A particular class of low-density parity-check codes referred to as cylinder-type BC-LDPC codes is proposed by Gholami and Eesmaeili. In this paper We represent a double cylinder-type parity-check matrix H by a graph called the block-structure graph of H and denoted by BSG(H). Using the properties of BSG(H) we propose some mother matrices with column-weight two such that the rate of correspondi...

This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from difference covering arrays. While the original construction by Gallagher was by randomly allocating bits in a sparse parity-check matrix, over the past 20 years researchers have used a variety of more structured approaches to construct these codes, with the more recent constructions of well-structured...

A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N ≥ 2) nonoverlapping components with the same size. Then, these components are combined together to form the parity-check matrix of a longer code, according to a given N×N Latin square....

In this paper we propose the construction of Spatially Coupled Low-Density Parity-Check (SC-LDPC) codes using a Quasi-Cyclic (QC) algorithm. The QC based approach is optimized to obtain memory efficiency in storing the parity-check matrix in the decoders. A hardware model of the parity-check storage units has been designed for Xilinx FPGA to compare the logic and memory requirements for various...

Performance of low-density parity-check (LDPC) codes with maximum likelihood decoding (MLD) for solid burst erasures is discussed. The columns of the paritycheck matrix of LDPC codes are permuted to increase the distance between elements (DBEs) which are defined as a number of symbol positions between elements 1 at each row of the parity-check matrix. The column permutation method can change th...

Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2m ), where m > 0 cyclic low-density paritycheck codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this construction method is the ability to in...

Gallager introduced LDPC codes in 1962, presenting a construction method to randomly allocate bits in a sparse parity-check matrix subject to constraints on the row and column weights. Since then improvements have been made to Gallager’s construction method and some analytic constructions for LDPC codes have recently been presented. However, analytically constructed LDPC codes comprise only a v...

In this letter, we propose an appealing class of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) cycle codes. The parity-check matrix is carefully designed such that the corresponding generator matrix has some nice properties: 1) systematic, 2) quasi-cyclic, and 3) sparse, which allows a parallel encoding with low complexity. Simulation results show that the performance of the propose...

We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update ...

First unequal error protection (UEP) proposals date back to the 1960’s (Masnick and Wolf; 1967), but now with the introduction of scalable video, UEP develops to a key concept for the transport of multimedia data. The paper presents an overview of some new approaches realizing UEP properties in physical transport, especially multicarrier modulation, or with LDPC and Turbo codes. For multicarrie...