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Symbol-Flipping Based Decoding of Generalized Low-Density Parity-Check Coded Constructed over GF(q)

F-C. Kuo, Lajos Hanzo

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

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.

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Symbol-flipping based decoding of generalized low-density parity-check codes over GF(q)

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International Conference on Networks Security, Wireless Communications and Trusted Computing (NSWCTC)•Jan 1, 2010•25 citations
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 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
A generalised 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 component or subcodes other than single parity checks. Gallager's bit-flipping algorithm for LDPCs is generalised to the class of GLDPCs with Hamming subcodes. The proposed weighted bit-flip voting (WBFV) method is iterative and uses only the hard decision decoder of the Hamming subcodes. Decoding of Hamming-based GLDPCs using WBFV has been simulated on the binary symmetric channel. Simulation results are presented showing the variation in performance with voting rule, graph construction and block length. In terms of the dependence of coding gains and complexity on the GLDPC block length, the proposed method is found to display a good performance to decoding complexity trade-off. Performance is found to compete well with other more conventional hard decision decoding schemes.
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.
A hybrid decoding algorithm which proposed for nonbinary and binary low density parity (LDPC) codes, both the algorithm combines the weighted symbol flipping (WSF) algorithm with the fast Fourier transform q-ary sum product algorithm (FFT-QSPA).The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low complexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. They are particularly effective for decoding LDPC codes constructed based on finite geometries and finite fields. Analyzing both the techniques nonbinary LDPC codes gives the better error performance and greatly reduces the computation complexity compared to binary LDPC codes. The proposed hybrid algorithm is used for some applications in communication systems for high speed and low power consumption. Keywords Nonbinary and binary low density parity-check (LDPC) code, Weighted symbol –flipping (WSF), Hybrid weighted symbol-flipping (HWSF), iterative decoding. 1.
A multiple-vote symbol-flipping (MV-SF) decoding algorithm for nonbinary low-density parity-check (NB-LDPC) codes is proposed in this paper. Our algorithm improves the generalized bit-flipping algorithm (GBFDA) by considering the multiplicity of the candidates at the check-node output, to perform a more accurate symbol-flipping decision at the variable node update. The MV-SF algorithm greatly improves the frame error rate performance of GBFDA and approaches the performance of the best state-of-the-art decoders [extended min-sum and min-max (Min–Max)] with lower complexity. For a(N=837,K=723)(N=837,K=723)(N=837,K=723)NB-LDPC code over GF(32), the decoder derived from the proposed algorithm can reach a throughput higher than 500 Mb/s and a coding gain of 0.44 dB compared with the most efficient GBFDA architecture with only twice the silicon area. Our architecture has 27% efficiency gain compared with the best Min–Max architecture found in the literature, with a performance loss of just 0.21 dB at frame error rate10−410^{-4}10−4.
In this paper, a new low-complexity symbol-flipping algorithm to decode nonbinary low-density parity-check (LDPC) codes is proposed. The decoding procedure updates iteratively the hard-decision received symbol vector in search of a valid codeword in the symbol vector space. Only one symbol is changed in each iteration, and symbol flipping function combines the number of failed checks and reliability of the received bits and calculated symbols. An optional mechanism to avoid infinite loops in high Galois field search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity over relatively low Galois field for short to medium code length.