Optimal two-level unequal error control codes for computer systems

Error control codes are now successfully applied to computer systems and co mmunication systems. When we consider some types of computer words or commu nication messages, the information in some part of the word is more importa nt than the other. Address and control information in computer words and co mmunication messages and pointer information in database words are good exa mples. The more important the part of the word is, or the! less reliable th e part is, the more strongly it should be protected from errors. Based on t his, this paper proposes a new class of codes, called unequal error control codes, which have some unequal error control levels in the codeword, that is, have some distinct code functions in the codeword and protect the part of the word from errors according to its importance or reliability level. F rom a simple and practical viewpoint, this paper adopts the model of the co deword which includes two unequal levels: one having strong error control l evel in some part of the codeword, called fixed-byte, and the other having relatively weak error control level outside the fixed-byte. This paper deal s with three basic unequal error control codes. For all types of codes, the paper clarifies necessary and sufficient conditions and bounds on code len gth and demonstrates code construction method of the optimal codes and eval uation of these codes from the perspectives of error correction/detection c apability and decoder hardware complexity.