Separable concatenated codes with iterative map filtering

In practice, very efficient signalling over radio channels requires more than designing very powerful codes. It requires designing very powerful codes that have special structure so that practical decoding schemes can be used with excellent, but not necessarily optimal, results. Examples of two such approaches include the concatenation of convolutional and Reed-Solomon coding, and the use of very large constraint-length convolutional codes with reduced-state decoding. In this paper, powerful codes are obtained by using simple block codes to construct multidimensional product codes. The decoding of multidimensional product codes, using separable symbol-by-symbol maximum a posteriori (MAP) “filters”, is described. Simulation results are presented for three-dimensional product codes constructed with the (16,11) extended Hamming code. The extension of the concept to concatenated convolutional codes is given. The relationship between the free distance and the interleaving factors is examined, and then exemplified with computer simulation. Potential applications are briefly discussed.