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Operational Duality Between Lossy Compression and Channel Coding

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2 Author(s)
Gupta, A. ; Samsung Telecommun. America, Richardson, TX, USA ; Verdu, S.

We explore the duality between lossy compression and channel coding in the operational sense: whether a capacity-achieving encoder-decoder sequence achieves the rate-distortion function of the dual problem when the channel decoder [encoder] is the source compressor [decompressor, resp.], and vice versa. We show that, if used as a lossy compressor, the maximum-likelihood channel decoder of a randomly chosen capacity-achieving codebook achieves the rate-distortion function almost surely. However, operational duality does not hold for every capacity achieving encoder-decoder sequence, or rate-distortion achieving compressor-decompressor sequence. We show that there exist optimal channel coding [lossy compression] schemes, which fail when used for the dual lossy compression [channel coding resp.] problem.

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Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 6 )