A Log-Domain Approximation of SOCS Decoding for Turbo Product Codes

2026-05-08

AI Summary

This work addresses the limitations of conventional Chase–Pyndiah decoders, which suffer from insufficient extrinsic information quality, and the high computational complexity of existing soft-output Chase–Pyndiah (SOCS) decoders in the probability domain, which hinders practical hardware implementation. To overcome these issues, the paper proposes a max-log approximation-based SOCS decoding scheme operating in the log domain. This approach reformulates SOCS decoding in the logarithmic domain for the first time, replacing complex probability-domain operations with piecewise linear functions to model reliability intervals. Integrated with a Chase-II list and soft-input soft-output (SISO) processing rules, the proposed decoder maintains compatibility with standard turbo product code (TPC) iterative decoding architectures while significantly reducing complexity. Evaluated on a (256,239) extended BCH-based TPC, the decoder outperforms the Chase–Pyndiah scheme at the same list size and achieves performance close to that of the original SOCS decoder.

Abstract

This paper studies low-complexity soft-output decoding of turbo product codes with extended Bose--Chaudhuri--Hocquenghem component codes. Recent soft-output from covered space (SOCS) decoding substantially improves the quality of extrinsic information compared with the conventional Chase--Pyndiah decoder, but its probabilistic-domain implementation is less attractive for hardware-oriented realizations. We therefore propose a log-domain approximation of SOCS based on max-log approach. The proposed soft-input soft-output rule replaces probability-domain operations with a piecewise-linear function of reliability gaps between competing Chase-II decoding list and out of the list hypotheses, which preserves compatibility with the standard iterative TPC decoding loop. Numerical results for a TPC built from (256,239) eBCH component codes show that the proposed decoder clearly outperforms the baseline Chase--Pyndiah decoder with the same list size and approaches the performance of SOCS decoder.

Problem

• Turbo Product Codes
• Soft-Output Decoding
• SOCS
• Low-Complexity
• Log-Domain

Innovation

• log-domain approximation
• SOCS decoding
• Turbo Product Codes
• soft-output decoding
• max-log