Spatial coupling of individual LDPC codes improves the BP threshold of the coupled ensemble to the MAP threshold of the underlying ensemble. In this report, we investigate the performance of spatial coupling on LDGM codes which might lead to constructing a new class of rateless codes. In what follows, we study Raptor codes as a class of rateless codes and investigate spatial coupling on LDPC en...

It is shown that some well-known and some new cyclic codes with orthogonal parity-check equations can be constructed in the finite-field transform domain. It is also shown that, for some binary linear cyclic codes, the performance of the iterative decoder can be improved by substituting some of the dual code codewords in the parity-check matrix with other dual code codewords formed from linear ...

Low-Density Parity-Check (LDPC) code is one kind of prominent error correcting codes (ECC) being considered in next generation industry standards. The decoder implementation complexity has been the bottleneck of its application. This paper presents an implementation of Quasi-Cyclic Low-Density Parity-Check decoder by using FPGA. Modified Min-Sum decoding algorithm is applied to reduce the memor...

A statistical theory of turbo-codes, treated as a special family of convolutional codes with a low-density parity-check matrix, is developed. The basic ideas are: the representation of the transposed parity-check matrix of turbo-codes as a product of a sparse (multiple) scrambler matrix and the transposed parity-check matrix of the basic code, the introduction of a special statistical ensemble ...

This paper presents high-performance encoder and decoder architectures for a class of Low Density Parity Check (LDPC) codes. The codes considered here are based on the Parallelly Concatenated Parity Check encoder structure. A major advantage of these codes is that the generator matrix and the parity check matrix are both sparse, which leads to efficient VLSI implementations for the encoder and ...

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...

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...

We investigate two techniques for reducing the error-floor of low-density parity-check codes under iterative decoding. Both techniques are developed based on comprehensive analytical and simulation studies of combinatorial properties of trapping sets in codes on graphs. The first technique represents an algorithmic modification of beliefpropagation based on data fusion principles and specialize...

Let q denote the finite field GF (q) and let b be a positive integer. MDS codes over the symbol alphabet b q are considered that are linear over q and have sparse (“low-density”) parity-check and generator matrices over q that are systematic over bq . Lower bounds are presented on the number of nonzero elements in any systematic parity-check or generator matrix of an q-linear MDS code over bq, ...