Coding for logical operations

  • Authors:
  • S. Winograd

  • Affiliations:
  • -

  • Venue:
  • IBM Journal of Research and Development
  • Year:
  • 1962

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Abstract

The behavior of a computation system consisting of encoders, an unreliable logical operator and a decoder is investigated. It is shown that for almost all Boolean functions, coding each block of k input bits into a block of n bits such that all sets of s or less errors will be corrected requires that n ≥ (2s + 1)k. This result suggests that the capacity (in the information theoretical sense) of such a computation system is zero.