On Optimum Conventional Quantization for Source Coding with Side Information at the Decoder

Let X and Y denote two jointly memoryless sources with finite alphabets. Suppose that X is to be encoded in a lossy manner with Y as the side information available only at the decoder. A common approach to this lossy source coding problem is to apply conventional vector quantization followed by Slep...

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Vydané v:2007 10th Canadian Workshop on Information Theory, Edmonton, AB, Canada, 6-8 June 2007 s. 97 - 100
Hlavní autori: Zheng, Lin, He, Da-ke, Yang, En-hui
Médium: Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: IEEE 01.06.2007
Predmet:
Convergence
Decoding
Distortion measurement
Helium
Particle measurements
Random variables
Rate-distortion
Source coding
Vector quantization
ISBN:9781424407682, 1424407680
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Shrnutí:Let X and Y denote two jointly memoryless sources with finite alphabets. Suppose that X is to be encoded in a lossy manner with Y as the side information available only at the decoder. A common approach to this lossy source coding problem is to apply conventional vector quantization followed by Slepian-Wolf coding. In this paper we are interested in the rate-distortion performance achievable asymptotically by this approach. Given an arbitrary single letter distortion measure d , it is shown that the best rate achievable asymptotically under the constraint that X is recovered with distortion level no greater than D ≥ 0 is R̂ wz (D) = min times [I(X;X̂)-I(Y; X̂)] , where the minimum is taken over all auxiliary random variables X such that Ed(X, X̂) ≤ D and X ̂⟶ X ⟶ Y is a Markov chain. An extended Blahut-Arimoto algorithm is then proposed to calculate R̂ wz (D) for any (X,Y) and any distortion measure, and the convergence of the algorithm is also proved. Interestingly, it is observed that the random variable X̂ achieving R̂ wz (D) is, in general, different from the random variable X̂' achieving the classical rate-distortion function R(D) of X at distortion D . In particular, it is shown that in the case of binary sources and Hamming distortion measure, the random variable X achieving R wz (D) is the same as the random variable X' achieving R(D) if and only if the channel P Y|X from X to Y is symmetric. Thus, the design of conventional quantization in the case of side information at the decoder should be different from the case of no side information.
ISBN:9781424407682
1424407680
DOI:10.1109/CWIT.2007.375710