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International Conference on Wireless Communications and Signal Processing (WCSP)

Improved Weighted Bit Flip Voting decoding algorithm for generalized LDPC

Yibin Yang, Jintao Li, Hui Ling Yu, Youyun Xu

Published Oct 1, 2012• 0 citations

Abstract

A generalized low-density parity-check code (GLDPC) is a low-density parity-check code in which the constraint nodes of the code's graph are replaced with a small linear block code referred to as the constituent code other than single parity checks. For the optical system or ultra-high speed wireless data transfer system, it is hard to gain soft LLRs which need to be supplied by ultra-high speed A/D converters, so the hard decision decoder is important for these systems. Similar with Gallager's bit-flipping algorithm for LDPC, the Weighted Bit Flip Voting (WBFV) algorithm has been proposed to decode GLDPC with only the hard decision which proved to be good performance. But the finding of max vote in the algorithm is intractability for the hardware implementation. If we find the max from thousands of data (code length is usually thousands) serially, thousands of cycles needed result to large latency; a lot of compare modules needed for parallel finding of the max, result to large resource. In this paper, we proposed an improved and simplified WBFV algorithm which without max voting finding is easy for hardware implementation. The proposed improved algorithm not only has no performance loss, but also speeds up the iteration convergence. Then we proposed a full parallel GLDPC decoder design for our algorithm with very low complexity.

DOI: 10.1109/wcsp.2012.6542910

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An efficient symbol-flipping based decoding algorithm designed for nonbinary generalized low-density parity-check (GLDPC) codes is proposed. By extending the concept of the weighted bit flip voting (WBFV) algorithm designed for binary Hamming-code based GLDPC codes, the symbol-flipping decoding algorithm can be beneficially employed for decoding the family of GLDPC codes constructed from nonbinary constituent codes, such as nonbinary Bose Chaudhuri Hocquenghem (BCH) codes or Reed Solomon (R-S) codes. The simulation results demonstrate that improvements of 1 dB and 2.7 dB are achieved by the proposed coding scheme in comparison to the more conventional binary GLDPC codes using the WBFV decoding algorithm, when using the Galois Field GF(32) for communicating over AWGN and uncorrelated Rayleigh fading channels, respectively

An efficient symbol-flipping based decoding algorithm designed for nonbinary Generalized Low-Density Parity-Check (GLDPC) codes is proposed. By extending the concept of the Weighted Bit Flip Voting (WBFV) algorithm designed for binary Hamming-code based GLDPC codes, the symbol-flipping decoding algorithm can be beneficially employed for decoding the family of GLDPC codes constructed from nonbinary constituent codes, such as nonbinary Bose Chaudhuri Hocquenghem (BCH) codes or Reed Solomon (RS) codes. The simulation results demonstrate that improvements of 1 dB and 2.7 dB are achieved by the proposed coding scheme in comparison to the more conventional binary GLDPC codes using the WBFV decoding algorithm, when using the Galois Field GF(32) for communicating over AWGN and uncorrelated Rayleigh fading channels, respectively.

An improved bit-flipping(BF) algorithm with low complexity for decoding structured low-density parity-check codes(LDPC) is proposed to improve the performance of the hard-decision BF algorithm.The hard-decision bits are divided into two groups based on the magnitudes of the received symbols,and at each iteration,the proposed algorithm can flip more than one bit with using two thresholds,and the flipping error probability is effectively decreased.The improved BF algorithm requires some real number comparisons before iterations and requires only logical operations during the iterations.Compared with the weighted bit-flipping algorithm and its modifications,the new method is with significantly lower complexity.Simulations show that the proposed algorithm is provided with very fast convergence speed and excellent performance with significantly low complexity.

Aiming at seeking a low-complexity decoder with fast decoding convergence speed for short or medium low-density parity-check (LDPC) codes, an improved parallel weighted bit-flipping (IPWBF) algorithm, which is applied flexibly for two classes of codes is presented here. For LDPC codes with low column weight in their parity check matrix, both bootstrapping and loop detection procedures, described in the existing literature, are included in IPWBF. Furthermore, a novel delay-handling procedure is introduced to prevent the codeword bits of high reliability from being flipped too hastily. For large column weight finite geometry LDPC codes, only the delay-handling procedure is included in IPWBF to show its effectiveness. Extensive simulation results demonstrate that the proposed algorithm achieves a good tradeoff between performance and complexity.

In order to improve the decoding speed of low density parity check code( LDPC) codes,a fast weighted bit flipping algorithm with partially parallel bit-chosen is proposed. In this scheme,all bits are firstly divided into several blocks according to the stochastic error distribution in the received vector. And then one bit is chosen from each block to form the candidate set of flipped bits. Finally,a proper number of bits are chosen from the candidate set and flipped to implement the decoding. Furthermore,the tree sorting and data pool methods are adopted to decrease the computational complexity of the key module of the proposed algorithm. Compared with the multi-bit flippin( MBF) algorithm by simulations,the proposed scheme and the method of hardware implement can achieve significant improvement in the decoding speed.