Graph-Theoretic Approaches to Two-Sender Index Coding

Consider a communication scenario over a noiseless channel where a sender is required to broadcast messages to multiple receivers, each having side information about some messages. In this scenario, the sender can leverage the receivers' side information during the encoding of messages in order to reduce the required transmissions. This type of encoding is called index coding. In this paper, we study index coding with two cooperative senders, each with some subset of messages, and multiple receivers, each requesting one unique message. The index coding in this setup is called two-sender unicast index coding (TSUIC). The main aim of TSUIC is to minimize the total number of transmissions required by the two senders. Based on graph-theoretic approaches, we prove that TSUIC is equivalent to single-sender unicast index coding (SSUIC) for some special cases. Moreover, we extend the existing schemes for SSUIC, viz., the cycle-cover scheme, the clique-cover scheme, and the local-chromatic scheme to the corresponding schemes for TSUIC.Comment: To be presented at 2016 IEEE Global Communications Conference (GLOBECOM 2016) Workshop on Network Coding and Applications (NetCod), Washington, USA, 201

Wireless Video Transmission with Over-the-Air Packet Mixing

In this paper, we propose a system for wireless video transmission with a wireless physical layer (PHY) that supports cooperative forwarding of interfered/superimposed packets. Our system model considers multiple and independent unicast transmissions between network nodes while a number of them serve as relays of the interfered/superimposed signals. For this new PHY the average transmission rate that each node can achieve is estimated first. Next, we formulate a utility optimization framework for the video transmission problem and we show that it can be simplified due to the features of the new PHY. Simulation results reveal the system operating regions for which superimposing wireless packets is a better choice than a typical cooperative PHY.Comment: 2012 Packet Video Worksho

Delay Reduction in Multi-Hop Device-to-Device Communication using Network Coding

This paper considers the problem of reducing the broadcast decoding delay of wireless networks using instantly decodable network coding (IDNC) based device-to-device (D2D) communications. In a D2D configuration, devices in the network can help hasten the recovery of the lost packets of other devices in their transmission range by sending network coded packets. Unlike previous works that assumed fully connected network, this paper proposes a partially connected configuration in which the decision should be made not only on the packet combinations but also on the set of transmitting devices. First, the different events occurring at each device are identified so as to derive an expression for the probability distribution of the decoding delay. The joint optimization problem over the set of transmitting devices and the packet combinations of each is, then, formulated. The optimal solution of the joint optimization problem is derived using a graph theory approach by introducing the cooperation graph and reformulating the problem as a maximum weight clique problem in which the weight of each vertex is the contribution of the device identified by the vertex. Through extensive simulations, the decoding delay experienced by all devices in the Point to Multi-Point (PMP) configuration, the fully connected D2D (FC-D2D) configuration and the more practical partially connected D2D (PC-D2D) configuration are compared. Numerical results suggest that the PC-D2D outperforms the FC-D2D and provides appreciable gain especially for poorly connected networks

The Single-Uniprior Index-Coding Problem: The Single-Sender Case and The Multi-Sender Extension

Index coding studies multiterminal source-coding problems where a set of receivers are required to decode multiple (possibly different) messages from a common broadcast, and they each know some messages a priori. In this paper, at the receiver end, we consider a special setting where each receiver knows only one message a priori, and each message is known to only one receiver. At the broadcasting end, we consider a generalized setting where there could be multiple senders, and each sender knows a subset of the messages. The senders collaborate to transmit an index code. This work looks at minimizing the number of total coded bits the senders are required to transmit. When there is only one sender, we propose a pruning algorithm to find a lower bound on the optimal (i.e., the shortest) index codelength, and show that it is achievable by linear index codes. When there are two or more senders, we propose an appending technique to be used in conjunction with the pruning technique to give a lower bound on the optimal index codelength; we also derive an upper bound based on cyclic codes. While the two bounds do not match in general, for the special case where no two distinct senders know any message in common, the bounds match, giving the optimal index codelength. The results are expressed in terms of strongly connected components in directed graphs that represent the index-coding problems.Comment: Author final manuscrip