Optimal random coding | Zendy

Peskin Charles S. | Zendy

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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 .

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