Index Coding Capacity: How Far Can One Go With Only Shannon Inequalities?


An interference alignment perspective is used to spot the simplest instances (minimum attainable range of edges in the alignment graph, less than two interfering messages at any destination) of index coding issues where non-Shannon info inequalities are necessary for capability characterization. In specific, this includes the primary known example of a multiple unicast (one destination per message) index coding problem where non-Shannon information inequalities are shown to be necessary. The simplest multiple unicast example has 7 edges within the alignment graph and 11 messages. The simplest multiple groupcast (multiple destinations per message) example has half-dozen edges within the alignment graph, six messages, and 10 receivers. For each the best multiple unicast and multiple groupcast instances, the most effective outer bound based on solely Shannon inequalities is 2/5, which is tightened to 11/28 by the utilization of the Zhang–Yeung non-Shannon sort info inequality, and therefore the linear capacity is shown to be five/thirteen using the Ingleton inequality. Conversely, identifying the minimal challenging aspects of the index coding problem permits an enlargement of the class of solved index coding problems up to (however not together with) these instances.

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