Overview of LDPC codes

Roxana Smarandache, David G. M. Mitchell, Danniel J. Costello

A significant amount of the analysis of protograph-based low-density parity-check (LDPC) codes has been devoted to the subclass of quasi-cyclic (QC) LDPC codes. Despite their implementation advantages and algebraic properties that make them easy to analyze, protograph-based QC-LDPC codes have undesirable fixed upper limits on important code parameters. This implies that picking a QC code from an asymptotically good or capacity approaching ensemble is suboptimal, since long QC codes will not perform close to the ensemble asymptotic limits. Indeed, these limits can only be achieved by codes that are not QC. In this paper we present an overview together with some new results on partially-QC protograph-based LDPC codes, i.e., LDPC codes whose parity-check matrix is partially composed of circulant submatrices. We perform both a minimum Hamming distance and girth analysis of these codes. Moreover, we present explicit partially-QC LDPC code constructions with parameters that exceed the restricted QC upper bounds.

W.E. Ryan

S Vengatesh Kumar

Low Density Parity Check (LDPC) codes are one of the most powerful error correction codes available today. Its Shannon capability that closely matches performance and lower decoding complexity has made them the best choice for many wired and wireless applications. This Paper provides an overview of the LDPC codes and compares the Gallager method, the Reed-Solomon-based algebraic method, and the combinatorial Progressive Growth (PEG) method for constructing regular LDPC codes and also Overlapped and Modified overlapped message passing algorithm for Non-Quasi Cyclic(NQC) LDPC codes.

Irene Márquez-Corbella, Edgar Martı́nez-Moro

Nisha Sarwade

Low-Density parity-check (LDPC) codes are one of the most powerful error correcting codes available today. Their Shannon capacity approaching performance and lower decoding complexity have made them the best choice for many wired and wireless applications. This paper gives an overview about LDPC codes and compares the Gallager’s method, Reed-Solomon based algebraic method and the Progressive edge growth (PEG) combinatorial method for the construction of regular LDPC codes.