Extremality Properties for Gallager's Random Coding Exponent

Mine Alsan

École Polytechnique Fédérale de Lausanne (EPFL)
Laboratory of Information Theory
Lausanne, Switzerland

Abstract:

We describe certain extremality properties for Gallager’s reliability function E0(ρ), for ρ ∈ [0, 1], for binary input symmetric DMCs. In particular, we show that amongst such DMC’s whose E0(ρ1) has a given value for a given ρ1, the BEC and BSC have the largest and smallest value of the derivative of E0(ρ2) for any ρ2 ≥ ρ1. As the random coding exponent is obtained by tracing the map ρ → (E0(ρ), E0(ρ) − ρE0(ρ)) this conclusion includes as a special case recent results by Fabregas et al. Furthermore, we show that amongst channels W with a given value of E0(ρ) for a given ρ the BEC and BSC are the most and least polarizing under Arıkan’s polar transformations in the sense that their polar transforms W + and W − have the largest and smallest difference in their E0 values.

Biography:

Mine Alsan received the B.Sc. degree in electrical and electronics engineering from the Middle East Technical University, Ankara, Turkey, in 2007. She received the M.Sc degree in communication systems from the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland, in 2010. Currently, she is pursuing a Ph.D degree in the laboratory of information theory at EPFL.