In this correspondence, we study the minimum pseudo-weight and minimum pseudo-codewords of low-density parity-check (LDPC) codes under linear programming (LP) decoding. First, we show that the lower bound of Kelly, Sridhara, Xu and Rosenthal on the pseudo-weight of a pseudo-codeword of an LDPC code with girth greater than 4 is tight if and only if this pseudo-codeword is a real multiple of a co...

This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging f...

Cooperative communication in wireless sensor network (WSN) explores the energy efficient wireless communication schemes between multiple sensors and data gathering node (DGN) by exploiting multiple input multiple output (MIMO) and multiple input single output (MISO) configurations. In this paper, an energy efficient cooperative MIMO (C-MIMO) technique is proposed where low density parity check ...

Due to their Shannon-limit-approaching performance and low-complexity decoding, low-density parity-check (LDPC) codes have been used for forward error correction in a broad-range of communication and storage systems. In addition to its low-complexity, the iterative decoding algorithm used for decoding LDPC codes is inherently parallel. To exploit the parallelism at a larger extent, a significan...

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...

Recently, low-density parity-check (LDPC) codes have attracted much attention because of their excellent errorcorrecting performance and highly parallelizable decoding scheme. However, the effective VLSI implementation of an LDPC decoder remains a big challenge and is a crucial issue in determining how well we can exploit the benefits of the LDPC codes in the real applications. In this paper, f...

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...

A low latency, low power LDPC decoder design is presented in the paper. Partial-parallel check node processors are designed to reduce the decoding latency with moderate complexity; the parity check matrices of the LDPC codes are column-wise reordered to facilitate the parallel processing. Meanwhile, an efficient early stopping algorithm is proposed to stop the ‘undecodable’ words so that at lea...

− Low density parity-check codes are one of the hottest topics in coding theory nowadays. Equipped with very fast encoding and decoding algorithms (probabilistically,) LDPC are very attractive both theoretically and practically. In this paper, I present a throughout view of LDPC. I discuss in detail LDPC’s popular decoding algorithm: belief propagation. I also present some noticeable encoding a...

1) Introduction Iterative decoding offers a practical way for implementing LDPC codes. LDPC code is defined by a sparse MxN parity check matrix H that has 0 entries everywhere except for t c 1’s in each column and t r 1’s in each row, where t c and t r are small numbers and they degrees. Irregular LDPC codes have varying number of t c and t r . An LDPC code can be represented by bipartite graph...