Errors and erasures decoding of Reed-Solomon codes for reduced M-ary orthogonal signaling

This paper presents a comparison of equivalent communication systems using M-ary orthogonal signaling and errors and erasures decoding of q-ary Reed-Solomon codes of differing rates, such that the bandwidth is the same for each system. In these comparisons the channel symbol size may differ from the code symbol size, so a code symbol can contain parts of more than one channel symbol. Thus, the normal assumption of independent code symbols does not apply, and thus consideration must be taken to obtain the best arrangement of channel symbols in each code symbol. Analytical expressions are developed to compare the bit error probability performance of comparable systems, based on individual codewords using errors and erasures decoding with transmission over a Rayleigh fading channel.