Title: On the Design of Punctured Low Density Parity Check Codes for Variable Rate Systems
Authors: Marco Baldi, Franco Chiaraluce
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) procedure to 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 the 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 codes with higher rate avoiding additional complexity of the co/decoding hardware. The efficiency of the solutions proposed is tested through a number of numerical simulations. The puncturing strategy, in particular, is applied for designing codes with rate variable from 0.715 to 0.906. The designed codes are used in conjunction with M-QAM constellations through a pragmatic approach, that however yields very promising results.