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Even after three decades of research, the Berger-Tung problem remains open. The usual method attempts to identify the eponymous inner and outer bounds, tacitly bypassing the natural reference of the unwieldy operational definition. In this context, we show that the inner and outer bounds sometimes differ, making the usual approach untenable. As an alternative, we axiomatically reformulate the problem...
Principles behind lossless and lossy coding are usually considered related, yet distinct. In contrast, we show that the direct statements of the rate-distortion theorem and the lossless coding theorem are consequences of a common distortion-abstracted phenomenon. Significantly, we extend such distortion abstraction to a more general multiterminal framework, and derive a canonical direct theorem that...
Consider the two-terminal partial side information problem, where one source is decoded under a distortion measure, while the other acts as a helper. There are two well known inner bounds on the (convex) achievable region: (i) a bound due to Berger et al., and (ii) a suitable specialization of the general Berger-Tung bound. While the former bound admits a simpler description compared to the latter,...
In this paper, we consider a class of multiterminal source coding problems, where all sources, except one, are reconstructed perfectly. Our framework generalizes the hitherto open single helper problems due to Csiszar and Korner, by adding complete side information at the decoder, and lossy reconstruction of the remaining source. In this setup we obtain a single-letter characterization (bearing resemblance...
The issue of source/channel duality is as old as information theory itself. Whereas type covering has been identified as a basis for source coding and sphere packing as the basis for channel coding, very little effort has been directed at tying covering and packing together. In this paper, a covering result has been derived which gives asymptotically optimal packing as well. We propose our covering/packing...
We present a single letter characterization of the secrecy capacity of the single-input multiple-outputs (SIMO) channel under Gaussian (and possibly colored) noise. To do so, we transform the channel into a scalar Gaussian wiretap channel using standard techniques of communications theory. The result is used to study the impact of slow fading on the secrecy capacity of the channel, and how the use...
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