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Optimal random coding
Author(s) -
Peskin Charles S.
Publication year - 1986
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160390104
Subject(s) - mathematics , sequence (biology) , limiting , function (biology) , discrete mathematics , probability of error , algorithm , coding (social sciences) , random sequence , combinatorics , mathematical analysis , statistics , distribution (mathematics) , mechanical engineering , genetics , evolutionary biology , engineering , biology
We consider a stochastic method for representing a real number x by a finite sequence of bits. The method is symmetrical with respect to interchange of the bits: it is characterized by a single function p (x) which gives the probability that any particular bit is on as a function of the real number x that is being encoded. We then consider the problem of reconstructing x from its representation. In the limiting case in which the number of bits is large, we determine the function p (x) that minimizes the expected k ‐th power of the absolute error in this reconstruction. The optimal choice of p (x) is independent of k .