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IEEE International Conference on Computer and Communications (ICCC)

Performance comparison of non-binary RA and QC-LDPC codes

Wenli Ni, Jing He

Published Oct 1, 2016• 1 citation
Publisher

Abstract

Repeat Accumulate (RA) codes are subclass of low-density parity-check (LDPC) codes with fast encoder structures. QC-LDPC codes are also a class of LDPC codes and easy to be implemented. There were some paper had researched that non-binary LDPC codes have better performance cover binary ones. In this paper, It constructed non-binary RA codes with linear encoding method and non-binary QC-LDPC codes with algebraic constructions method. The BER performance of RA and QC-LDPC codes over GF(q) were compared by simulation over the Additive White Gaussian Noise (AWGN) channels. The simulation results concluded when code length and code rate are same, the BER performance of this two non-binary LDPC codes are very close, but they still have a little different point.

DOI
10.1109/compcomm.2016.7924699

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Repeat Accumulate (RA) codes are subclass of low-density parity-check (LDPC) codes with fast encoder structures. QC-LDPC codes are also a class of LDPC codes and easy to be implemented. There were some paper had researched that non-binary LDPC codes have better performance cover binary ones. In this paper, It constructed non-binary RA codes with linear encoding method and non-binary QC-LDPC codes with algebraic constructions method. The BER performance of RA and QC-LDPC codes over GF(q) were compared by simulation over the Additive White Gaussian Noise (AWGN) channels. The simulation results concluded when code length and code rate are same, the BER performance of this two non-binary LDPC codes are very close, but they still have a little different point.
Low-density parity check (LDPC) codes are known to perform well in the presence of additive white Gaussian noise (AWGN) but for very large block lengths. It has been proposed to define the codes over high order Galois fields to overcome this limitation. In this paper we construct new quasi-cyclic non-binary LDPC codes with moderate code lengths from Reed-Solomon codes with two message symbols proposed by Lin et al defined over large finite fields. We evaluate the performance of these codes on the AWGN channel by computer simulation and show that they outperform binary LDPC codes of the same length in binary bits.
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.
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.
In this paper, we proposed a novel method for constructing quasi-cyclic low-density parity-check (QC LDPC) codes based on cyclic subgroup over GF(q) . LDPC codes constructed by this method are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN) with sum product algorithm (SPA). The main advantage is that QC LDPC codes with a variety of block lengths and rates can be easily constructed with no cycles of length four or less. Simulation results show that the proposed QC LDPC codes perform slight better than the random regular LDPC codes for short to moderate block lengths. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.
Low Density Parity Check (LDPC) codes are one of the block coding techniques that can approach the Shannon’s limit within a fraction of a decibel for high block lengths. In many digital communication systems these codes have strong competitors of turbo codes for error control. LDPC codes performance depends on the excellent design of parity check matrix and many diverse research methods have been used by different study groups to evaluate the performance. In this research work finite fields construction method is used and diverse techniques like masking, dispersion and array dispersion for the construction of parity check matrix H. These constructed codes are then simulated to make the performance evaluation. The key interest of this research work was to inspect the performance of LDPC codes based on finite fields. A comprehensive masking technique was also an objective of this research work. Simulation was done for different rates using additive white Gaussian noise (AWGN) channel. In MATLAB a library of different functions was created to perform the task for base matrix construction, dispersion, masking, generator matrix construction etc. Results give an idea that even at BER of 10-6 these short length LDPC codes performed much better and have no error floor. BER curves are also with 2-3dB from Shannon’s limit at BER of 10-6 for different rates.
This paper is concerned with the construction of a class of nonbinary irregular repeat accumulate (IRA) codes. Since they are defined on the finite field GF(q) (q>2), we will refer to the constructed codes as q-ary IRA (QIRA) codes. While preserving the excellent error correcting capability of q-ary LDPC codes, QIRA codes can be efficiently encoded like conventional binary IRA codes. By adopting the progressive edge growth (PEG) algorithm to construct the parity check matrices, we can achieve the increased girth of their factor graphs and improved decoding performance. Simulation results show that, using the sum-product algorithm on GF(q), QIRA codes outperform binary LDPC codes and turbo codes in terms of bit error ratio and frame error ratio on AWGN channels. Especially, they could achieve excellent error performance when combined with high order modulations. Feasibility study indicates, with the use of the extended min-sum (EMS) decoding algorithm, QIRA codes are competitive candidates for practical applications.