Construction and Decoding of Short Codes

Explore the construction and decoding of short-length codes in this 43-minute lecture by Xiao Ma from Sun Yat-sen University. Delve into staircase matrix codes (SMCs) and their unique staircase-like generator or parity-check matrices, enabling parallel implementation of Gaussian elimination for efficient decoding. Learn about the ordered statistic decoding (OSD)-like algorithm for SMCs, which offers low decoding latency and capacity-approaching performance. Discover the locally constrained OSD (LC-OSD) algorithm, which reduces the number of searches compared to conventional OSD through serial list Viterbi algorithm and tailored early termination criteria. Examine a new decoding algorithm for polar codes that combines successive-cancellation list (SCL) decoding with enumerative search and guessing random additive noise decoding (GRAND), resulting in reduced complexity and latency without compromising performance.