Error-Aware SCFlip Decoding of Polar Codes

Abstract

The successive-cancellation flip (SCFlip) decoder and its variants provide a significant coding gain with the average complexity practically identical to that of the successive cancellation (SC) decoder in a wide range of signal-to-noise ratios (SNRs). But, they suffer from high complexity and long latency when the SNR decreases, since the average number of extra decoding attempts becomes inevitably large. To mitigate this problem, we propose a novel SCFlip decoder, called an error-aware SCFlip (EA-SCFlip) decoder, for distributed cyclic-redundancy-check (CRC) polar codes. Based on the distributed CRC bits, it employs early termination at each extra decoding attempt so that it can reduce the decoding complexity and latency on the average. It also reduces the search space of candidate bit-flips in the dynamic building of the bit-flip list by exploiting the parity-check relationship (PCR) of the first error-detected CRC bit at each extra decoding attempt. Furthermore, we propose a greedy algorithm to design a distributed CRC code such that the obtained PCRs make the early-error-detection capability of the EA-SCFlip decoder as high as possible. Numerical results demonstrate that the EA-SCFlip decoder can indeed achieve an early termination gain as well as a complexity reduction, when a polar code is concatenated with the distributed CRC code designed by the proposed algorithm.