Decoding Techniques based on Ordered Statistics

Short code design and related decoding algorithms have gained a great deal of interest among industry and academia recently, triggered by the stringent requirements of the new ultra-reliable and low-latency communications (URLLC) service for mission-critical Internet of Things (IoT) services. URLLC services mandate the use of short block-length codes to achieve hundred-of-microsecond time-to-transmit latency and ultra-low block error rates. As a theoretical milestone, Polyanskiy et al. have given new capacity bounds tighter than Shannon's work at the finite block length regime. However, with most conventional channel codes such as LDPC, Polar, Turbo, and convolutional codes suffering from performance degradation when the code length is short, it is still an open research problem to seek potential coding schemes for URLLC. As a kind of maximum-likelihood decoding algorithm, ordered statistics decoding (OSD) can be applied with classical strong channel codes, e.g. BCH codes and Reed-Solomon codes, to potentially meet the requirements of URLLC. In this thesis, I am taking a step towards seeking practical decoders for URLLC by revisiting the OSD and significantly reducing its decoding complexity. I first provide a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance, and the weighted Hamming distance (WHD) from codeword estimates to the received sequence in the OSD algorithm. I prove that the distance distributions in OSD can be characterized as mixture models capturing the decoding error probability and code weight distribution, reflecting the inherent relations between error rate performance, distance, and channel conditions. Based on the statistical properties of distances and with the aim to reduce the decoding complexity, several decoding techniques are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can be conveniently combined with the OSD algorithm and its variants to significantly reduce the decoding complexity with a negligible loss in decoding error performance. Finally, I proposed two complete decoding designs, namely segmentation-discarding decoding, and probability-based ordered statistics decoding, as potential solutions for URLLC scenarios. Simulation results for different codes show that our proposed decoding algorithm can significantly reduce the decoding complexity compared to the existing OSD algorithms in the literature