Ordered Reliability Bits Guessing Codeword Decoding of Short Codes

In this paper, we investigate the guessing codeword decoding (GCD) algorithm and the guessing noise decoding (GND) algorithm for short codes, revealing the universality (in terms of code rates) and efficiency (in terms of search numbers) of GCD over GND. As inspired by the ordered reliability bits guessing random additive noise decoding (ORBGRAND), we propose the ORB-GCD and the ORB ordered statistic decoding with local constraints (ORB-LC-OSD) for practical applications. For early termination, we introduce an integer-based dynamic approximate ideal (DAI) termination criterion. Simulation results show that: 1) With a limited maximum number of guesses, GCD offers better performance and lower complexity over GND in the high code rate region, which is widely accepted as the region suitable for the GND, and 2) ORB-GCD exhibits universality for various code rates and requires a smaller search number compared to ORBGRAND.