An analytical analysis of a concatenated Reed-Solomon (RS)/Viterbi coding system both with and without RS interleaving

A new Markov chain (MC) technique which analytically calculates the word, symbol and bit error rates (BERs) of a concatenated Reed-Solomon (RS)/Viterbi coding system in an additive white Gaussian noise environment is presented. This technique can analyze a system with no RS interleaving, ideal RS interleaving, and finite RS interleaving. It is faster than the standard simulation method of analysis for low noise environments since its run time is independent of the BER, while the run time of a simulation is inversely proportional to the BER. This analysis models the output of the Viterbi decoder with a geometric distribution. The MC analysis uses this output to find the probability of a given number of symbol errors in a RS codeword, which is then used to calculate the error rates. Results for the commonly used combination of an inner 1/2 rate convolutional code of constraint length seven and an outer RS (255,223) code are presented.<>