Partial Ordered Statistics Decoding with Enhanced Error Patterns.

Guessing Random Additive Noise Decoding (GRAND) excels at decoding high-rate codes but struggles to decode low-rate codes with reasonable complexity. Ordered Statistics Decoding (OSD) specifically excels in decoding short codes irrespective of rates; however, OSD necessitates the use of Gaussian elimination which introduces additional time, space and computational complexity. Partial Ordered Statistics Decoding (POSD) was proposed to reduce the time, space, and computational complexity of OSD; however, the current partition-based POSD has poor decoding performance since it does not generate test error patterns across partitions. In this paper, we propose to improve the decoding performance of POSD by incorporating test error patterns inspired by GRAND methods. This work offers a trade-off between performance and complexity compared to existing decoders such as GRAND and OSD. We enhance POSD by optimizing the scheduling of Test Error Patterns (TEPs) and show that our technique can be applied to any code in a standard form. At a target BER 10 ⁻⁴ with eBCH (128,64) the enhanced error patterns achieve more than 0.6 dB gain in performance compared to the POSD with partition-based error patterns. Moreover, at a target frame error rate of 10 ⁻⁵ , POSD uses 10× less binary operations compared to GRAND when decoding eBCH (128,64) and RLC(128,64) codes. With BCH (127,29) and RLC(128,32), at a target frame error rate of 10 ⁻² , POSD with enhanced error patterns with a maximum number of queries (MQ) of 10 ⁴ achieves up to a 2 dB gain to its GRAND equivalent which is using 10 ⁷ maximum number of queries.