To extend the applications of polar codes within next-generation wireless communication systems, it is essential to incorporate support for Incremental Redundancy (IR) Hybrid Automatic Repeat Request (HARQ) schemes. The baseline IRHARQ scheme's reliance on set-based operations leads to irregular memory access patterns, posing significant challenges for efficient hardware implementation. Furthermore, the introduction of new bit types increases the number of fast nodes that are decoded without traversing the sub-tree, resulting in a substantial area overhead when implemented in hardware. To address these issues and improve hardware compatibility, we propose transforming the set-based operations within the polar IR-HARQ scheme into binary vector operations. Additionally, we introduce a new fast node integration approach that avoids increasing the number of fast nodes, thereby minimizing the associated area overhead. Our proposed scheme results in a memory overhead of$25-27 \%$compared to successive cancellation list (SCL) decoding without IR-HARQ support.

Projection-aggregation decoders have been used in conjunction with a list structure to achieve near maximum-likelihood decoding for short-length and low-rate Reed-Muller (RM) codes but suffer from high computational complexity. We reduce the worst-case computational complexity of projection-aggregation (PA) decoders by more than 50% using a scheduling scheme compared to PA decoders without the scheduling scheme, and propose a redesigned syndrome check pattern to avoid repeated syndrome computations in the decoder. A latency model based on the existing hardware architecture is proposed. Input distribution aware (IDA) decoding is adopted as a pre-possessing tool, and the average list size when using IDA decoding is analytically derived under additive white Gaussian noise and uncorrelated normalized Rayleigh fading channels. Using IDA, the average list size is reduced by 30% with less than 0.1 dB loss. The proposed list decoders require a smaller computational complexity than the state-of-the-art iterative decoder, automorphism ensemble decoding with the belief propagation constituent decoder (AED-BP) for decoding RM(7, 3) and RM(8, 3) codes. Based on the developed latency models, the PA list decoder has a smaller latency than the AED-BP and the successive cancellation list decoder to reach near maximum-likelihood decoding performance.

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 10−4with 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 104achieves up to a 2 dB gain to its GRAND equivalent which is using 107maximum number of queries.