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 paper presents for the first time automatic module acquisition and evolution within the graph based Cartesian Genetic Programming method. The method has been tested on a set of even parity problems and compared with Cartesian Genetic Programming without modules. Results are given that show that the new modular method evolves solutions up to 20 times quicker than the original non-modular met...

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...

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 work we study codes characterized by the property that their parity check matrix is circulant, i.e., that rows are obtained as all the distinct cyclic shifts of the rst row. For these codes, we give simple expressions for their dimension and for a lower bound on their minimum distance. We also present an O(nd) algorithm to solve the problem of deciding whether codes satisfying given con...

We construct the relationship between nonrenormalizable, effective , time-reversal violating (TV) parity-conserving (PC) interactions of quarks and gauge bosons and various low-energy TVPC and TV parity-violating (PV) observables. Using effective field theory methods , we delineate the scenarious under which experimental limits on permanent electric dipole moments (EDM's) of the electron, neutr...

Heterogeneity of (co)variances for US Jersey linear and final scores was investigated with data from February 2000 USDA genetic evaluations. (Co)variances were estimated from datasets defined by parity, contemporary group size, and mean final score. First-appraisal scores during first or second parity from records that included all traits were studied. Contemporary groups within each parity wer...

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...