Algebraic Network Coding Approach to Deterministic Wireless Relay Networks

The deterministic wireless relay network model, introduced by Avestimehr et al., has been proposed for approximating Gaussian relay networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless medium and interference. Avestimehr et al. showed that the Min-cut Max-flow theorem holds in the ADT network. In this paper, we show that the ADT network model can be described within the algebraic network coding framework introduced by Koetter and Medard. We prove that the ADT network problem can be captured by a single matrix, called the "system matrix". We show that the min-cut of an ADT network is the rank of the system matrix; thus, eliminating the need to optimize over exponential number of cuts between two nodes to compute the min-cut of an ADT network. We extend the capacity characterization for ADT networks to a more general set of connections. Our algebraic approach not only provides the Min-cut Max-flow theorem for a single unicast/multicast connection, but also extends to non-multicast connections such as multiple multicast, disjoint multicast, and two-level multicast. We also provide sufficiency conditions for achievability in ADT networks for any general connection set. In addition, we show that the random linear network coding, a randomized distributed algorithm for network code construction, achieves capacity for the connections listed above. Finally, we extend the ADT networks to those with random erasures and cycles (thus, allowing bi-directional links). Note that ADT network was proposed for approximating the wireless networks; however, ADT network is acyclic. Furthermore, ADT network does not model the stochastic nature of the wireless links. With our algebraic framework, we incorporate both cycles as well as random failures into ADT network model.Comment: 9 pages, 12 figures, submitted to Allerton Conferenc

Distributed space-time coding for two-way wireless relay networks

In this paper, we consider distributed space-time coding for two-way wireless relay networks, where communication between two terminals is assisted by relay nodes. Relaying protocols using two, three, and four time slots are proposed. The protocols using four time slots are the traditional amplify-and-forward (AF) and decode-and-forward (DF) protocols, which do not consider the property of the two-way traffic. A new class of relaying protocols, termed as partial decode-and-forward (PDF), is developed for the two time slots transmission, where each relay first removes part of the noise before sending the signal to the two terminals. Protocols using three time slots are proposed to compensate the fact that the two time slots protocols cannot make use of direct transmission between the two terminals. For all protocols, after processing their received signals, the relays encode the resulting signals using a distributed linear dispersion (LD) code. The proposed AF protocols are shown to achieve the diversity order of min{N,K}(1- (log log P/log P)), where N is the number of relays, P is the total power of the network, and K is the number of symbols transmitted during each time slot. When random unitary matrix is used for LD code, the proposed PDF protocols resemble random linear network coding, where the former operates on the unitary group and the latter works on the finite field. Moreover, PDF achieves the diversity order of min{N,K} but the conventional DF can only achieve the diversity order of 1. Finally, we find that two time slots protocols also have advantages over four-time-slot protocols in media access control (MAC) layer

OFDM based Distributed Space Time Coding for Asynchronous Relay Networks

Recently Li and Xia have proposed a transmission scheme for wireless relay networks based on the Alamouti space time code and orthogonal frequency division multiplexing to combat the effect of timing errors at the relay nodes. This transmission scheme is amazingly simple and achieves a diversity order of two for any number of relays. Motivated by its simplicity, this scheme is extended to a more general transmission scheme that can achieve full cooperative diversity for any number of relays. The conditions on the distributed space time block code (DSTBC) structure that admit its application in the proposed transmission scheme are identified and it is pointed out that the recently proposed full diversity four group decodable DSTBCs from precoded co-ordinate interleaved orthogonal designs and extended Clifford algebras satisfy these conditions. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Finally, four group decodable distributed differential space time block codes applicable in this new transmission scheme for power of two number of relays are also provided.Comment: 5 pages, 2 figures, to appear in IEEE International Conference on Communications, Beijing, China, May 19-23, 200