Rényi divergence and generalized channel capacity relation

Let QQ be a non-uniform distribution and UU the uniform distribution on a support of cardinality 2n2^n. Let TT be the matrix with two rows, QQ and UU, and 2n2^n columns. The quantities D1/2(QU)D_{1/2}(Q\|U) and C1/2(T)C_{1/2}(T) denote, respectively, Rényi's divergence of degree 1/21/2 and the generalized channel capacity of degree 1/21/2 (identified here with the standard Shannon channel capacity). The Rényi–capacity conjecture.

D1/2(QU)=2C1/2(T).D_{1/2}(Q\|U)=2\cdot C_{1/2}(T).

This conjecture proposes an exact quantitative relation between Rényi divergence and channel capacity for the binary-input channel whose rows are QQ and UU. The supplied text gives no evidence that the relation has been proved or disproved.

Sources & referencesView supporting material

Primary source

Yi Janet Lu, “New Results on the DMC Capacity and Renyi's Divergence”, arXiv:1708.00979 (2017).

Additional references

2 papers in this index state this conjecture (2016–2017). The statement above is taken from the most recent of them; the others are arXiv:1602.00095.

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