Alisrruct-Linear block codes are studied for improving the reliability of message storage in computer memory with stuck-at defects and noise. The case when the side information about the state of the defects is available to the decoder or to the encoder is considered. In the former case, stuck-at cells act as erasures so that techniques for decoding linear block codes for erasures and errors can be directly applied. We concentrate on the complimentary problem of incorporating stuck-at information in the encoding of linear block codes. An algebraic model for stuck-at defects and additive errors is presented. The notion of a "partitioned " linear block code is Manuscript received November 16, 1981; revised April 18, 1983. This work was supported under NSF Grant ECS78-23334 and DARPA Contract MDA 903-79-C-0680. This work was presented at the IEEE Intemational Symposium on Information Theory, Les Arcs, France, June 1982. The author was with the Department of Electrical Engineering, Stanford University, CA 94305. He is now with the School of Electrical Engineering, Cornell University, Ithaca, NY 14853. introduced to mask defects known at the encoder and to correct random errors at the decoder. The defect and error correction capability of partitioned linear block codes is characterized in terms of minimum distances. A class of partitioned cyclic codes is introduced. A BCH-type bound for these cyclic codes is derived and employed to construct partitioned linear block codes with specified bounds on the minimum distances. Finally, a probabilistic model for the generation of stuck-at cells is presented. It is shown that partitioned linear block codes achieve the Shannon capacity for a computer memory with symmetric defects and errors.
Moreover, in REF , a partitioned cyclic code and partitioned BCH were proposed to mask stuck cells and correct errors.
Partitioned linear block codes for computer memory with 'stuck-at' defects
IEEE Trans. Inf. Theory
IEEE Trans. Inf. Theory
Computer Science