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Lossy Compression With Universal distortion

IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第6期69卷 3552-3573页

作者： Mahmood, Adeel Wagner, Aaron B. Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

We consider a novel variant of d-semifaithful lossy coding in which the distortion measure is revealed only to the encoder and only at run-time, as well as an extension of it in which the distortion constraint d is also revealed at run-time. Two forms of rate redundancy are used to analyze the performance, and achievability results of both a pointwise and minimax nature are demonstrated. The first coding scheme uses ideas from VC dimension and growth functions, the second uses appropriate quantization of the space of distortion measures, and the third relies on a random coding argument.

关键词： Lossy compression universal source coding quantization VC dimension d-semifaithful code

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On Universal d-semifaithful Coding for Memoryless Sources With Infinite Alphabets

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IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第4期68卷 2782-2800页

作者： Silva, Jorge F. Piantanida, Pablo Univ Chile Informat & Decis Syst IDS Grp Santiago 8370451 Chile Univ Paris Saclay Lab Signaux & Syst L25 CNRS Cent Supelec F-91190 Gif Sur Yvette France

The problem of variable length and fixed-distortion universal source coding (or d-semifaithful source coding) for stationary and memoryless sources on countably infinite alphabets (infinity -alphabets) is addressed in this paper. The main results of this work offer a set of sufficient conditions (from weaker to stronger) to obtain weak minimax universality, strong minimax universality, and corresponding achievable rates of convergences for the worst-case redundancy for the family of stationary memoryless sources whose densities are dominated by an envelope function (or the envelope family) on infinity-alphabets. An important implication of these results is that universal d-semifaithful source coding is not feasible for the complete family of stationary and memoryless sources on infinity-alphabets. To demonstrate this infeasibility, a sufficient condition for the impossibility is presented for the envelope family. Interestingly, it matches the well-known impossibility condition in the context of lossless (variable-length) universal source coding. More generally, this work offers a simple description of what is needed to achieve universal d-semifaithful coding for a family of distributions Lambda. This reduces to finding a collection of quantizations of the product space at different blocklengths - reflecting the fixed distortion restriction - that satisfy two asymptotic requirements: the first is a universal quantization condition with respect to Lambda, and the second is a vanishing information radius (I-radius) condition for Lambda reminiscent of the condition known for lossless universal source coding.

关键词： Lossy compression variable length source coding d-semifaithful code universal source coding infinite alphabets strong minimax universality information radius universal quantization envelope families

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Minimax Rate-distortion

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第12期69卷 7712-7737页

作者： Mahmood, Adeel Wagner, Aaron B. Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

We show the existence of variable-rate rate distortion codes that meet the distortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is revealed only to the encoder and only at runtime. If we only require minimax universality with respect to the source distribution and not the distortion measure, then we provide an achievable O(1/root n) redundancy rate, which we show is optimal. This is in contrast to prior work on universal lossy compression, which provides O (log n/n) redundancy guarantees for weakly universal codes under various regularity conditions. We show that either eliminating the regularity conditions or upgrading to strong universality while keeping these regularity conditions entails an inevitable increase in the redundancy to O(1/root n). Our construction involves random coding with non-i.i.d. codewords and a zero-rate uncoded transmission scheme. The proof uses exact asymptotics from large deviations, acceptance-rejection sampling, and the VC dimension of distortion measures.

关键词： Lossy compression universal source coding quantization VC dimension d-semifaithful code

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Lossy Compression with Universal distortion

Lossy Compression with Universal Distortion

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IEEE International Symposium on Information Theory (ISIT)

作者： Mahmood, Adeel Wagner, Aaron B. Cornell Univ Sch Elect & Comp Engn Ithaca NY 14850 USA

ISBN: (纸本)9781665421607;9781665421591

We consider a novel variant of lossy coding in which the distortion measure is revealed only to the encoder and only at run-time, as well as an extension of it in which the distortion constraint is also revealed at run-time. Two forms of rate redundancy are used to analyze the performance, and achievability results of both a pointwise and minimax nature are demonstrated. One proof uses appropriate quantization of the space of distortion measures while another uses ideas from VC dimension and growth functions.

关键词： compression universal source coding quantization VC dimension d-semifaithful code

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Minimax Rate-distortion

Minimax Rate-Distortion

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IEEE International Symposium on Information Theory (ISIT)

作者： Mahmood, Adeel Wagner, Aaron B. Cornell Univ Sch Elect & Comp Engn Ithaca NY 14850 USA

ISBN: (纸本)9781665421607;9781665421591

We show the existence of universal, variable-rate rate-distortion codes that meet the distortion constraint almost surely and approach the rate-distortion function uniformly with respect to an unknown source distribution and a distortion measure that is only revealed to the encoder and only at run-time. If the convergence only needs to be uniform with respect to the source distribution and not the distortion measure, then we provide an explicit bound on the minimax rate of convergence. Our construction combines conventional random coding with a zero-rate uncoded transmission scheme. The proof uses exact asymptotics from large deviations, acceptance-rejection sampling, the VC dimension of distortion measures, and the identification of an explicit, code-independent, finite-blocklength quantity, which converges to the rate-distortion function, that controls the performance of the best codes.

关键词： Lossy compression universal source coding quantization VC dimension d-semifaithful code

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