Performance of reed solomon error-correcting codes

In this paper, our aim is to evaluate the performance of Reed Solomon (RS) codes when used to protect Asynchronous Transfer Mode (ATM) cells (424 bits) over fading channels. The well-known Gilbert-Elliott model (GE) represents the memory-fading channel. Its parameters like transition probabilities are related to physical quantities associated with fading statistics (Doppler normalized frequency, fading margin,..). Analytical expressions for code-word error probability ( ), residual error rate ( ) and cell loss ratio ( ) are derived. The GE channel model is used to compare the performance of a large set of codes including those lengths that are 7,15,31,63 and 127. Contrarily to situations where binary symmetric channel is applied, the performance obtained is improved using short codes and imperfect interleaving. The Doppler normalized frequency and the variation of signal-to-noise ratio affect noticeably performance parameters. Also, theoretical and simulation results are compared to verify and to validate the accuracy of the GE model. In fact, simulation results obtained for a certain class of parameters seem to be in excellent agreement with analytical formulas.