Trapping-Set-Assisted Decoding for Short-Length Low-Density Parity-Check Codes

To guarantee that every device in industrial Internet of Things (IoT) is reliable for fast data exchange, ultrareliable and low-latency communication (URLLC) technology from 5G is crucial. To reduce latency, typically, only up to 1000 code blocklength is allowed. Indeed, a block error rate (BLER) of less than $10^{-5}$ and latency of less than 1 ms are achievable in 5G URLLC. The short code blocklength feature is also required in satellite IoT. Though low-density parity-check (LDPC) decoding via belief propagation (BP) shows promise for achieving low BLER with long blocklength, its BLER is high in short LDPC codes due to error-prone patterns, with the trapping set (TS) being one of the most significant patterns. To alleviate the damage of TS, which can be identified offline, we propose two decoding algorithms named dynamic TS-assisted reinforced BP (DTS-RBP) and TS-assisted relaxation for neural-network BP (TSR-NNBP), respectively. Compared with previous works, only proposed TS assisted decoders can meet URLLC requirements under 308 code blocklength at a 3 dB signal-to-noise ratio (SNR). Moreover, under 128 code blocklength for satellite IoT, our DTS-RBP decoder provides the best memory-performance tradeoff with approximately the same number of iterations as BP.