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We consider a stationary source emitting letters from a finite alphabet A. The source is described by a stationary probability measure α on the space Ω:=A^{IN} of sequences of letters. Denote by Ω_{n} the set of words of length n and by α_{n} the probability measure induced on Ω_{n } by α. We consider sequences {Γ_{n}⊂Ω_{n}: n∈IN} having special properties. Call {Γ_{n}⊂Ω_{n}: n∈IN} a supporting sequence for α if lim_{n} α _{n}[Γ_{n}]=1. It is well known that the exponential growth rate of a supporting sequence is bounded below by h _{Sh}(α), the Shannon entropy of the source α. For efficient simulation, we require Γ_{n} to be as large as possible, subject to the condition that the measure α_{n} is approximated by the equipartition measure β_{n}[·|Γ_{n}], the probability measure on Ω_{n} which gives equal weight to the words in Γ_{n} and zero weight to words outside it. We say that a sequence {Γ_{n}⊂Ω_{n}: n∈IN} is a reconstruction sequence for α if each Γ_{n} is invariant under cyclic permutations and lim_{n} β_{n }[·|Γ_{n}]=α_{m} for each m∈IN. We prove that the exponential growth rate of a reconstruction sequence is bounded above by h_{Sh}(α). We use a large-deviation property of the cyclic empirical measure to give a constructive proof of an existence theorem: if α is a stationary source, then there exists a reconstruction sequence for α having maximal exponential growth rate; if α is ergodic, then the reconstruction sequence may be chosen so as to be supporting for α. We prove also a characterization of ergodic measures which appears to be new

- Page(s):
- 1935 - 1947
- ISSN :
- 0018-9448
- INSPEC Accession Number:
- 5776995
- DOI:
- 10.1109/18.641557

- Date of Publication :
- Nov 1997
- Date of Current Version :
- 06 August 2002
- Issue Date :
- Nov 1997
- Sponsored by :
- IEEE Information Theory Society
- Publisher:
- IEEE