The Sphere Packing Bound for DSPCs With Feedback à la Augustin

Nakiboğlu, Barış

doi:10.1109/tcomm.2019.2931302

Cited by 6 publications

(7 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Polyanskiy and Verdú [ 34 ] extended the exponential strong converse theorem to channels with feedback. Augustin [ 21 ] and Nakiboğlu [ 35 , 36 ] extended the sphere packing bound to channels with feedback.…”

Section: Sibson’s Conditional Rényi Divergencementioning

confidence: 99%

Conditional Rényi Divergences and Horse Betting

Bleuler

Lapidoth

Pfister

2020

Entropy

View full text Add to dashboard Cite

Motivated by a horse betting problem, a new conditional Rényi divergence is introduced. It is compared with the conditional Rényi divergences that appear in the definitions of the dependence measures by Csiszár and Sibson, and the properties of all three are studied with emphasis on their behavior under data processing. In the same way that Csiszár’s and Sibson’s conditional divergence lead to the respective dependence measures, so does the new conditional divergence lead to the Lapidoth–Pfister mutual information. Moreover, the new conditional divergence is also related to the Arimoto–Rényi conditional entropy and to Arimoto’s measure of dependence. In the second part of the paper, the horse betting problem is analyzed where, instead of Kelly’s expected log-wealth criterion, a more general family of power-mean utility functions is considered. The key role in the analysis is played by the Rényi divergence, and in the setting where the gambler has access to side information, the new conditional Rényi divergence is key. The setting with side information also provides another operational meaning to the Lapidoth–Pfister mutual information. Finally, a universal strategy for independent and identically distributed races is presented that—without knowing the winning probabilities or the parameter of the utility function—asymptotically maximizes the gambler’s utility function.

show abstract

Section: Sibson’s Conditional Rényi Divergencementioning

confidence: 99%

Conditional Rényi Divergences and Horse Betting

Bleuler

Lapidoth

Pfister

2020

Entropy

View full text Add to dashboard Cite

show abstract

“…The formal definition of the product channels with feedback and the proof of the SPB on these channels without the symmetry assumptions can be found in [6,38,39].…”

Section: Remark 54mentioning

confidence: 99%

A simple derivation of the refined sphere packing bound under certain symmetry hypotheses

Nakiboğlu¹

2020

Turk J Math

Self Cite

View full text Add to dashboard Cite

A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is Ω (n −0.5(1−E ′ sp (R))) for all codes on certain families of channels (including the Gaussian channels and the nonstationary Rényi symmetric channels) and for the constant composition codes on stationary memoryless channels. The resulting nonasymptotic bounds have definite approximation error terms. As a preliminary result that might be of interest on its own, the trade-off between type I and type II error probabilities in the hypothesis testing problem with (possibly non-stationary) independent samples is determined up to some multiplicative constants, assuming that the probabilities of both types of error are decaying exponentially with the number of samples, using the Berry-Esseen theorem.

show abstract

“…Palaiyanur discussed Augustin's proof sketch in more detail in his thesis [55, A.8]. A complete proof following Augustin's sketch can be found in [47].…”

Section: A Non-asymptotic Spb For Product Channels With Feedbackmentioning

confidence: 99%

“…41.7] are O n − 1 /3 ln n rather than O n − 1 /4 ln n . A complete proof of SPB for codes on DSPCs with feedback following Augustin's sketch can be found in [47].…”

Section: Extensions and Comparisonsmentioning

confidence: 99%

See 1 more Smart Citation

The Sphere Packing Bound via Augustin’s Method

Nakiboğlu

2019

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

Canım halam Fatma Nakiboglu Aydiç'in anısına adanmıştır. Dedicated to the memory of my dear aunt Fatma Nakiboglu Aydiç.Abstract-A sphere packing bound (SPB) with a prefactor that is polynomial in the block length n is established for codes on a length n product channel W [1,n] assuming that the maximum order ½ Rényi capacity among the component channels, i.e. max t∈[1,n] C1 /2,Wt , is O(ln n). The reliability function of the discrete stationary product channels with feedback is bounded from above by the sphere packing exponent. Both results are proved by first establishing a non-asymptotic SPB. The latter result continues to hold under a milder stationarity hypothesis.

show abstract

The Sphere Packing Bound for DSPCs With Feedback à la Augustin

Cited by 6 publications

References 33 publications

Conditional Rényi Divergences and Horse Betting

Conditional Rényi Divergences and Horse Betting

A simple derivation of the refined sphere packing bound under certain symmetry hypotheses

The Sphere Packing Bound via Augustin’s Method

Contact Info

Product

Resources

About