Iterative Soft-Decision Decoding of Hermitian Codes

This paper proposes an iterative soft-decision decoding algorithm for one of the most popular algebraic-geometric (AG) codes - Hermitian codes. The algorithm is designed by integrating the two most powerful soft-decision decoding algorithms, the adaptive belief propagation (ABP) algorithm and the Koetter-Vardy (KV) list decoding algorithm. The ABP algorithm performs iterative decoding based on an adapted parity-check matrix of a Hermitian code to enhance the reliability of the soft received information. With the enhanced reliability, the KV algorithm performs soft-decision list decoding to obtain the original message. Since the matrix adaptation relies on bit reliabilities, regrouping of the unreliable bits is introduced to assist the ABP decoding. A complexity reducing ABP-KV decoding approach is proposed based on assessing the soft information provided by the ABP algorithm and determining whether the following KV decoding steps should be carried out. Geometric interpretation of the ABP algorithm is presented, demonstrating the necessity of performing matrix adaptation. Our performance analysis shows the proposed iterative decoding algorithm outperforms both the existing decoding approaches for Hermitian codes and the ABP-KV decoding of Reed-Solomon (RS) codes.