Dynamic Index Coding for Wireless Broadcast Networks

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. We represent the problem by a bipartite demand graph. Uncoded transmission is optimal if and only if this graph is acyclic. Next, we define a code-constrained capacity region that restricts attention to any prespecified set of coding actions. A dynamic max-weight algorithm that acts over variable length frames is developed. The algorithm allows for random packet arrivals and supports any traffic inside the code-constrained capacity region. A simple set of codes that exploit cycles in the demand graph are shown to be optimal for a class of broadcast relay problems.

[1]  Noga Alon,et al.  Broadcasting with Side Information , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[2]  Alexander Sprintson,et al.  On the Index Coding Problem and Its Relation to Network Coding and Matroid Theory , 2008, IEEE Transactions on Information Theory.

[3]  Yitzhak Birk,et al.  Informed-source coding-on-demand (ISCOD) over broadcast channels , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[4]  Alexandros G. Dimakis,et al.  Bipartite index coding , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[5]  M.A.R. Chaudhry,et al.  Efficient algorithms for Index Coding , 2008, IEEE INFOCOM Workshops 2008.

[6]  Ziv Bar-Yossef,et al.  Index Coding With Side Information , 2006, IEEE Transactions on Information Theory.

[7]  Alexander Sprintson,et al.  On the Minimum Number of Transmissions in Single-Hop Wireless Coding Networks , 2007, 2007 IEEE Information Theory Workshop.

[8]  Muriel Médard,et al.  XORs in the Air: Practical Wireless Network Coding , 2006, IEEE/ACM Transactions on Networking.

[9]  Yitzhak Birk,et al.  Coding on demand by an informed source (ISCOD) for efficient broadcast of different supplemental data to caching clients , 2006, IEEE Transactions on Information Theory.

[10]  Yunnan Wu,et al.  The Local Mixing Problem , 2006 .

[11]  Yunnan Wu,et al.  Information Exchange in Wireless Networks with Network Coding and Physical-layer Broadcast , 2004 .

[12]  Michael Langberg,et al.  On the Hardness of Approximating the Network Coding Capacity , 2008, IEEE Transactions on Information Theory.

[13]  Xuemin Chen,et al.  Error-Control Coding for Data Networks , 1999 .

[14]  M. Neely.  Queue Stability and Probability 1 Convergence via Lyapunov Optimization , 2010, 1008.3519.

[15]  Leandros Tassiulas,et al.  Dynamic server allocation to parallel queues with randomly varying connectivity , 1993, IEEE Trans. Inf. Theory.

[16]  Vineeth Bala Sukumaran,et al.  Average-delay optimal policies for the point-to-point channel , 2009, 2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks.

[17]  Zhen Zhang,et al.  Dynamic index coding for wireless broadcast networks , 2012, INFOCOM.

[18]  Tracey Ho,et al.  A Random Linear Network Coding Approach to Multicast , 2006, IEEE Transactions on Information Theory.

[19]  Sachin Katti,et al.  The Importance of Being Opportunistic: Practical Network Coding for Wireless Environments , 2005 .

[20]  Michael J. Neely,et al.  Stability and Probability 1 Convergence for Queueing Networks via Lyapunov Optimization , 2012, J. Appl. Math..

[21]  Uri Stav,et al.  Nonlinear Index Coding Outperforming the Linear Optimum , 2007, IEEE Transactions on Information Theory.