This paper presents a construction of low-density parity-check (LDPC) codes based on the incidence matrices of oval designs. The new LDPC codes have regular parity-check matrices and Tanner graphs free of 4-cycles. Like the finite geometry codes, the codes from oval designs have parity-check matrices with a large proportion of linearly dependent rows and can achieve significantly better minimum...

Forward error correction codes (FEC) are used for error detection and correction in communication systems. Low density parity check code (LDPC) is used as a powerful Forward Error Correction code in long distance communication systems which works close to the Shannon limit. Unlike other conventional channel code, the decoding algorithm used for LDPC codes is an iterative message passing algorit...

We design sequences of low-density parity check codes that provably perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on 1]. Additionally, based on the assumption that the underlying communication channel is symmetric, we prove th...

This paper develops a general theory for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes (EAQECCs) with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error corre...

This paper extends the class of low-density paritycheck (LDPC) codes that can be algebraically constructed. We present regular LDPC codes based on resolvable Steiner 2-designs which have Tanner graphs free of four-cycles. The resulting codes are -regular or -regular for any value of and for a flexible choice of code lengths.

Low-density parity-check (LDPC) codes were introduced in 1962, but were almost forgotten. The introduction of turbo-codes in 1993 was a real breakthrough in communication theory and practice, due to their practical effectiveness. Subsequently, the connections between LDPC and turbo codes were considered, and it was shown that the latter can be described in the framework of LDPC codes. In recent...

Genetic algorithms are successfully used for decoding some classes of error correcting codes, and offer very good performances for solving large optimization problems. This article proposes a new decoder based on Serial Genetic Algorithm Decoder (SGAD) for decoding Low Density Parity Check (LDPC) codes. The results show that the proposed algorithm gives large gains over sum-product decoder, whi...

In this paper, we derive the maximum likelihood (ML) performance for low-density parity check (LDPC) codes, considering BPSK and QPSK transmission over a Gaussian channel. We compare the theoretical ML performance with the performance of the iterative decoding algorithm. It turns out that the performance of the iterative decoding algorithm is close to the ML performance when the girth of the co...

In this paper we prove two results related to low-density parity-check (LDPC) codes. The first is to show that the generating function attached to the pseudo-codewords of an LDPC code is a rational function, answering a question raised in [6]. The combinatorial information of its numerator and denominator is also discussed. The second concerns an infinite family of q-regular bipartite graphs wi...