Abstract
In this thesis, we propose a soft-decision decoding algorithms for Reed-Solomon codes based on symbol reliability. Our algorithm starts from the relationship between RS codewords and polynomials over a finite field. For an (n, k, d) RS code C over a finite field F, every codeword corresponds to a polynomial with degree less than k. Our algorithm defines a subset of F composed of locators corresponding to least reliable positions, then works on a subset of C corresponding to polynomials without any root in the specified subset of F. All polynomials without any root in a specified subset could be found by combination of primes in F[X], and primes are independent of the received word and could be stored in advance. With this advantage and efficiency of finite field arithmetic, our algorithm could be easily implemented in hardware. Simulations results confirm the validity of our decoding algorithm and show 1.5 dB coding gain over hard-decision decoding algorithms.