Product accumulate codes are a special case of differentially coded low density parity check (LDPC) codes. This work analyzes the noncoherent performance of PA codes and general differentially-coded LDPC codes on flat Rayleigh fading channels using extrinsic information transfer charts, and proposes a convergence-constraint method to design good LDPC ensembles matched to differential coding.

Aiming at seeking a low complexity decoder of the low-density parity-check (LDPC) codes, we present one modified multi-bit flipping (MMBF) algorithm. For those LDPC codes whose parity check matrices have light column weight, both the bootstrap step and a novel delay-handling step are included in MMBF, based on one framework which is the combination of conventional PWBF and IWBF. On the other ha...

This paper proposes an improved new structure of Single Parity Check (SPC) product codes with an embedded interleaver. The complexity of decoding the new SPC product codes is the same as the one of the existing single parity check product codes by use of the message passing algorithm. Simulation results and bound analysis demonstrate a significant bite error rate (BER) performance improvement c...

We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of one’s of the parity-check matrix of the codes presented is typically higher than the number of one’s of the parity-check matrix of low-density paritycheck (LDPC) codes. But, still lower than those of the parity-check matrix of classical block c...

An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding based on linear programming, crucially depend on the efficient representation of a code in a graphical model. In order to understand the performance of these alg...

A code symbol of a linear code is said to have locality r if this symbol could be recovered by at most r other code symbols. An (n, k, r) locally repairable code (LRC) with all symbol locality is a linear code with length n, dimension k, and locality r for all symbols. Recently, there are lots of studies on the bounds and constructions of LRCs, most of which are essentially based on the generat...

The problem of fast evaluation of a matrix-vector product over GF (2) is considered. The problem is reduced to erasure decoding of a linear error-correcting code. A large set of redundant parity check equations for this code is generated. The multiplication algorithm is derived by tracking the execution of the message-passing algorithm on the obtained set of parity check equations. The obtained...

In this correspondence, low-density parity-check (LDPC) codes are applied to lossy source coding and we study how the asymptotic performance of MacKay’s LDPC codes depends on the sparsity of the parity-check matrices in the source coding of the binary independent and identically distributed (i.i.d.) source with Pr = 1 = 0 5. In the sequel, it is shown that an LDPC code with column weight (log )...

Low-density parity check codes (LDPC codes) were introduced by Gallager [2] and have received intensive study in the last few years, as advances in technology have made their implementation far more practical than when they were originally proposed. Basically, an LDPC code is a binary linear block code defined by a sparse m × n parity-check matrix H . Equivalently such a code can be thought of ...

We introduce a class of iteratively decodable trellis-constrained codes as a generalization of turbocodes, low-density parity-check codes, serially-concatenated con-volutional codes, and product codes. In a trellis-constrained code, multiple trellises interact to deene the allowed set of codewords. As a result of these interactions, the minimum-complexity single trellis for the code can have a ...