QC-LDPC Codes: Algebraic and Combinatorial Design

Ponente(s): Henry Chimal Dzul

Low-Density Parity-Check (LDPC) Codes were discovered by Gallager in the early 1960s. These linear binary codes are Shannon capacity-approaching. The subclass of quasi-cyclic LDPC (QC-LDPC) codes is attractive for implementation purposes since they can be encoded in linear time with shift registers and their simple structure leads to efficiencies in decoder design. This is the reason why QC-LDPC codes appear in many industry standards, including those developed by the Consultative Committee for Space Data System (CCSDS). In this presentation we will introduce this class of codes and discuss their algebraic structure. Moreover, we will present a combinatorial design for which the Tanner graph of such codes will have girth at least 6; a parameter that is important for practical applications of these binary codes.