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.

OF THE THESIS Properties of LDGM-LDPC codes With Applications to Secrecy Coding by Manik Raina Thesis Directors: Professor Predrag Spasojević The ensemble of low-density generator-matrix/low-density parity-check (LDGM-LDPC) codes has been proposed in literature. In this thesis, an irregular LDGM-LDPC code is studied as a sub-code of an LDPC code with some randomly punctured outputbits. It is sh...

Error-correcting codes have contributed in a significant way for both the theoretical referred to as random errors, or else errors can appear in bursts of many errors each It was shown that long LDPC codes with iterative decoding achieve. LDPC codes provide good random error performance nearer to Shannon limit. iterations such errors can be corrected by concatenating LDPC codes with RS codes. b...

This paper introduces three new classes of structured regular (n, 2, k) LDPC codes with girth 12, 16, and 20, respectively. These codes are systematically constructed, well structured, and have uniform row and column weights, which make them able to greatly simplify the implementation of LDPC coders. Their large girth improves their decoding performance. Simulation results compare their bit err...

In this paper, we suggest a new technique for LDPC parity-check matrix (H-matrix) generation and a corresponding decoding process. The key idea is to construct LDPC H-matrix by using a convolutional encoder. It is easy to have many different coderates from a mother code with convolutional codes. However, it is difficult to have many different coderates with LDPC codes. Constructing LDPC Hmatrix...

In this paper, we compare the finite-length performance of protograph-based spatially coupled lowdensity parity-check (SC-LDPC) codes and LDPC block codes (LDPC-BCs) over GF(q). In order to reduce computational complexity and latency, a sliding window decoder with a stopping rule based on a soft bit-error-rate (BER) estimate is used for the q-ary SC-LDPC codes. Two regimes are considered: one w...

Low density parity check (LDPC) codes are one of the best error correcting codes in today’s coding world and are known to approach the Shannon limit. As with all other channel coding schemes, LDPC codes add redundancy to the uncoded input data to make it more immune to channel impairments. In addition to coding, the best modulation techniques available today are MSK (Minimum Shift Keying) and G...

In this paper, we discuss a construction of CSS codes derived from pairs of practical irregular LDPC codes. Intersection studies between quantum error-correcting codes and LDPC codes are current hot research topics [1], [3], [4], [5], [6], [7], [8], [9]. One of aims of quantum error-correcting code theory is to construct quantum error-correcting codes with small length and high error-correcting...

Low-Density Parity Check codes are a special class of linear block codes widely used in communication and disk storage systems, due to their Shannon limit approaching performance and their favourable structure. A special class of LDPC codes, called QC-LDPC codes, allows for efficient hardware implementations of encoding and decoding algorithms by exploiting the structure of the Parity Check Mat...

This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of MET-LDPC codes for given values of the maximum number of edge-types and maximum node degrees. This joint optimization is particularly important for MET-LDPC c...