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Beta-beta bounds: Finite-blocklength analog of the golden formula
Journal article, 2018

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 (2002) 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 exponentialnoise 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.

finite-blocklength regime

Channel coding

hypothesis testing

golden formula

achievability bound

## Author

### Wei Yang

Qualcomm Technologies

### Austin Collins

Massachusetts Institute of Technology (MIT)

### Giuseppe Durisi

Chalmers, Electrical Engineering, Communication and Antenna Systems, Communication Systems

### Yury Polyanskiy

Massachusetts Institute of Technology (MIT)

### Vincent Poor

Princeton University

#### IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 64 9 6236-6256 8360156### SWIFT : short-packet wireless information theory

Swedish Research Council (VR), 2017-01-01 -- 2020-12-31.

### Areas of Advance

Information and Communication Technology

### Subject Categories

Telecommunications

Signal Processing

Mathematical Analysis

### DOI

10.1109/TIT.2018.2837104