In this paper we investigate the minimum code distance of QC LDPC codes [1], [2], [3]. These codes form an important subclass of LDPC codes [4], [5]. These codes also are a subclass of protograph-based LDPC codes [6]. QC LDPC codes can be easily stored as their parity-check matrices can be easily described. Besides such codes have efficient encoding [7] and decoding [8] algorithms. All of these...

The concepts of pseudocodeword and pseudoweight play a fundamental role in the finitelength analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding minimum pseudoweight equals its minimum Hamming distance. By using the value assignment of Chen and Kløve we present new results on the pseudo...

We study a modification method for constructing lowdensity parity-check (LDPC) codes for solid burst erasures. Our proposed modification method is based on a column permutation technique for a parity-check matrix of the original LDPC codes. It can change the burst erasure correction capabilities without degradation in the performance over random erasure channels. We show by simulation results t...

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...

This work applies earlier results on Quasi-Cyclic (QC) LDPC codes to the codes specified in six separate IEEE 802 standards, specifying wireless communications from 54 MHz to 60 GHz. First, we examine the weight matrices specified to upper bound the codes’ minimum distance independent of block length. Next, we search for the minimum distance achieved for the parity check matrices selected at ea...

The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes—characterised by admitting a sparse parity check matrix—with good correction capabilities. In the present paper the orbits of subspaces of a finite projectiv...

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...

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...

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...