SOGRAND Decoding of Non-binary Product Codes

Non-binary product codes are matrices with entries in an extension field, where the rows and columns are protected by linear non-binary component codes. As with binary product codes, non-binary product codes can be decoded via turbo product decoding and are referred to as turbo product codes (TPCs). This paper assesses the performance of non-binary TPCs with the recently developed soft-input soft-output GRAND decoder (SOGRAND). Owing to the more accurate soft output, decoding of non-binary TPCs with SOGRAND outperforms existing turbo product decoders. We demonstrate that non-binary TPCs can also provide a better block error rate performance than a selection of low-density parity-check (LDPC) codes found in the 5G New Radio standard. This extends the design space of TPCs beyond binary TPCs, demonstrating their potential as a viable alternative to LDPC codes. Empirical results show that non-binary TPCs converge in fewer iterations than binary TPCs of the same size. We show TPCs that converge with up to three times fewer decoding iterations than the corresponding LDPC code from the 5G New Radio standard. This indicates they hold promise for low-latency, high-throughput applications.