.6025/dspaial/2022/1/1/28-36

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In this paper, a new algorithm called Reliability Ratio Weighted Bit Flipping-Sum Product (RRWBFSP) decoding is proposed for low-density parity-check codes.The new algorithm combines two different algorithms, Sum Product [4] and Reliability Ratio Weighted Bit Flipping [6].The results of the simulation show that the new algorithm achieves a 0.34 dB performance gain over of the standard Sum-Product decoding algorithms.Furthermore, RRWBFSP algorithm has almost the same computational complexity compared to the standard Sum-Product algorithm.
In this study, we propose a “New Reliability Ratio Weighted Bit Flipping” (NRRWBF) algorithm for Low‐Density Parity‐Check (LDPC) codes. This algorithm improves the “Reliability Ratio Weighted Bit Flipping” (RRWBF) algorithm by modifying the reliability ratio. It surpasses the RRWBF in performance, reaching a 0.6 dB coding gain at a Binary Error Rate (BER) of 10−4 over the Additive White Gaussian Noise (AWGN) channel, and presents a significant reduction in the decoding complexity. Furthermore, we improved NRRWBF using the sum of the syndromes as a criterion to avoid the infinite loop. This will enable the decoder to attain a more efficient and effective decoding performance.
In this paper, a modified weighted bit-flipping (WBF) algorithm is proposed for finite geometry low-density parity-check (FG-LDPC) codes. The calculation for the flipping function in the new method includes all the elements in sum product algorithm (SPA) instead of the minimum one in most existing methods. Simulation results show that the proposed method exhibits better performance than the best method available in the literature so far. The performances of different algorithms are also considered in random constructed LDPC codes. The reliability ratio based WBF (RRWBF) method performs the best in this kind of codes and the proposed method performs very closely to the RRWBF method. The decoding complexities for both FG-LDPC and random constructed LDPC are also analyzed.
In this contribution, a novel reliability-ratio based weighted bit-flipping (RRWBF) algorithm is proposed for decoding low density parity check (LDPC) codes. The RRWBF algorithm proposed is benchmarked against the conventional weighted bit-flipping (WBF) algorithm and the improved weighted bit-flipping (IWBF) algorithm. More than 1 and 2 dB coding gain was achieved at a BER of 10/sup -5/ while invoking the RRWBF algorithm in comparison to the two benchmarking schemes, when communicating over an AWGN and an uncorrelated Rayleigh channel, respectively. Furthermore, the decoding complexity of the proposed RRWBF algorithm is maintained at the same level as that of the conventional WBF algorithm.
In this paper we present Low Density Parity Check decoding algorithm that assemble two different algorithms: Sum-Product and Bit-Flipping; we denote Bit Flipping-Sum Product Algorithm (BFSP). To reduce the bit error rate, we perform the Bit-Flipping algorithm after the Sum-Product algorithm. Simulation results over an additive white Gaussian channel show that the error performance of a LDPC codes with Bit Flipping-Sum Product decoding is within 0.2 dB of the standard Sum-Product decoding algorithms. Furthermore, the decoding complexity of the proposed BFSP algorithm is maintained at the same level as that of the standard Sum-Product algorithm.
It was recently shown that the reliability ratio based bit-flipping (RRWBF) decoding algorithm for low-density parity-check (LDPC) codes performs best among existing bit-flipping-based algorithms. A new version of this algorithm is proposed such that decoding time is significantly reduced, especially when the iteration number is small and the code length is large. Simulation results showed the proposed version has up to 2322.39%, 823.90%, 511.79%, and 261.92% speedup compared to the original algorithm on a UNIX workstation for 10, 30, 50, and 100 iterations. It is thus much more efficient to adopt this version for simulation and hardware implementation. Moreover, this version of the RRWBF algorithm provides a more intuitive way of interpreting its superior performance over other bit-flipping-based algorithms.