Gastvortrag am 07.06.2017 um 13:15 Uhr von Dr. Joseph Renes (ETH Zürich) mit dem Thema "Duality of channels and codes"
Am Mittwoch, 7. Juni 2017, 13:15 Uhr (Raum N4110) hält Dr. Joseph Renes vom Institute for Theoretical Physics (ETH Zürich) einen Gastvortrag zum Thema
Duality of channels and codes
For any given channel with classical inputs and possibly quantum outputs, quantum mechanics allows us to define a dual classical-input channel by viewing both as different parts of the same quantum channel. In this talk I will describe how the new uncertainty relations for a general class of entropies imply that the performance of a given code over a given channel is entirely characterized by the performance of the dual code on the dual channel. This has several applications. In the context of polar codes, it implies that the rates of polarization to ideal and useless channels must be identical. Duality also relates the tasks of channel coding and privacy amplification, implying that the finite blocklength performance of extractors and codes is precisely linked, and that optimal rate extractors can be transformed into capacity-achieving codes, and vice versa. Finally, duality also extends to the EXIT function of any channel and code. Here it implies that for any channel family, if the EXIT function for a fixed code has a sharp transition, then it must be such that the rate of the code equals the capacity at the transition. This may give a different route to proving a code family achieves capacity by establishing sharp EXIT function transitions.