Modelling of a trellis decoder used as inner code in a concatenated coding system

Concatenated coding systems can offer very good immunity against noise and can provide noiseless transmission over severely degraded channels. The combination of an inner convolutional code and an outer Reed-Solomon (RS) code has been a popular choice since it offers a good compromise between performance and complexity. Trellis coded modulation (TCM) is a technique that achieves significant coding gains over systems where the code and the modulating scheme has been design independently. Concatenated coding systems based on TCM codes and RS codes have been discussed in the literature. However, in most analysis the bit error rate at the output of the inner decoder is obtained, computed or by computer simulation, and then the performance of the outer decoder is computed using the binomial expression assuming that an interleaver would remove time memory in the error sequence. This paper presents a decoding model for time output of a trellis decoder which allows for a more general analysis of concatenated coding systems where interleaving is not required but can be taken into account if needed. A Markov chain model is used to represent the errors generated by the trellis decoder. The performance of the TCM code can easily be determined from this model