Abstract
This paper is concerned with error correcting codes for asymmetric memories or channels. An asymmetric memory cell is one which has a much higher probability of 1 → 0 (0 → 1) type transition or failure compared with the 0 → 1 (1 → 0) type transition. Starting with a new metric, the asymmetric distance da(X, Y) between two binary n-tuples X and Y and using the minimum asymmetric distance requirement for an error correcting code, we introduce a new class of codes suitable for asymmetric channels, which we refer to as “group-theoretic codes.” The single asymmetric error correcting property of these codes is proved, and their superiority in information rate over previously developed codes for asymmetric channels is established. We present some theory leading towards group-theoretic codes with the highest information rate for a given length n. Some open questions of interest in the area are posed.
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