Iterative soft-decision decoding of Hermitian codes

Algebraic-geometric (AG) codes have long been identified as a possible candidate to replace Reed-Solomon (RS) codes for error-correction. This paper proposes an iterative soft-decision decoding algorithm for one of the most popular AG codes - Hermitian codes. The algorithm is designed by integrating the legacy belief propagation (BP) algorithm and the Koetter-Vardy (KV) soft-decision list decoding algorithm. The BP algorithm performs iterative decoding based on an adapted parity-check matrix whose density has been reduced, namely the adaptive BP (ABP) algorithm. It enhances the reliability of the received information, with which the KV algorithm performs soft-decision list decoding to obtain the intended message. Since the matrix adaptation is bit reliability oriented, re-grouping of the unreliable bits is introduced to assist the ABP algorithm. Geometric analysis of the ABP algorithm is presented, demonstrating the necessity of performing matrix adaptation and integrating the ABP and KV algorithms. The performance evaluation shows the proposed iterative decoding algorithm is an advanced decoding approach that outperforms the existing decoding algorithms for Hermitian codes. It can also outperform ABP-KV decoding of RS codes.