Title :
Extremality properties for Gallager´s random coding exponent
Author_Institution :
LTHI, EPFL, Lausanne, Switzerland
Abstract :
We describe certain extremality properties for Gallager´s reliability function Eo 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 Eo(ρ2) for any ρ2 ≥ ρ1. As the random coding exponent is obtained by tracing the map ρ → (E0´(ρ), E0(ρ) - pE´0(ρ)) this conclusion includes as a special case the results of [1]. 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- has the largest and smallest difference in their Eo values.
Keywords :
binary codes; random codes; BEC; BSC; Gallager´s random coding exponent; Gallager´s reliability function; binary input symmetric; extremality properties; polar transforms; Encoding; Equations; Erbium; Random variables; Reliability; Transforms; Channel reliability function; channel polarization; random coding exponent;
Conference_Titel :
Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
978-1-4673-2580-6
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2012.6284065