Minimum Polarized Distance Codes

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Abstract
The choice of a code for a given application is influenced by many factors, such as economics, compatibility, and reliability. This paper is concerned solely with the reliability of codes, and shows how, for a given number of bits per character and a given minimum distance, the probability of undetected error in an asymmetric channel may be reduced by many orders of magnitude merely by the proper selection of coded characters. For a given minimum distance, an optimum selection of characters requires, as nearly as possible, the same number of "one" and "zero" bit failures to change one character to another. The concept of polarized distance is introduced, and it is shown how the probability of undetected error is related to the minimum distance of a code only in a symmetric channel, while the probability of undetected error is related to the minimum polarized distance in both symmetric and asymmetric channels. The purpose of this paper is to present new theoretical concepts useful in the evaluation of codes, and not to recommend one code over another. The codes in the paper are used only as examples to illustrate the theoretical concepts involved.

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