Parallel Decoding of PIC-LDPC Codes Aided by Free-Ride Coding

In this paper, we apply free-ride coding, a recently proposed technique, to the partial information coupling (PIC) low-density parity-check (LDPC) codes. Such an integration admits parallel decoding of PIC-LDPC codes, suggesting that high-speed decoders can be implemented. At the transmitter, the coupled information bits are periodically sampled and transmitted by the free-ride coding. At the receiver, these free-ride coded bits are first decoded and then used to decouple the whole PICLDPC coded chain into multiple shorter chains, each of which can be decoded separately and in parallel. This benefits from the fact that free-ride coded bits typically have higher reliability than others, as confirmed by the numerical results. Numerical results also show that the word error rate (WER) performance of the proposed codes is close to the genie-aided (GA) lower bound in the high SNR region.