Finite block length converse results for channel coding and assistance by non-signalling correlations

Physics – Quantum Physics

Scientific paper

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8 pages

Scientific paper

A non-signalling assisted code is a block code in which the sender and receiver can be correlated in any way that would not by itself allow signalling between them. The maximum rate that can be achieved by such a code for a given block length and error probability is formulated as a linear program. This provides a finite block length converse for classical codes which we show is identical to one derived by Polyanskiy, Poor and Verd\'{u}. This shows that the many classical asymptotic and finite converse results which can be derived from this converse apply equally to entanglement assisted codes which have been recently studied. It also gives an explicit linear programming formulation of the converse which has some useful features.

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