On the trellis structures of geometric augmented product codes

Abstract

A new simple decomposable code construction technique, Geometric Augmented Product (GAP), is recently proposed in [12, 20]. It generates codes with the full information rate for all of the minimum Hamming distance-4 binary linear block codes of even length greater than or equal to 8. Additionally, some optimal Hamming distance-8 and higher distance codes are obtained with the proposed scheme. This paper elaborates the generic trellis structure of GAP codes. It is shown that the trellis structures provide lower decoding complexity in comparison to the trellises of some other well-known block codes and it is suitable for adaptive decoder applications because of its parallel and identical generic trellis structure.