the paper presents lower and upper bounds on the number of parity check digits required for a linear code that detects solid bursts of length $b$ or less and simultaneously any $e$ or less random errors. an example of such a code is also provided. further, codes capable of detecting and simultaneously correcting such errors have also been dealt with.

1) Introduction Iterative decoding offers a practical way for implementing LDPC codes. LDPC code is defined by a sparse MxN parity check matrix H that has 0 entries everywhere except for t c 1’s in each column and t r 1’s in each row, where t c and t r are small numbers and they degrees. Irregular LDPC codes have varying number of t c and t r . An LDPC code can be represented by bipartite graph...

An algebraic group ring method for constructing codes with no short cycles in the check matrix is derived. It is shown that the matrix of a group ring element has no short cycles if and only if the collection of group differences of this element has no repeats. When applied to elements in the group ring with small support this gives a general method for constructing and analysing low density pa...

In this paper, we investigate an efficient encoding approach for generalized low-density (GLD) parity check codes, a generalization of Gallager’s low-density parity check (LDPC) codes. We propose a systematic approach to construct approximate upper triangular GLD parity check matrix which defines a class of efficientencoding GLD codes. It’s shown that such GLD codes have equally good performanc...

This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from difference covering arrays. While the original construction by Gallagher was by randomly allocating bits in a sparse parity-check matrix, over the past 20 years researchers have used a variety of more structured approaches to construct these codes, with the more recent constructions of well-structured...

In this letter, we propose an appealing class of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) cycle codes. The parity-check matrix is carefully designed such that the corresponding generator matrix has some nice properties: 1) systematic, 2) quasi-cyclic, and 3) sparse, which allows a parallel encoding with low complexity. Simulation results show that the performance of the propose...

A) , (L J regular QC-LDPC code of length N is defined by a parity-check matrix L L p I p I p I p I p I p I p I p I p I H     (1) where 1 1    J j , 1 1    L l and   l j p I , represents the p p  circulant permutation matrix obtained by cyclically right-shifting the p p  identity matrix   0 I by l j p , positions, with. / L N p  For a specific QC-LDPC code we define the correspo...

Amongst the contributions to the theory of LDPC codes deriving from finite geometries ([13], [12], [9]), we present a study of the code C which has as parity-check matrix H the incidence matrix of the Hermitian curve of PG(2, q) and the q + 1-secant to it. The good performance of C with iterative decoding algorithm is showed by Johnson and Weller in [11]. In this paper we prove the ”double” cyc...

Gallager introduced LDPC codes in 1962, presenting a construction method to randomly allocate bits in a sparse parity-check matrix subject to constraints on the row and column weights. Since then improvements have been made to Gallager’s construction method and some analytic constructions for LDPC codes have recently been presented. However, analytically constructed LDPC codes comprise only a v...

This article explains the design and implementation of both regular and irregular LDPC codes as carried out by me at the Institute of Communications Engineering, Technical University of Munich. The design of a good irregular LDPC code needs a pair of distributions to be specified. This article discusses a randomized construction which attempts to form a parity check matrix whose row and coloumn...