Journal ArticleDOI
On codes for checking logical operations
W. W. Peterson,Michael O. Rabin +1 more
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It is shown that for both types of coding and for all nontrivial logical functions of two variables, except "exclusive or" and its complement, there is no system of checking simpler than duplication.Abstract:
Two types of codes for checking logical operations digit by digit on two vectors of binary digits are studied. The first type attaches a check symbol to each vector of binary digits and requires that the check symbol for the logical function of two vectors can be determined from the check symbols of the two input vectors. The second type of coding is ordinary block coding into vectors of binary digits, with the added requirement that the coded vectors be processed digit by digit.
The constraints on the codes resulting from the assumptions for the coding system are studied by typical algebraic arguments. It is shown that for both types of coding and for all nontrivial logical functions of two variables, except "exclusive or" and its complement, there is no system of checking simpler than duplication. For "exclusive or" and its complement, group alphabets can be used, and for the block coding these are the only codes which can be used.read more
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References
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Journal ArticleDOI
Error detecting and error correcting codes
TL;DR: The author was led to the study given in this paper from a consideration of large scale computing machines in which a large number of operations must be performed without a single error in the end result.
Journal ArticleDOI
A class of binary signaling alphabets
TL;DR: A class of binary signaling alphabets called “group alphABets” is described, which are generalizations of Hamming's error correcting codes and possess the following special features: all letters are treated alike in transmission; the encoding is simple to instrument; maximum likelihood detection is relatively simple to Instrument.
Journal ArticleDOI
On checking an adder
TL;DR: It is shown that independent adding and checking circuits are possible only with systems of this type and a method of handling residue-class check symbols when overflow occurs is discussed.
Journal ArticleDOI
Computation in the presence of noise
TL;DR: 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.
Journal ArticleDOI
On coding for the binary symmetric channel
A. B. Fontaine,W. W. Peterson +1 more
TL;DR: Questions concerning coding for the binary symmetric channel might be divided into three categories: for a specified error probability and with no restriction on the length of a code, what is the maximum rate at which information can be transmitted, and how can optimum codes with a given rate and word length be constructed.