This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descenda...

The convergence rate of LDPC decoding is comparatively slower than turbo code decoding: 25 LDPC iterations versus 8-10 iterations for turbo codes. Recently, Mansour proposed a ‘turbo-schedule’ to improve the convergence rate of LDPC decoders. In this letter, we first extend the turbo-scheduling principle to the check messages. Second, we show analytically that the convergence rate of both turbo...

The performance of low-density parity-check (LDPC) codes serially concatenated with generalized partial response channels is investigated. Various soft-input/soft-output detection schemes suitable for use in iterative detection/decoding systems are described. A low-complexity near-optimal detection algorithm that incorporates soft-input reliability information and generates soft-output reliabil...

This paper considers the achievable rates and decoding complexity of low-density parity-check (LDPC) codes over statistically independent parallel channels. The paper starts with the derivation of bounds on the conditional entropy of the transmitted codeword given the received sequence at the output of the parallel channels; the component channels are considered to be memoryless, binary-input, ...

We describe a novel approach for designing lowdensity parity-check (LDPC) codes based on a particular class of very simple component codes, that are a generalization of single parity-check (SPC) codes. The proposed method allows the design of LDPC codes with good performance while requiring encoder circuits with easy implementation. In addition, the proposed technique permits us to obtain rate-...

The decoding of Low-Density Parity-Check (LDPC) codes is operated over a redundant structure known as the bipartite graph, meaning that the full set of bit nodes is not absolutely necessary for decoder convergence. In 2008, Soyjaudah and Catherine designed a recovery algorithm for LDPC codes based on this assumption and showed that the error-correcting performance of their codes outperformed co...

In general, encoding for LDPC codes can be difficult to realize efficiently. This paper presents techniques and architectures for LDPC encoding that are efficient and practical for a particular class of codes. These codes are the irregular partitioned permutation LDPC codes recently introduced by the author at ICC’03, [4]. Since these codes are quasi-cyclic, it is known that a simpler encoding ...

We present a systematic construction of a class of highrate, well-structured low density parity check (LDPC) codes based on combinatorial designs. We show that the proposed -design results in a class of -regular LDPC codes, which are systematic, quasicyclic, free of length-4 and length-6 cycles, linear-time encodable and decodable, and which have high code rates of . Analysis from the maximum l...

This paper attempts to examine the optimality of LDPC codes for compression of nonuniform source with Slepian-Wolf coding using density evolution technique. The primary goal is to evaluate the performance of LDPC codes with reference to turbo codes (in SF-ISF setup). The appreciable difference between LDPC and turbo codes is also discussed in this paper. The threshold values obtained from the d...