Low-density parity-check (LDPC) code is linear-block error-correcting code defined by sparse parity-check matrix. It is decoded using the massage-passing algorithm, and in many cases, capable of outperforming turbo code. This paper presents a class of low-density parity-check (LDPC) codes showing good performance with low encoding complexity. The code is constructed using difference families fr...

In this work we present a practical approach to the iterative decoding of Reed-Solomon (RS) codes. The presented methodology utilizes an architecture in which the output produced by steps of Belief-Propagation (BP) is successively applied to a legacy decoding algorithm. Due to the suboptimal performance of BP conducted on the inherently dense RS parity-check matrix, a method is first provided f...

Let q denote the finite field GF (q) and let b be a positive integer. MDS codes over the symbol alphabet b q are considered that are linear over q and have sparse (“low-density”) parity-check and generator matrices over q that are systematic over bq . Lower bounds are presented on the number of nonzero elements in any systematic parity-check or generator matrix of an q-linear MDS code over bq, ...

In this paper, we conclude five kinds of methods for construction the regular low-density parity matrix H and three irregular parity-check H. Through analysis code rate parameters these eight structures, find that tends to be more flexible parameter variability is enhanced. We propose current development cost should lower with progress electronic technology need research on practical Low-Densit...

In this paper, we propose a novel low-density parity-check real-number code, based on compressed sensing. A real-valued message is encoded by a coding matrix (with more rows than columns) and transmitted over an erroneous channel, where sparse errors (impulsive noise) corrupt the codeword. In the decoding procedure, we apply a structured sparse (low-density) parity-check matrix, the Permuted Bl...

In this paper a new construction of MDS array codes is introduced. In order to obtain a code with this property, the parity-check matrix is constructed just using a superregular matrix by blocks composed by powers of the companion matrix of a primitive polynomial. Also a decoding algorithm for these codes is introduced.

Two new iterative soft decision decoding methods for Reed-Solomon (RS) codes are proposed. These methods are based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In the first propos...

This paper describes a method for packet synchronization and error detection for use in a synchronous digital communications system. The method relies upon a class of linear block codes that have parity checks that are expressed in terms of a finite-impulse response (FIR) filter. This system is incorporated in the newly established ITU standard of digital cable television standard, J.83 appendi...