Loading [MathJax]/extensions/MathMenu.js
On the Capacity of Computation Broadcast | IEEE Journals & Magazine | IEEE Xplore

On the Capacity of Computation Broadcast


Abstract:

The two-user computation broadcast problem is introduced as the setting where User 1 wants message W1 and has side-information W1', User 2 wants message W2 and has side-i...Show More

Abstract:

The two-user computation broadcast problem is introduced as the setting where User 1 wants message W1 and has side-information W1', User 2 wants message W2 and has side-information (W2', and W1, W1', W2, W2') may have arbitrary dependencies. The rate of a computation broadcast scheme is defined as the ratio H(W1, W2)/H(S), where S is the information broadcast to both users to simultaneously satisfy their demands. The supremum of achievable rates is called the capacity of computation broadcast CCB. It is shown that CCB ≤ H(W1, W2)/[H(W1|W1')+H(W2|W2')- min (I(W1; W2, W2'|W1'), I(W2; W1, W1'|W2'))] . For the linear computation broadcast problem, where W1, W1', W2, W2' are comprised of arbitrary linear combinations of a basis set of independent symbols, the bound is shown to be tight. For non-linear computation broadcast, it is shown that this bound is not tight in general. Examples are provided to prove that different instances of computation broadcast that have the same entropic structure, i.e., the same entropy for all subsets of {W1, W1', W2, W2'}, can have different capacities. Thus, extra-entropic structure matters even for two-user computation broadcast. The significance of extra-entropic structure is further explored through a class of non-linear computation broadcast problems where the extremal values of capacity are shown to correspond to minimally and maximally structured problems within that class.
Published in: IEEE Transactions on Information Theory ( Volume: 66, Issue: 6, June 2020)
Page(s): 3417 - 3434
Date of Publication: 16 December 2019

ISSN Information:

Funding Agency:


References

References is not available for this document.