An Ordered-Reliability-Bits Chase Decoding Algorithm for BCH Codes

2026-08-06

AI Summary

This work addresses the high computational complexity of Chase decoding for BCH codes by proposing a low-complexity Ordered Reliability Bits Chase (ORB-Chase) decoding algorithm. The method replaces conventional reliability metrics with logically weighted test error patterns and incorporates an integer-based early termination criterion to eliminate redundant computations. Integrated within the Chase framework and leveraging the Berlekamp–Massey decoder, the proposed algorithm achieves near-maximum-likelihood performance on both (127,113,5) BCH and (256,239,6) eBCH codes while reducing the number of Berlekamp–Massey decoder invocations by up to 98.1%, thereby significantly enhancing decoding efficiency.

Abstract

In this paper, we propose a low-complexity ordered-reliability-bits Chase (ORB-Chase) decoding algorithm for BCH codes. The proposed algorithm differs from the traditional Chase algorithm in two key aspects. First, it employs the logical weight as a metric to generate test error patterns (TEPs). Second, it introduces an integer-based early termination criterion that ensures computation can stop at the earliest possible stage if the maximum-likelihood codeword is identified, thereby minimizing unnecessary computational effort. Simulation results for (127, 113, 5) BCH codes and (256, 239, 6) eBCH codes demonstrate that the ORB-Chase algorithm achieves near-ML performance with significantly fewer test patterns compared to the Chase algorithm. Moreover, the average number of Berlekamp-Massey (BM) decoding calls decreases rapidly as $E_b / N_0$ increases, achieving a reduction of up to 98.1% compared to the Chase algorithm at the same BLER performance.

Problem

• BCH codes
• Chase decoding
• decoding complexity
• maximum-likelihood performance
• test error patterns

Innovation

• ORB-Chase
• logical weight
• early termination
• BCH codes
• low-complexity decoding