Optimal two-level unequal error control codes for computer systems

Error control codes are now successfully applied to computer systems and communication systems. When we consider some types of computer words or communication messages, the information in some part of the word is more important than the other. Address and control information in computer words and communication messages and pointer information in database words are good examples. The more important the part of the word is, or the less reliable the part is, the more strongly it should be protected from errors. Based on this, 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. From a simple and practical viewpoint, this paper adopts the model of the codeword which includes two unequal levels: one having strong error control level in some part of the codeword, called fixed-byte, and the other having relatively weak error control level outside the fixed-byte. This paper deals with three basic unequal error control codes. For all types of codes, the paper clarifies necessary and sufficient conditions and bounds on code length and demonstrates code construction method of the optimal codes and evaluation of these codes from the perspectives of error correction/detection capability and decoder hardware complexity