Extremality Properties for Gallager's Random Coding Exponent

We describe certain extremality properties for Gallager's reliability function E-0 for binary input symmetric DMCs. In particular, we show that amongst such DMC's whose E-0(rho(1)) has a given value for a given rho(1), the BEC and BSC have the largest and smallest value of the derivative of E-0(rho(2)) for any rho(2) >= rho(1). As the random coding exponent is obtained by tracing the map rho -> (E-0'(rho), E-0(rho) - rho E-0'(rho)) this conclusion includes as a special case the results of [1]. Furthermore, we show that amongst channels W with a given value of E-0(rho) for a given rho the BEC and BSC are the most and least polarizing under Arikan's polar transformations in the sense that their polar transforms W+ and W- has the largest and smallest difference in their E-0 values.


Published in:
2012 Ieee International Symposium On Information Theory Proceedings (Isit)
Presented at:
IEEE International Symposium on Information Theory
Year:
2012
Publisher:
New York, Ieee
ISBN:
978-1-4673-2579-0
Keywords:
Laboratories:




 Record created 2013-03-28, last modified 2018-03-17

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