No abstract

We consider a wireless broadcast station that transmits packets to multiple users. The packet requests for each user may overlap, and some users may already have certain packets. This presents a problem of broadcasting in the presence of side information, and is a generalization of the well known (and unsolved) index coding problem of information theory. Rather than achieving the full capacity region, we develop a code-constrained capacity region, which restricts attention to a pre-specified set of coding actions. We develop a dynamic maxweight algorithm that allows for random packet arrivals and supports any traffic inside the code-constrained capacity region. Further, we provide a simple set of codes based on cycles in the underlying demand graph. We show these codes are optimal for a class of broadcast relay problems.

The Singleton bound and MDS codes 4.3 Network erasure/error correction and error detection 4.4 Further remarks II MULTIPLE SOURCES 5 Superposition Coding and Max-Flow Bound 5.1 Superposition coding 5.2 The max-flow bound 6 Network Codes for Acyclic Networks 6.1 Achievable information rate region 6.2 Inner bound R in 6.3 Outer bound R out 6.4 R LP-An explicit outer bound 7 Fundamental Limits of Linear Codes 7.1 Linear network codes for multiple sources 7.2 Entropy and the rank function 7.3 Can nonlinear codes be better asymptotically?