### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 69-73 |

Number of pages | 5 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1986 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Peskin, C. S. (1986). Optimal random coding.

*Communications on Pure and Applied Mathematics*,*39*(1), 69-73. https://doi.org/10.1002/cpa.3160390104