Vlad-Andrei Lazar (undergraduate student at IUB)
Prof. Dr.-Ing. Werner Henkel
We calculate the error probabilities in Reed-Solomon coded words taking into account both errors and erasures. This is calculated for Gray coded QAM constellations assuming only one bit to be erroneous. The occurring errors and erasures are considered statistically independent and the transmission channel is considered to be a Gaussian. Under these assumptions, we will obtain a closed form for the average bit error/erasure probability function for the QAM constellation, error probability function for the RS coded words and perform a numerical maximization for the last function by tuning the width of the “nowhere land”, where the erasures are defined, and the probability to recover a codeword (given some specific error correcting capabilities). Our goal is to investigate whether we obtain a coding gain which is significantly larger by including erasures in our calculations (we expect that under these hypothesis’ the gain should be below 1 dB, which may not justify the introduction of erasure decoding). In the case of bursty channel noise, the situation would look different. However as a first step, we will only focus on additive white Gaussian (AWGN) noise.