Confidence intervals for simulations using Reed-Solomon codes

The minimum length confidence interval (CI) for the decoded binary symbol error probability is considered for a Monte Carlo communication system simulation which includes a Reed-Solomon (RS) code. The binary errors at the demodulator output are assumed to be independent with probability P_ch, and the RS decoder is assumed to be an errors-only, incomplete (bounded distance) decoder with decoded bit error probability P_c,b. Let z denote the number of codewords sent through the channel for a simulation trial and let random variable (RV) N_z be the number of errors observed to occur at the RS decoder output. To compute the CI, the discrete probability density function (pdf) P{N_z}, is derived for P_c,b ≪ P _ch and shown to compare well with simulation results. It is shown that P{N_z} is unimodal (one maximum) for z ≫ 1 but is generally multimodal (multiple maxima) for small z. In this paper, the minimum length CI is considered for z ≫ 1 subject to P_c,b ≪ P_ch