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Computation in the Presence of Noise

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The behavior of a system consisting of a preliminary coder, an unreliable computer, and a decoder is investigated. Coding input blocks of k binary digits into output blocks of n>k binary digits, it is shown that a simple combinational computer which can take the and or or of k or more input blocks can only be made arbitrarily reliable by making n/k arbitrarily large, so that the capacity for computation, in an information theory coding sense, is zero. Incomplete results for a single and or or circuit give the same result if the output gives no information about the inputs except for the information about their and or or; if this is not demanded, then for n>2k, reliable computation through noisy computing circuits is possible, but the computing is done in the decoder.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

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IBM Journal of Research and Development  (Volume:2 ,  Issue: 4 )