The Sphere Packing Bound via Augustin's Method

Baris Nakiboglu

doi:10.1109/tit.2018.2882547

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arXiv · 1611.06924

The Sphere Packing Bound via Augustin's Method

Baris Nakiboglu

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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 $1/2$ Renyi capacity among the component channels, i.e. $\max_{t\in[1,n]} C_{1/2,W_{t}}$, is $\mathit{O}(\ln n)$. 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.

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Baris Nakiboglu. 2016-11-21. The Sphere Packing Bound via Augustin's Method. https://doi.org/10.1109/tit.2018.2882547

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