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Random sequential coding by Hamming distance

Published online by Cambridge University Press:  14 July 2016

Yoshiaki Itoh  and
Herbert Solomon
Yoshiaki Itoh*
Affiliation:
Institute of Statistical Mathematics, Tokyo
Herbert Solomon*
Affiliation:
Stanford University
*
∗Postal address: The Institute of Statistical Mathematics, 4–6–7 Minami-Azabu, Minato-ku, Tokyo, Japan.
∗∗Postal address: Department of Statistics, Sequoia Hall, Stanford University, Stanford, CA 94305–2195, USA.
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Abstract

Here we introduce two simple models: simple cubic random packing and random packing by Hamming distance. Consider the packing density γ d of dimension d by cubic random packing. From computer simulations up to dimension 11, γ d+1/γ d seems to approach 1. Also, we give simulation results for random packing by Hamming distance and discuss the behavior of packing density when dimensionality is increased. For the case of Hamming distances of 2 or 3, d–α fits the simulation results of packing density where α is an empirical constant. The variance of packing density is larger when k is even and smaller when k is odd, where k represents Hamming distance.

Keywords

SEQUENTIAL RANDOM PACKINGCUBIC PACKINGCODING THEORY
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 688 - 695
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

This paper was prepared at Stanford University with the partial support of the Office of Naval Research under Contract N00014–76–C–0475.

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