The Performance of Focused Error Control Codes

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Consider an additive noise channel with inputs and outputs in the field GF (q ) where q > 2; every time a symbol is transmitted over such a channel, there are q - 1 different errors that can occur, corresponding to the q - 1 non-zero elements that the channel can add to the transmitted symbol. In many data communication/ storage systems, there are some errors that occur much more 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 designed a class of codes, called focused error control codes, that offer different levels of protection against "common" and "uncommon" errors; the idea is to define the level of protection in a way based not only on the number of errors, but the kind as well. In this paper, the performance of these codes is analyzed with respect to idealized "skewed" channels as well as realistic non-binary modulation schemes. It is shown that focused codes, used in conjunction with PSK and QAM signaling, can provide more than 1.0 dB of additional coding gain when compared with Reed- Solomon codes for small blocklengths.