Implementation of Reed Solomon Code Over GF(9) and 9-Ary Symmetric Channel

Abstract

Reed-Solomon and related codes have recently become very important for erasure correction in large disk arrays used in data centers. In this paper, we will implement a 3-error correcting Reed-Solomon encoder and decoder over the field GF(9) generated by the primitive polynomial D^2 + D + 2 over GF(3) and the decoding is carried out by the Berlekamp. We simulate the encoder and decoder using Monte-Carlo simulations over the 9-ary symmetric channel that outputs the correct symbol with probability (1-p), and outputs one of the other 8 possible incorrect symbols with probability p/8. Then, we compare the simulated probability of symbol error P(E) of out code with the union upper bound.