English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The rate-distortion saddle-point problem considered by Lapidoth (1997)consists in finding the minimum rate to compress an arbitrary ergodic sourcewhen one is constrained to use a random Gaussian codebook and minimum(Euclidean) distance encoding is employed. We extend Lapidoth's analysis inseveral directions in this paper. Firstly, we consider refined asymptotics. Inparticular, when the source is stationary and memoryless, we establish thesecond-order, moderate, and large deviation asymptotics of the problem.Secondly, by "random Gaussian codebook", Lapidoth referred to a collection ofrandom codewords, each of which is drawn independently and uniformly from thesurface of an $n$-dimensional sphere. To be more precise, we term this as aspherical codebook. We also consider i.i.d.\ Gaussian codebooks in which eachrandom codeword is drawn independently from a product Gaussian distribution. Wederive the second-order, moderate, and large deviation asymptotics when i.i.d.\Gaussian codebooks are employed. In contrast to the recent work on the channelcoding counterpart by Scarlett, Tan and Durisi (2017), the dispersions forspherical and i.i.d.\ Gaussian codebooks are identical. The ensembleexcess-distortion exponents for both spherical and i.i.d.\ Gaussian codebooksare established for all rates. Furthermore, we show that the i.i.d.\ Gaussiancodebook has a strictly larger excess-distortion exponent than its sphericalcounterpart for any rate greater than the ensemble rate-distortion functionderived by Lapidoth.

Refined Asymptotics for Rate-Distortion using Gaussian Codebooks for Arbitrary Sources