Low Complexity Rate Compatible Puncturing Patterns Design for LDPC Codes

In contemporary digital communications design, two major challenges should be addressed: adaptability and flexibility. The system should be capable of flexible and efficient use of all available spectrums and should be adaptable to provide efficient support for the diverse set of service characteristics. These needs imply the necessity of limit-achieving and flexible channel coding techniques, to improve system reliability. Low Density Parity Check (LDPC) codes fit such requirements well, since they are capacity-achieving. Moreover, through puncturing, allowing the adaption of the coding rate to different channel conditions with a single encoder/decoder pair, adaptability and flexibility can be obtained at a low computational cost.In this paper, the design of rate-compatible puncturing patterns for LDPCs is addressed. We use a previously defined formal analysis of a class of punctured LDPC codes through their equivalent parity check matrices. We address a new design criterion for the puncturing patterns using a simplified analysis of the decoding belief propagation algorithm, i.e., considering a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, recently defined by the Authors, to estimate the threshold for regular and irregular LDPC codes on memoryless binary-input continuous-output Additive White Gaussian Noise (AWGN) channels

Randomly Punctured LDPC Codes

In this paper, we present a random puncturing analysis of low-density parity-check (LDPC) code ensembles. We derive a simple analytic expression for the iterative belief propagation (BP) decoding threshold of a randomly punctured LDPC code ensemble on the binary erasure channel (BEC) and show that, with respect to the BP threshold, the strength and suitability of an LDPC code ensemble for random puncturing is completely determined by a single constant that depends only on the rate and the BP threshold of the mother code ensemble. We then provide an efficient way to accurately predict BP thresholds of randomly punctured LDPC code ensembles on the binary- input additive white Gaussian noise channel (BI-AWGNC), given only the BP threshold of the mother code ensemble on the BEC and the design rate, and we show how the prediction can be improved with knowledge of the BI-AWGNC threshold. We also perform an asymptotic minimum distance analysis of randomly punctured code ensembles and present simulation results that confirm the robust decoding performance promised by the asymptotic results. Protograph-based LDPC block code and spatially coupled LDPC code ensembles are used throughout as examples to demonstrate the results