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Rate-compatible LDPC convolutional codes for capacity-approaching hybrid ARQ

In this paper we construct a family of rate-compatible LDPC convolutional codes for Type-II HARQ systems. For each code family, the codes of lower rates are constructed by successively extending the graph of the high-rate base code. Theoretically, the proposed rate-compatible family includes all rates from 0 to 1. We prove analytically that all LDPC convolutional codes in the family are capacity achieving over the binary erasure channel (BEC). Thus, if applied to an idealized HARQ system over the BEC where the channel parameter stays constant within one complete information delivery, the throughput achieves the capacity of the channel. Moreover, the code construction is realized by regular degree distributions, which greatly simplifies the optimization.