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International Conference on Circuit, Power and Computing Technologies

Non zero syndrome parallel concatenated gallager codes

G P Aswathy, Niyas K. Haneefa

Published Apr 1, 2017• 4 citations
Publisher

Abstract

Parallel Concatenated Gallager Code (PCGC) is a class of concatenated error correcting codes designed to reduce the encoding and decoding complexity of long block length Low Density Parity Check (LDPC) codes. In this paper, we present a novel class of PCGC in which one constituent code satisfies zero syndrome criteria and the other one satisfies non-zero syndrome criteria. Simulation results show that proposed non-zero syndrome PCGC outperforms existing non-zero syndrome PCGC in terms of its bit error rate (BER) performance in Binary Symmetric Channel (BSC). We also show that proposed concatenation method gives better performance than dedicated LDPC of same frame length and code rate over BSC.

DOI
10.1109/iccpct.2017.8074180

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Parallel Concatenated Gallager Code (PCGC) is a class of concatenated error correcting codes designed to reduce the encoding and decoding complexity of long block length Low Density Parity Check (LDPC) codes. In this paper, we present a novel class of PCGC in which one constituent code satisfies zero syndrome criteria and the other one satisfies non-zero syndrome criteria. Simulation results show that proposed non-zero syndrome PCGC outperforms existing non-zero syndrome PCGC in terms of its bit error rate (BER) performance in Binary Symmetric Channel (BSC). We also show that proposed concatenation method gives better performance than dedicated LDPC of same frame length and code rate over BSC.
In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its “strength.” The introduction of this additional bit increases the guaranteed error correction capability by a factor of at least 2. An additional bit can also be employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis of the proposed algorithms is described. These algorithms outperform the Gallager A/B algorithm and the min-sum algorithm at much lower complexity. Concatenation of two-bit bit flipping algorithms show a potential to approach the performance of belief propagation (BP) decoding in the error floor region, also at lower complexity.
Focused on the problem that short cycles degrade the iterative decoding performance of finite length LDPC, a class of improved low density parity check (LDPC) codes constructed based on Gallager's form is designed. On the basis of keeping down the basic form of Gallager's construction, a quasi-cyclic form is used, then the new codes are free of cycles of length 4 and have good minimum distance. Simulation results demonstrated that the improved codes are better than Gallager's codes when block length is small
Low-rate non-binary low-density parity-check (LDPC) codes for coherent and blockwise non-coherent additive white Gaussian noise (AWGN) channels are developed. The proposed construction is based on the concatenation of non-binary outer LDPC codes with inner binary codes. In case the binary codes are chosen to be Hadamard or Reed-Muller (RM) codes, the complexity of the decoding scheme is considerably reduced. An asymptotic analysis of the concatenation with help of composite capacity considerations anddensity evolution (DE) is provided, from which guidelines on the choice of both inner and outer codes are devised. Finite length designs presented in this work confirm the excellent performance of the proposed codes.