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|a Yang, Wei
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|a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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|a Collins, Austin Daniel
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|a Durisi, Giuseppe
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|a Polyanskiy, Yury
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|a Poor, H. Vincent
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|a Beta-Beta Bounds: Finite-Blocklength Analog of the Golden Formula
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|b Institute of Electrical and Electronics Engineers (IEEE),
|c 2020-03-25T14:31:20Z.
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|z Get fulltext
|u https://hdl.handle.net/1721.1/124314
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|a It is well known that the mutual information between two random variables can be expressed as the difference of two relative entropies that depend on an auxiliary distribution, a relation sometimes referred to as the golden formula. This paper is concerned with a finite-blocklength extension of this relation. This extension consists of two elements: 1) a finite-blocklength channel-coding converse bound by Polyanskiy and Verdú, which involves the ratio of two Neyman-Pearson $\beta $ functions (beta-beta converse bound); and 2) a novel beta-beta channel-coding achievability bound, expressed again as the ratio of two Neyman-Pearson $\beta $ functions. To demonstrate the usefulness of this finite-blocklength extension of the golden formula, the beta-beta achievability and converse bounds are used to obtain a finite-blocklength extension of Verdú's wideband-slope approximation. The proof parallels the derivation of the latter, with the beta-beta bounds used in place of the golden formula. The beta-beta (achievability) bound is also shown to be useful in cases where the capacity-achieving output distribution is not a product distribution due to, e.g., a cost constraint or structural constraints on the codebook, such as orthogonality or constant composition. As an example, the bound is used to characterize the channel dispersion of the additive exponential-noise channel and to obtain a finite-blocklength achievability bound (the tightest to date) for multiple-input multiple-output Rayleigh-fading channels with perfect channel state information at the receiver.
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|a National Science Foundation (10.13039/100000001)
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|a Swedish Research Council
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|a Center for Science of Information
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|a en
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|a Article
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|t IEEE Transactions on Information Theory
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