The role of coding in the choice between routing and coding for wireless unicast

International audienceWe consider the benefits of coding in wireless networks, specifically its role in exploiting the local broadcast property of the wireless medium. We first argue that for unicast, the throughput achieved with network coding is the same as that achieved without any coding. This argument highlights the role of a general max-flow min-cut duality and is more explicit than previous proofs. The maximum throughput can be achieved in multiple ways without any coding, for example, using backpressure routing, or using some centralized flow scheduler that is aware of the network topology. However, all such schemes, in order to take advantage of the local broadcast property, require dynamic routing decisions for choosing the next hop for each packet from among the nodes where it is successfully received. This choice seems to depend critically on feedback signaling information like queue lengths, or ARQ. In contrast, note that the use of network coding can achieve the same without such feedback, in exchange for decoding overhead. A key issue to be resolved in making a comparison between routing and coding would be how critical feedback signaling is, for the throughput of routing policies. With this motivation, we first explore how feedback at a given node affects its throughput, with arbitrary rates of its one-hop neighbors to the destination. Static routing policies which are essentially feedback independent , are considered. An explicit characterization of the optimal policies under such a feedback constraint is obtained, which turns out to be a natural generalization of both flooding and traditional routing (which does not exploit local broadcast, because the next hop is fixed prior to the transmission). When losses at the receivers are independent (still allowing for dependencies on transmissions by two different nodes, to model interference), the reduction in capacity due to constraining the feedback is limited to a constant fraction (e−1=37%) of the coding capacity, and gets arbitrarily close to optimal as the unconstrained capacity goes to zero. We also extend this analysis to a layered multihop network and also compare the throughput of flooding to backpressure via simulations for a layered network assuming independent losses. Finally, if there are dependencies in the losses seen by receivers from a single broadcast, the reduction could be arbitrarily bad, even with just two hops

Computing the Capacity Region of a Wireless Network

We consider a wireless network of n nodes that communicate over a common wireless medium under some interference constraints. Our work is motivated by the need for an efficient and distributed algorithm to determine the n2 dimensional unicast capacity region of such a wireless network. Equivalently, given a vector of end-to-end rates between various source-destination pairs, we seek to determine if it can be supported by the network through a combination of routing and scheduling decisions. This question is known to be NP-hard and hard to even approximate within n1-o(1)[superscript 1-o1] factor for general graphs. In this paper, we first show that the whole n2 [superscript 2] dimensional unicast capacity region can be approximated to (1 plusmn epsiv) factor in polynomial time, and in a distributed manner, whenever the Max Weight Independent Set (MWIS) problem can be approximated in a similar fashion for the corresponding topology. We then consider wireless networks which are usually formed between nodes that are placed in a geographic area and come endowed with a certain geometry, and argue that such situations do lead to approximations to the MWIS problem (in fact, in a completely distributed manner, in a time that is essentially linear in n). Consequently, this gives us a polynomial algorithm to approximate the capacity of wireless networks to arbitrary accuracy. This result hence, is in sharp contrast with previous works that provide algorithms with at least a constant factor loss. An important ingredient in establishing our result is the transient analysis of the maximum weight scheduling algorithm, which can be of interest in its own right.National Science Foundation (U.S.) (Grant NSF CNS-0437415) (Grant NSF ECCS-0426831) (Grant NSF CNS-0834409) (CAREER grant NSF CNS-0546590) (Grant NSF CCF-0728554