Matching Q-ary Reed-Solomon codes with M-ary modulation

Reed-Solomon (RS) error-correcting codes are often proposed for communication systems requiring burst and/or erasure correction capabilities. In most cases, the modulation symbol size is fixed a priori. Therefore, the effective application of RS coding implies proper matching of the code symbol size with the modulation symbol size. Previous results have assumed that the RS codeword symbol size is an integer multiple of the modulation symbol size or have been based on simple approximations. In this paper, the exact symbol error probability with K-bit M-ary modulation symbols and q-bit RS codeword symbols is presented.