This paper proposes a soft input decoding algorithm and a decoder architecture for generalized concatenated (GC) codes. The GC codes are constructed from inner nested binary Bose-Chaudhuri-Hocquenghem (BCH) codes and outer Reed-Solomon codes. In order to enable soft input decoding for the inner BCH block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code. In this paper, a representation of the block codes based on the trellises of supercodes is proposed in order to reduce the memory requirements for the representation of the BCH codes. This enables an efficient hardware implementation. The results for the decoding performance of the overall GC code are presented. Furthermore, a hardware architecture of the GC decoder is proposed. The proposed decoder is well suited for applications that require very low residual error rates.

Codes over Gaussian integers have been proposed for coding over two‐dimensional (2D) signal spaces, for example, using quadrature amplitude modulation. Here, it is demonstrated that the concept of set partitioning can be applied to Gaussian integer constellations that are isomorphic to 2D modules over rings of integers modulo p . This enables multilevel code constructions over Gaussian integers. The authors derive upper bounds on the achievable minimum distance in the subsets and present a construction for the set partitioning. This construction achieves optimal or close to optimal minimum distances. Furthermore, it is demonstrated that this set partitioning can be applied to an interleaving technique for correcting 2D cyclic clusters of errors. The authors propose a novel combination of generalised concatenated codes with 2D interleaving to correct 2D error clusters and independent errors.