Abstract
This talk is concerned with construction and decoding of short-length codes.
First, we present the staircase matrix codes (SMCs), which have staircase-like generator matrices or parity-check matrices. The most distinguished feature of the SMCs is that the staircase-like matrices enable parallel implementation of the Gaussian elimination (GE).
As a result, the SMCs are suitably decoded by the presented ordered statistic decoding (OSD)-like algorithm, resulting in a low decoding latency and a capacity-approaching performance.
Second, we present a new OSD-like decoding algorithm, referred to as the locally constrained OSD (LC-OSD).
Compared with the conventional OSD, the LC-OSD significantly reduces both the maximum and average number of searches.
The former is achieved by performing the serial list Viterbi algorithm (SLVA) over a trellis
with local constraints on the test error patterns, while the latter is achieved by incorporating tailored early termination criteria.
Third, we propose a new decoding algorithm over a pruned tree for the polar codes, referred to as the successive-cancellation list (SCL) decoding algorithm by enumerative search and guessing random additive noise decoding (GRAND), where the list-GRAND algorithm is applied to the high-rate leaves and the enumerative search decoding algorithm is applied to the low-rate leaves, both of which are multiple-bit-wise list decoding algorithms.
Simulation results show that, without any performance loss as justified by analysis, the proposed decoding algorithm can significantly reduce the decoding complexity and latency of the polar codes.