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Proving linear inequalities and identities of Shannon's information measures,possibly with linear constraints on the information measures, is an importantproblem in information theory. For this purpose, ITIP and other variantalgorithms have been developed and implemented, which are all based on solvinga linear program (LP). In particular, an identity $f = 0$ is verified bysolving two LPs, one for $f \ge 0$ and one for $f \le 0$. In this paper, wedevelop a set of algorithms that can be implemented by symbolic computation.Based on these algorithms, procedures for verifying linear informationinequalities and identities are devised. Compared with LP-based algorithms, ourprocedures can produce analytical proofs that are both human-verifiable andfree of numerical errors. Our procedures are also more efficientcomputationally. For constrained inequalities, by taking advantage of thealgebraic structure of the problem, the size of the LP that needs to be solvedcan be significantly reduced. For identities, instead of solving two LPs, theidentity can be verified directly with very little computation.

Proving Information Inequalities and Identities with Symbolic Computation