Randomly Punctured LDPC Codes.pdf

408 IEEE JOURNAL ON SELECTED AREAS MUNICATIONS, VOL. 34, NO. 2, FEBRUARY 2016 Randomly Punctured LDPC Codes David G. M. Mitchell, Member, IEEE , Michael Lentmaier, Senior Member, IEEE , Ali E. Pusane, Member, IEEE , and Daniel J. Costello, Jr., Life Fellow, IEEE Abstract— In this paper, we present a random puncturing analy- sis 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 pletely determined by a single constant that depends only on the rate and the BP threshold of the mother code ensemble. We then provide an ef?cient 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 con?rm 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. Index Terms— Low-density parity-check (LDPC) codes, spa- tially coupled codes, patible codes, punctured codes, iter- ative decoding, belief propagation, decoding thresholds, binary erasure channel, additive white Gaussian noise channel, minimum distance. I. I NTRODUCTION I T IS OFTEN desirable in applications that experience changing channel conditions to be able to employ a vari- ety of code rates. Coding schemes that can adapt to the changing conditions of time-varying cha