THE PERFORMANCE OF FOCUSED ERROR CONTROL CODES

Consider an additive noise channel with inputs and outputs in the fiel d GF(q) where q > 2; every time a symbol is transmitted over such a ch annel, there are q-1 different errors that can occur, corresponding to the q-1 non-sero elements that the channel can add to the transmitted symbol. In many data communication/storage systems, there are some er rors that occur much wore frequently than others; however, traditional error correcting codes - designed with respect to the Hamming metric - treat each of these q-1 errors the same. Fuja and Heegard have desig ned a class of codes, called focused error control codes, that offer d ifferent levels of protection against 'common'' and ''uncommon'' error s; the idea is to define the level of protection in a way based not on ly on the number of errors, but the kind as well. In this paper, the p erformance of these codes is analyzed with respect to idealized ''skew ed'' channels as well as realistic non-binary modulation schemes. It i s shown that focused codes, used in conjunction with PSK and QAM signa ling, can provide more than 1.0 dB of additional coding gain when comp ared with Reed-Solomon codes for small blocklengths.