Diagonal space time Hadamard codes with erasure decoding algorithm

A major challenge in the area of space time (ST) codes is to find codes suitable for efficient decoding, thus overcoming the problem of many existing ST code designs which require maximum-likelihood (ML) decoding. A solution could be to apply single-input single-output (SISO) channel codes and theory over temporal channel fading to the multi-input single-output (MISO) code construction and classical suboptimum decoding methods. For these purposes, an ST code construction which allows the use of efficient decoding algorithms is described. We propose a concatenated code, where the inner code is the diagonal ST Hadamard (D-STH) code with Paley constructions and the outer code is an algebraic block code, such as a Reed-Solomon (RS) code. As a decoding method, we investigate a bounded minimum distance (BMD) with erasure decoding algorithm. A simple method to achieve the optimum threshold for deciding on an erased symbol is derived. Using this, the proposed concatenated scheme is able to exploit almost all of the spatial diversity of the system.