On the Design of Punctured Low Density Parity Check Codes for Variable Rate Systems

Abstract

The authors face the problem of designing good LDPC codes for applications requiring variable, that is adaptive, rates. More precisely, the object of the paper is twofold. On one hand, we propose a deterministic (not random) procedureto construct good LDPC codes without constraints on the code dimension and rate. The method is based on the analysis and optimization of the local cycles length in the Tanner graph and gives the designer the chance to control complexity of the designed codes. On the other hand, we present a novel puncturing strategy which acts directly on the parity check matrix of the code, starting from the lowest rate needed, in order to allow the design of higher rate codes avoiding additional complexity of the co/decoding hardware. The efficiency of the proposed solution is tested through a number of numerical simulations. In particular, the puncturing strategy is applied for designing codes with rate variable between 0.715 and 0.906. The designed codes are used in conjunction with M-QAM constellations through a pragmatic approach that, however, yields very promising results.