Information Rates for Poisson Point Processes

Hiroshi SATO  Tsutomu KAWABATA  

IEICE TRANSACTIONS (1976-1990)   Vol.E70   No.9   pp.817-822
Publication Date: 1987/09/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Information Theory and Coding Theory

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Rate-distortion theory for the points that are distributed with the uniform density (Poisson point processes) is studied. The rate-distortion function per point for n neighboring points Rn(D) is introduced and the function R (D) is defined as a limitting function of Rn(D) for infinitely large n. A Shannon lower bound for the rate-distortion function is obtained and it is shown that the rate-distortion function for an interval length between neighboring points is the better lower bound. The behavior of Dmax(n), the value of D where Rn(D) first reaches zero, is studied. A coding scheme that constitutes an upper bound to R(D) is evaluated and it is shown that the rate-distortion function for the corresponding Wiener process is the better upper bound for large distortion. Some discussions are made on the coding theorem for our problem.