Network Code Design for Orthogonal Two-hop Network with Broadcasting Relay: A Joint Source-Channel-Network Coding Approach

This paper addresses network code design for robust transmission of sources over an orthogonal two-hop wireless network with a broadcasting relay. The network consists of multiple sources and destinations in which each destination, benefiting the relay signal, intends to decode a subset of the sources. Two special instances of this network are orthogonal broadcast relay channel and the orthogonal multiple access relay channel. The focus is on complexity constrained scenarios, e.g., for wireless sensor networks, where channel coding is practically imperfect. Taking a source-channel and network coding approach, we design the network code (mapping) at the relay such that the average reconstruction distortion at the destinations is minimized. To this end, by decomposing the distortion into its components, an efficient design algorithm is proposed. The resulting network code is nonlinear and substantially outperforms the best performing linear network code. A motivating formulation of a family of structured nonlinear network codes is also presented. Numerical results and comparison with linear network coding at the relay and the corresponding distortion-power bound demonstrate the effectiveness of the proposed schemes and a promising research direction.Comment: 27 pages, 9 figures, Submited to IEEE Transaction on Communicatio

Access Policy Design for Cognitive Secondary Users under a Primary Type-I HARQ Process

In this paper, an underlay cognitive radio network that consists of an arbitrary number of secondary users (SU) is considered, in which the primary user (PU) employs Type-I Hybrid Automatic Repeat Request (HARQ). Exploiting the redundancy in PU retransmissions, each SU receiver applies forward interference cancelation to remove a successfully decoded PU message in the subsequent PU retransmissions. The knowledge of the PU message state at the SU receivers and the ACK/NACK message from the PU receiver are sent back to the transmitters. With this approach and using a Constrained Markov Decision Process (CMDP) model and Constrained Multi-agent MDP (CMMDP), centralized and decentralized optimum access policies for SUs are proposed to maximize their average sum throughput under a PU throughput constraint. In the decentralized case, the channel access decision of each SU is unknown to the other SU. Numerical results demonstrate the benefits of the proposed policies in terms of sum throughput of SUs. The results also reveal that the centralized access policy design outperforms the decentralized design especially when the PU can tolerate a low average long term throughput. Finally, the difficulties in decentralized access policy design with partial state information are discussed

Groups having complete bipartite divisor graphs for their conjugacy class sizes

Given a finite group G, the bipartite divisor graph for its conjugacy class sizes is the bipartite graph with bipartition consisting of the set of conjugacy class sizes of G-Z (where Z denotes the centre of G) and the set of prime numbers that divide these conjugacy class sizes, and with {p,n} being an edge if gcd(p,n)\neq 1. In this paper we construct infinitely many groups whose bipartite divisor graph for their conjugacy class sizes is the complete bipartite graph K_{2,5}, giving a solution to a question of Taeri.Comment: 5 page