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Journal of Computational and Theoretical Nanoscience

Analysis of a Code Construction Method for Non-Binary Quasi-Cyclic Irregular Low Density Parity Check Decoder

M. Anbuselvi, P. Saravanan, S. Joseph Gladwin

Published Jan 19, 2018• 1 citation
Publisher

Abstract

Non-binary LDPC codes is a class of linear block code outperform in the short and moderate block length, closer to Shannon's limit. The numerical strength of the decoder is proportional to the sparsity of the parity check matrix. A Hierarchically Diagonal Parity Check Matrix (HDPCM) with better sparseness is constructed to optimize the computation complexity and decoding performance. The decoder based on the proposed matrix using FFT-SP decoding algorithm is analyzed, with different modulation schemes and channel environment. The positive impact of the constructed matrix is elaborated, concludes with the suitability of the HDPCM structure in AWGN channel and BPSK modulation environment.

DOI
10.1166/jctn.2018.7151

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Non-binary LDPC codes is a class of linear block code outperform in the short and moderate block length, closer to Shannon's limit. The numerical strength of the decoder is proportional to the sparsity of the parity check matrix. A Hierarchically Diagonal Parity Check Matrix (HDPCM) with better sparseness is constructed to optimize the computation complexity and decoding performance. The decoder based on the proposed matrix using FFT-SP decoding algorithm is analyzed, with different modulation schemes and channel environment. The positive impact of the constructed matrix is elaborated, concludes with the suitability of the HDPCM structure in AWGN channel and BPSK modulation environment.
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Non-binary LDPC code can achieve better error correcting performance than its binary counterpart especially when the code length is short or moderate. A novel Non-Binary LDPC code is presented in this paper to replace the traditional binary standard in 802.11n system. The proposed Parity Check Matrix (PCM) is optimized by eliminating short-girths and low weight code-words. Partially-parallel quasi-cyclic structure is adopted for the encoder and the check matrix is quasi diagonal line structure. Encoding process directly utilizes check matrix rather than generator matrix to generate check sequence. For decoding process, the (Forward Backward Extended Minimum Sum (FB-EMS) algorithm is adopted. The performance of the proposed Non-binary LDPC code over GF(16) shows more than 1dB coding gain at 10^(-6) BER compared to the traditional binary standard with same bit length for 802.11n standard. Encoder structure and decoder algorithm have been also presented. For practical purposes, this Non-binary quasi-cyclic LDPC code with low complexity makes our proposed system very attractive.
Low Density Parity Check Codes (LDPC) are a group of channel codes which can be decoded using a graph. LDPC codes are known to give near Shannon limit performance in Additive White Gaussian Channel (AWGN), but for large block-lengths and irregular construction. To overcome this limitation, it has been proposed to define codes over a higher order Galois Field. In this paper,we construct a regular cycle non binary LDPC code over GF(q), where q=2p.We use a Fast Fourier Transform (FFT) based low complexity algorithm to decode the LDPC code defined over a large Galois Field. We evaluate the performance of these codes in AWGN channel using computer simulations and show that they are giving excellent BER performance.
Non-binary LDPC (NB-LDPC) codes has inherent parallelism and excellent error correcting performance. By comparing with other traditional algorithm, FFT-SPA based non-binary LDPC code gives reduced computation complexity with better decoding performance. In this paper, FFT-SPA based NB-LDPC decoding performance is analyzed for the specification of IEEE 802.11n standard. Parity check matrix (PCM) defines the strength of the LDPC codes. By retaining the properties of the PCM structures, in this paper we propose two modified parity check matrices to reduce the computation strength. For various order of Galois Field with different PCM structures, non-binary LDPC codes performances are analyzed.
The non-binary LDPC is the promotion to the finite GF(q) of binary LDPC codes.The parity check matrix elements is no longer 0 and 1,but collections(0,1,2,…,q-1),while the decoding still uses the efficient iterative decoding based on belief propagation algorithm.This paper focuses on the check matrix of structure of the quasi-cyclic LDPC codes(QC-LDPC) as well as the min-sum decoding algorithm.Then the LDPC codes decoding performance is simulated under different conditions in white Gaussian noise channel(AWGN) with Matlab.Finally,the impact of non-binary LDPC Decoding performance factors is analyzed.
In order to implement efficient encoding,a class of nonbinary quasi-cyclic low-density parity-check(QC-LDPC) codes is proposed,which can be encoded with Richardson-Urbanke algorithm.The right part of the parity-check matrix has weight-2 columns,which allows the construction of both regular and irregular codes.Constraints on the parity-check matrix ensure a linear encoding complexity. Simulation results show that the proposed codes,when combined with higher order modulation,perform favorably with the codes constructed by the progressive-edge-growth(PEG) constructed code and close to the Shannon limits.