Universal codes for finite sequences of integers drawn from a monotone distribution

نویسندگان

  • Dean P. Foster
  • Robert A. Stine
  • Abraham J. Wyner
چکیده

We offer two noiseless codes for blocks of integers Xn = (X1, . . . , Xn). We provide explicit bounds on the relative redundancy that are valid for any distribution F in the class of memoryless sources with a possibly infinite alphabet whose marginal distribution is monotone. Specifically we show that the expected code length L(Xn) of our first universal code is dominated by a linear function of the entropy of Xn. Further, we present a second universal code that is efficient in that its length is bounded by nHF + o(nHF ), where HF is the entropy of F which is allowed to vary with n. Since these bounds hold for any n and any monotone F we are able to show that our codes are strongly minimax with respect to relative redundancy (as defined by Elias). Key Phrases: Universal noiseless coding of integers, Elias codes, Wyner’s inequality, relative redundancy, strongly minimax. ∗Version Id: blockCode.tex,v 1.31 2001/10/24 16:06:28 bob Exp

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عنوان ژورنال:
  • IEEE Trans. Information Theory

دوره 48  شماره 

صفحات  -

تاریخ انتشار 2002