IEEE International Symposium on Information Theory (ISIT)

Iterative majority logic decoding of a class of Euclidean Geometry codes

Andrew Thangaraj, S.W. McLaughlin

Published Jun 25, 2003• 1 citation

Abstract

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/.

DOI: 10.1109/isit.2002.1023637

Related papers

Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and More

Yu Kou, Shu Lin, M.P.C. Fossorier

Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.

Oct 20, 199989 citations

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

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

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.

May 31, 20140 citations

An Efficient Majority Error Detection in Logic Decoding with Euclidean Geometry Low Density Parity Check (Eg-Ldpc) Codes

M .Vengadapathiraj Mr, U. Maheswaran, A.Karunakaran Mr

In a recent article, a technique was proposed to step up the majority logic decoding of variation set low density parity check codes. This is helpful as majority logic decoding can be implemented serially with trouble-free hardware but requires a huge decoding time. The method detect whether a word has errors in the initial iterations of majority logic decoding, and at what time there are no errors the decoding split ends without completing the rest of the iterations. While the majority words in a memory will be error-free, the average decoding time is significantly reduced. The outcome obtained proves that the technique is also effective for EG-LDPC codes. General simulation results are given to precisely estimate the prospect of error detection for different code sizes and numbers of errors.

International Journal of Business IntelligentsJun 11, 20190 citations

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 TechnologyMay 30, 20141 citation

On the Hard-Decision Multi-Threshold Decoding of Binary and Non-Binary LDPC Codes

Andrei Dzis, Pavel S. Rybin, Alexey Frolov

In this paper, we investigate the effect of single and multiple thresholds approaches applied to iterative hard-decision decoders for binary and non-binary low-density parity-check (LDPC) codes in terms of error correction and managed to optimize the performance of decoding algorithms for these codes.

International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY)Oct 1, 20190 citations

Computation of Parity Check Matrices for Binary EG-LDPC Codes used in Communication Systems

Jyothi Chinna Babu, C. Chinnapu Reddy

The Low Density Parity Check (LDPC) are direct codes, which are true block and Shannon Limit codes.These codes are attained least error floors of data bits for data transfer applications used in communication systems.However, the proposed LDPC codes are more beneficial than Turbo codes because of reduction in the decoding complexity and detection of the errors in less cycle time.This results the reduction of decoding time, low decoding latency, complexity and as well as least error floorings in communication, when the transmitted data contains multiple error bits.This paper is proposed to represent the majority logic decoding/detecting of LDPC codes.This paper proposes the Generation of Originator and Parity estimated matrices for the Binary LDPC Codes.Here, the proposed techniques are hard decision decrypting and soft decision decrypting schemes.These schemes uses majority logic decoding based on the data transmission and reception in communication channel.This paper also elaborates the effective calculation of Euclidean distance and algorithm for constructing the LDPC codes.

HelixFeb 28, 20190 citations