Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

PERFORMANCE COMPARISON OF EG-LDPC CODES WITH MAXIMUM LIKELIHOOD ALGORITHM OVER NON-BINARY LDPC CODES

M.Sakthivel, M.Karthick Raja, KR.Ragupathy, K. Sathis Kumar

Published May 31, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.3517938

Related papers

Performance Comparison of Eg-Ldpc Codes With Maximum Likelihood Algorithm Over Non-Binary Ldpc Codes

M. Sakthivel, M. Karthick Raja, KR.Ragupathy +1 more

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.

International Journal of Computational Science and Information Technology•May 30, 2014•1 citation

E-IHRB Decoder Architectures for Non-Binary LDPC Codes

Madamsetti, Kalyani, M, Suseela

In the information theory , the non- binary low density parity check  (NB-LDPC) code is a  linear error correcting code , a method of transmitting message over a  noisy transmission channel. LDPCcodes are  capacity-approaching codes , which  means  that  practical constructions exist  that allow the noise threshold to be set very close to the theoretical maximum for a symmetric memory less channel.Using iterative  belief propagation techniques, NB-LDPC codes can be decoded in time linear to their block length. Non-binary low-density parity-check codes can achieve higher performance than their binary counterparts. Recently, two algorithms were developed for decoding NB-LDPC codes: iterative hard reliability-based majority-logic decoding (IHRB-MLGD) and iterative soft reliability-based majority-logic decoding (ISRB-MLGD has better performance-complexity tradeoffs than previous algorithms. This paper first proposes message-passing in such a way that we can reduce the memory consumption to a greater extent at the same time there should not be performance loss. By using enhanced iterative reliability-based majority-logic decoding algorithms we can achieve effective complexity-performance and noise free design. Compared to previous designs, our proposed decoders have at least tens of times lower complexity with moderate coding gain loss.

•Aug 31, 2014•0 citations

Iterative majority logic decoding of a class of Euclidean Geometry codes

Andrew Thangaraj, S.W. McLaughlin

Hard decision decoding of low density parity check (LDPC) codes has potential applications in practical settings like data storage. For this purpose, it is important for the code to have an assured minimum distance and, hence, guaranteed error correction capability. In this paper, we show that with very high probability the guaranteed error correction capability of Euclidean geometry (EG) codes using threshold-optimized, iterative majority logic (ML) decoding is much greater than the usual single iteration ML decoding, making these codes much more attractive for hard decision decoding. For instance, the (262143, 242461, t/spl ges/256) EG code (a (512, 512)-regular LDPC code) can correct t=580 bit errors with probability better than 1-1/spl times/10/sup -58/.

IEEE International Symposium on Information Theory (ISIT)•Jun 25, 2003•1 citation

On Decoding of Low-Density Parity-Check Codes Over the Binary Erasure Channel

Hossein Pishro-Nik, Faramarz Fekri

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.

IEEE Transactions on Information Theory•Mar 1, 2004•147 citations

LDPC Codes Over the BEC: Bounds and Decoding Algorithms

Irina E. Bocharova, Boris D. Kudryashov, Vitaly Skachek +2 more

The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average weight spectrum is presented. For LDPC codes from the Gallager ensemble and the Richardson-Urbanke ensemble, new upper bounds on the ML decoding performance based on computing the rank of submatrices of the code parity-check matrix are derived. A new lower bound on the ML decoding threshold followed from the latter error probability bound is obtained. An improved lower bound on the error probability for codes with a known estimate on the minimum distance is presented as well. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the simulated belief propagation and ML decoding performance and simulated performance of the best known improved iterative decoding techniques, as well as, with the derived upper bounds on the ML decoding performance and with decoding thresholds obtained by the density evolution technique.

IEEE Transactions on Communications•Nov 6, 2018•5 citations

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

Mahmoud El Kobi, Mohamad Zein, Ali Chamas Al Ghouwayel +1 more

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.

International Conference on e-Technologies and Networks for Development (ICeND)•Apr 1, 2014•0 citations
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.
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.
In the information theory , the non- binary low density parity check  (NB-LDPC) code is a  linear error correcting code , a method of transmitting message over a  noisy transmission channel. LDPCcodes are  capacity-approaching codes , which  means  that  practical constructions exist  that allow the noise threshold to be set very close to the theoretical maximum for a symmetric memory less channel.Using iterative  belief propagation techniques, NB-LDPC codes can be decoded in time linear to their block length. Non-binary low-density parity-check codes can achieve higher performance than their binary counterparts. Recently, two algorithms were developed for decoding NB-LDPC codes: iterative hard reliability-based majority-logic decoding (IHRB-MLGD) and iterative soft reliability-based majority-logic decoding (ISRB-MLGD has better performance-complexity tradeoffs than previous algorithms. This paper first proposes message-passing in such a way that we can reduce the memory consumption to a greater extent at the same time there should not be performance loss. By using enhanced iterative reliability-based majority-logic decoding algorithms we can achieve effective complexity-performance and noise free design. Compared to previous designs, our proposed decoders have at least tens of times lower complexity with moderate coding gain loss.
Hard decision decoding of low density parity check (LDPC) codes has potential applications in practical settings like data storage. For this purpose, it is important for the code to have an assured minimum distance and, hence, guaranteed error correction capability. In this paper, we show that with very high probability the guaranteed error correction capability of Euclidean geometry (EG) codes using threshold-optimized, iterative majority logic (ML) decoding is much greater than the usual single iteration ML decoding, making these codes much more attractive for hard decision decoding. For instance, the (262143, 242461, t/spl ges/256) EG code (a (512, 512)-regular LDPC code) can correct t=580 bit errors with probability better than 1-1/spl times/10/sup -58/.
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.
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average weight spectrum is presented. For LDPC codes from the Gallager ensemble and the Richardson-Urbanke ensemble, new upper bounds on the ML decoding performance based on computing the rank of submatrices of the code parity-check matrix are derived. A new lower bound on the ML decoding threshold followed from the latter error probability bound is obtained. An improved lower bound on the error probability for codes with a known estimate on the minimum distance is presented as well. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the simulated belief propagation and ML decoding performance and simulated performance of the best known improved iterative decoding techniques, as well as, with the derived upper bounds on the ML decoding performance and with decoding thresholds obtained by the density evolution technique.
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.