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On the cost of finite block length in quantizing unbounded memoryless sources

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2 Author(s)
Linder, T. ; Dept. of Math. & Comput. Sci., Tech. Univ. Budapest, Hungary ; Zeger, K.

The problem of fixed-rate block quantization of an unbounded real memoryless source is studied. It is proved that if the source has a finite sixth moment, then there exists a sequence of quantizers Qn of increasing dimension n and fixed rate R such that the mean squared distortion Δ(Qn) is bounded as Δ(Qn )⩽D(R)+O(√(log n/n)), where D(R) is the distortion-rate function of the source. Applications of this result include the evaluation of the distortion redundancy of fixed-rate universal quantizers, and the generalization to the non-Gaussian case of a result of Wyner on the transmission of a quantized Gaussian source over a memoryless channel

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Information Theory, IEEE Transactions on  (Volume:42 ,  Issue: 2 )