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International Conference on e-Technologies and Networks for Development (ICeND)

Decoding of short non-binary LDPC codes using a non iterative decoding algorithm

Mahmoud El Kobi, Mohamad Zein, Ali Chamas Al Ghouwayel, Hussein Hijazi

Published Apr 1, 2014• 0 citations
Publisher

Abstract

In this paper, we investigate the decoding of short Non-Binary (NB)-LDPC codes of rate 1/2 using a non-iterative approach based on the Maximum-Likelihood (ML) principle. The traditional decoding algorithms used to decode the NB-LDPC codes are by nature iterative where the Variables Nodes (VN) and Check Nodes (CN) exchange data iteratively during, at least, eight iterations which imposes a long decoding time to achieve good performance in terms of Frame Error Rate (FER). In this paper we propose a decoding algorithm based on the Maximum Likelihood (ML) search named Near ML approach where the number of tested words considered as potential codewords is highly reduced. Simulation of codes of lengths 16 and 48 are presented and the results show that the proposed algorithm achieves the performance offered by the EMS algorithm. The NB-LDPC of length 16 is shown to outperform the EMS algorithm.

DOI
10.1109/icend.2014.6991187

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•May 31, 2014•0 citations
In this paper, we investigate the decoding of short Non-Binary (NB)-LDPC codes of rate 1/2 using a non-iterative approach based on the Maximum-Likelihood (ML) principle. The traditional decoding algorithms used to decode the NB-LDPC codes are by nature iterative where the Variables Nodes (VN) and Check Nodes (CN) exchange data iteratively during, at least, eight iterations which imposes a long decoding time to achieve good performance in terms of Frame Error Rate (FER). In this paper we propose a decoding algorithm based on the Maximum Likelihood (ML) search named Near ML approach where the number of tested words considered as potential codewords is highly reduced. Simulation of codes of lengths 16 and 48 are presented and the results show that the proposed algorithm achieves the performance offered by the EMS algorithm. The NB-LDPC of length 16 is shown to outperform the EMS algorithm.
This paper investigates the decoding of rate 1/2 Non-Binary LDPC codes using a non-iterative approach based on the Maximum-Likelihood (ML) principle. The iterative decoding approach based on the well known Extended-Min-Sum (EMS) algorithm, considered as the most efficient decoding algorithm to decode NB-LDPC codes, executes the decoding process iteratively. The main operations of this algorithm are the variable and check node updates which are performed at least eight times requiring a long decoding time to achieve good performance in terms of Frame Error Rate (FER). The proposed decoding near ML approach is based on ML search where the number of candidates is highly reduced using a technique privileging the most reliable and nearest codewords. Simulation results show that the proposed algorithm achieves, at a reduced list of 5 searched candidates in average at 3 dB, the performance offered by the EMS algorithm. We also show that by slightly increasing the list of candidates, the proposed algorithm outperforms the EMS algorithm.
Non-binary low-density parity-check (NB-LDPC) codes are an extension of binary LDPC codes with significantly better performance when the code length is moderate. Previously, forward-backward schemes are used to implement check node processing, which need large memory. In this paper, a novel approach is proposed for EMS NB-LDPC decoding. Compared to EMS decoding algorithm, the message memory and the average number of iterations have been reduced. Also, the overall decoder architecture is proposed.
Non-binary low-density parity-check (NB-LDPC) codes are an extension of binary LDPC codes with significantly better performance when the code length is moderate. Previously, forward-backward schemes are used to implement check node processing, which need large amount of memory. In this paper, a novel approach-TCL-EMS is proposed for NB-LDPC decoding. Compared to original EMS decoding algorithm, the memory efficiency is improved and the average number of iterations is reduced significantly. Also, the overall decoder architecture is proposed.
Error correcting coding has become one essential part in nearly all the modern data transmission and storage systems.Low density parity check (LDPC) codes are a class of linear block code has the superior performance closer to the Shannon's limit.In this paper two error correcting codes from the family of LDPC codes specifically Euclidean Geometry Low Density Parity Check (EG-LDPC) codes and Nonbinary low density parity check (NB-LDPC) codes are compared in terms of power consumption, number of iterations and other parameters.For better performance of EG-LDPC codes, Maximum Likelihood (ML) Algorithm was proposed.NB-LDPC codes can provide better error correcting performance with an average of 10 to 30 iterations but has high decoding complexity which can be improve by EG-LDPC codes with ML algorithm having only three iterations for detecting and correcting errors.One step majority logic decodable (MLD) codes is a subclass of EG-LDPC codes are used to avoid high decoding complexity.The power Consumed by NB-LDPC codes is 2.729W whereas the power consumed by EG-LDPC codes with ML algorithm is 1.148W.
This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.
ABSTRACT Error correcting coding has become one essential part in nearly all the modern data transmission and storage systems. Low density parity check (LDPC) codes are a class of linear block code has the superior performance closer to the Shannon’s limit. In this paper two error correcting codes from the family of LDPC codes specifically Euclidean Geometry Low Density Parity Check (EG-LDPC) codes and Nonbinary low density parity check (NB-LDPC) codes are compared in terms of power consumption, number of iterations and other parameters. For better performance of EG-LDPC codes, Maximum Likelihood (ML) Algorithm was proposed. NB-LDPC codes can provide better error correcting performance with an average of 10 to 30 iterations but has high decoding complexity which can be improve by EG-LDPC codes with ML algorithm having only three iterations for detecting and correcting errors. One step majority logic decodable (MLD) codes is a subclass of EG-LDPC codes are used to avoid high decoding complexity. The power Consumed by NB-LDPC codes is 2.729W whereas the power consumed by EG-LDPC codes with ML algorithm is 1.148W. KEYWORDS Euclidean Geometry - Low Density Parity Check code, Maximum Likelihood Algorithm, Non Binary - Low Density Parity Check Code.