In this paper the low density party check (LDPC) codes used in the IEEE 802.16 standard physical layer are studied, and two novel techniques to enhance the performance of such codes are introduced. In the first technique, a novel parity check matrix for LDPC codes over GF(4) with the non-zero entries chosen to maximize the entropy is proposed, the parity check matrix is based on the binary pari...

In this paper, we consider how to partition the parity-check matrices (PCMs) reduce hardware complexity and increase decoding throughput for row layered of quasi-cyclic low-density (QC-LDPC) codes. First, formulate PCM partitioning as an optimization problem, which targets minimize maximum column weight each layer while maintaining a block cyclic shift property among different layers. As result...

In this paper, a method to design regular (2, dc)LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping ...

We use Cayley graphs to construct several dual-containing codes, all of which have sparse graphs. These codes’ properties are promising compared to other quantum error-correcting codes. This paper builds on the ideas of the earlier paper Sparse-Graph Codes for Quantum ErrorCorrection (quant-ph/0304161), which the reader is encouraged to refer to. To recap: Our aim is to make classical error-cor...

We investigate how sensitive Gallager’s codes are, when decoded by the sum-product algorithm, to the assumed noise level. We have found a remarkably simple function that fits the empirical results as a function of the actual noise level at both high and low noise levels. A linear code may be described in terms of a generator matrix G or in terms of a parity check matrix H, which satisfies Hx = ...

We report the empirical performance of Gallager's low density parity check codes on Gaus-sian channels. We show that performance substantially better than that of standard convolu-tional and concatenated codes can be achieved; indeed the performance is almost as close to the Shannon limit as that of Turbo codes. A linear code may be described in terms of a generator matrix G or in terms of a pa...

Spatially coupled low-density parity-check (LDPC) codes have attracted considerable attention due to their promising performance. Recursive encoding of the codes with low delay and low complexity has been proposed in the literature but with constraints or restrictions. In this manuscript we propose an efficient method to construct parity-check matrices for recursively encoding spatially coupled...

The subject of this paper is transmission over a general class of binary-input memoryless symmetric channels using error correcting codes based on sparse graphs, namely low-density generator-matrix and low-density parity-check codes. The optimal (or ideal) decoder based on the posterior measure over the code bits, and its relationship to the sub-optimal belief propagation decoder, are investiga...

This paper investigates decoding of binary linear block codes over the binary erasure channel (BEC). Of the current iterative decoding algorithms on this channel, we review the Recovery Algorithm and the Guess Algorithm. We then present a Multi-Guess Algorithm extended from the Guess Algorithm and a new algorithm – the In-place Algorithm. The Multi-Guess Algorithm can push the limit to break th...

An improved Quasi Cyclic Low Density Parity Check code (QC-LDPC) is proposed to reduce the complexity of the Low Density Parity Check code (LDPC) while obtaining the similar performance. The proposed QC-LDPC presents an improved construction at high SNR with circulant sub-matrices. The proposed construction yields a performance gain of about 1 dB at a 0.0003 bit error rate (BER) and it is teste...