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Achievable rates and optimal schedules for half duplex multiplerelay networks
 in Proc. 46th Allerton Conf. on Commun., Control, and Comput
"... Abstract — We study the half duplex multiplerelay channel (MRC) where every node can either transmit or listen but not both at the same time. We derive a capacity upper bound based on a maxflow mincut argument and achievable transmission rates based on the decodeforward coding strategy (DF), for ..."
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Abstract — We study the half duplex multiplerelay channel (MRC) where every node can either transmit or listen but not both at the same time. We derive a capacity upper bound based on a maxflow mincut argument and achievable transmission rates based on the decodeforward coding strategy (DF), for both the half duplex discrete memoryless MRC and the half duplex phase fading Gaussian MRC. The upper bound and achievable rates are functions of the transmit state vector (a description of which nodes transmit and which receive). More precisely, they are functions of the time fraction of different transmit state vectors, which we term a schedule. We formulate the optimal scheduling problem as a maxmin optimization to find the schedule that maximizes the DF rate for the half duplex MRC. We use a technique based on minimax hypothesis testing to solve this problem and demonstrate it on a fournode MRC, getting closed form solutions in certain scenarios. For the phase fading Gaussian channel, surprisingly, we discover that optimal schedules can be solved using linear programming. I.
Myopic Coding in Multiple Relay Channels
"... Abstract — In this paper, we investigate achievable rates for data transmission from sources to sinks through multiple relay networks. We consider myopic coding, a constrained communication strategy in which each node has only a local view of the network, meaning that nodes can only transmit to and ..."
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Abstract — In this paper, we investigate achievable rates for data transmission from sources to sinks through multiple relay networks. We consider myopic coding, a constrained communication strategy in which each node has only a local view of the network, meaning that nodes can only transmit to and decode from neighboring nodes. We compare this with omniscient coding, in which every node has a global view of the network and all nodes can cooperate. Using Gaussian channels as examples, we find that when the nodes transmit at low power, the rates achievable with twohop myopic coding are as large as that under omniscient coding in a fivenode multiple relay channel and close to that under omniscient coding in a sixnode multiple relay channel. These results suggest that we may do local coding and cooperation without compromising much on the transmission rate. Practically, myopic coding schemes are more robust to topology changes because encoding and decoding at a node are not affected when there are changes at remote nodes. Furthermore, myopic coding mitigates the high computational complexity and large buffer/memory requirements of omniscient coding. I.
Optimal Routing for DecodeForward in Cooperative Wireless Networks
"... Abstract—We investigate routing in cooperative multipleterminal wireless networks in which the nodes can collaborate with each other in data transmission. First, we motivate cooperation by showing that decodeforward, an informationtheoretic cooperative coding strategy, achieves rates significantly ..."
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Abstract—We investigate routing in cooperative multipleterminal wireless networks in which the nodes can collaborate with each other in data transmission. First, we motivate cooperation by showing that decodeforward, an informationtheoretic cooperative coding strategy, achieves rates significantly higher than those achievable by the conventional multihop routing, a pointtopoint noncooperative coding strategy. We then construct an algorithm to find optimal (ratemaximizing) routes for decodeforward. We show that the algorithm is able to find shortest optimal routes and is optimal in fading channels. However, the algorithm runs in factorial time in the worst case. So, we propose a nearoptimal heuristic algorithm that runs in polynomial time. The heuristic algorithm always outputs optimal routes when the nodes transmit independent codewords, and outputs optimal routes with high probability when the nodes transmit arbitrarily correlated codewords. Lastly, we implement decodeforward using lowdensity paritycheck codes to compare the bit error rate performance of different routes. Index Terms—Routing, wireless networks, cooperative systems, information theory, multiuser channels. I.
Optimal Schedules for the Dnode Half Duplex Phase Fading MRC
"... Abstract—In this paper, we extend our previous work on the half duplex multiplerelay channel (MRC). A capacity upper bound based on the maxflow mincut argument and achievable transmission rates based on the decodeforward coding strategy (DF) for the half duplex MRC have been shown to be function ..."
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Abstract—In this paper, we extend our previous work on the half duplex multiplerelay channel (MRC). A capacity upper bound based on the maxflow mincut argument and achievable transmission rates based on the decodeforward coding strategy (DF) for the half duplex MRC have been shown to be functions of the schedule of the network, which is defined as the probability mass function of the transmit state vector (a description of which nodes transmit and which receive). Finding the optimal (ratemaximizing) schedule for DF can be formulated as a maximin optimization problem which is not easily solved in general. In our recent paper, we presented a technique to find optimal schedules for the 4node MRC based on minimax hypothesis testing. Closedform solutions were obtained for certain channel topologies. In this paper, we extend the technique to solve for optimal schedules for the general Dnode half duplex MRC, where D ≥ 3. I.
1On Capacity and Optimal Scheduling for the HalfDuplex MultipleRelay Channel
"... Abstract—We study the halfduplex multiplerelay channel (HDMRC) where every node can either transmit or listen but cannot do both at the same time. We obtain a capacity upper bound based on a maxflow mincut argument and achievable transmission rates based on the decodeforward (DF) coding strate ..."
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Abstract—We study the halfduplex multiplerelay channel (HDMRC) where every node can either transmit or listen but cannot do both at the same time. We obtain a capacity upper bound based on a maxflow mincut argument and achievable transmission rates based on the decodeforward (DF) coding strategy, for both the discrete memoryless HDMRC and the phasefading HDMRC. We discover that both the upper bound and the achievable rates are functions of the transmit/listen state (a description of which nodes transmit and which receive). More precisely, they are functions of the time fraction of the different states, which we term a schedule. We formulate the optimal scheduling problem to find an optimal schedule that maximizes the DF rate. The optimal scheduling problem turns out to be a maximin optimization, for which we propose an algorithmic solution. We demonstrate our approach on a fournode multiplerelay channel, obtaining closedform solutions in certain scenarios. Furthermore, we show that for the received signaltonoise ratio degraded phasefading HDMRC, the optimal scheduling problem can be simplified to a max optimization. Index Terms—Decodeforward (DF), half duplex, multiplerelay channel (MRC), scheduling, phase fading. I.