Achievable Throughput in Two-Scale Wireless Networks

We propose a new model of wireless networks which we refer to as "two-scale networks." At a local scale, characterised by nodes being within a distance r, channel strengths are drawn independently and identically from a distance-independent distribution. At a global scale, characterised by nodes being further apart from each other than a distance r, channel connections are governed by a Rayleigh distribution, with the power satisfying a distance-based decay law. Thus, at a local scale, channel strengths are determined primarily by random effects such as obstacles and scatterers whereas at the global scale channel strengths depend on distance. For such networks, we propose a hybrid communications scheme, combining elements of distance-dependent networks and random networks. For particular classes of two-scale networks with N nodes, we show that an aggregate throughput that is slightly sublinear in N, for instance, of the form N/ log^4 N is achievable. This offers a significant improvement over a throughput scaling behaviour of O(√N) that is obtained in other work

Statistical Pruning for Near-Maximum Likelihood Decoding

In many communications problems, maximum-likelihood (ML) decoding reduces to finding the closest (skewed) lattice point in N-dimensions to a given point xisin CN. In its full generality, this problem is known to be NP-complete. Recently, the expected complexity of the sphere decoder, a particular algorithm that solves the ML problem exactly, has been computed. An asymptotic analysis of this complexity has also been done where it is shown that the required computations grow exponentially in N for any fixed SNR. At the same time, numerical computations of the expected complexity show that there are certain ranges of rates, SNRs and dimensions N for which the expected computation (counted as the number of scalar multiplications) involves no more than N3 computations. However, when the dimension of the problem grows too large, the required computations become prohibitively large, as expected from the asymptotic exponential complexity. In this paper, we propose an algorithm that, for large N, offers substantial computational savings over the sphere decoder, while maintaining performance arbitrarily close to ML. We statistically prune the search space to a subset that, with high probability, contains the optimal solution, thereby reducing the complexity of the search. Bounds on the error performance of the new method are proposed. The complexity of the new algorithm is analyzed through an upper bound. The asymptotic behavior of the upper bound for large N is also analyzed which shows that the upper bound is also exponential but much lower than the sphere decoder. Simulation results show that the algorithm is much more efficient than the original sphere decoder for smaller dimensions as well, and does not sacrifice much in terms of performance

Communication Over a Wireless Network With Random Connections

A network of nodes in which pairs communicate over a shared wireless medium is analyzed. We consider the maximum total aggregate traffic flow possible as given by the number of users multiplied by their data rate. The model in this paper differs substantially from the many existing approaches in that the channel connections in this network are entirely random: rather than being governed by geometry and a decay-versus-distance law, the strengths of the connections between nodes are drawn independently from a common distribution. Such a model is appropriate for environments where the first-order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. It is shown that the aggregate traffic flow as a function of the number of nodes n is a strong function of the channel distribution. In particular, for certain distributions the aggregate traffic flow is at least n/(log n)^d for some d≫0, which is significantly larger than the O(sqrt n) results obtained for many geometric models. The results provide guidelines for the connectivity that is needed for large aggregate traffic. The relation between the proposed model and existing distance-based models is shown in some cases

Efficient near-ML decoding via statistical pruning

Maximum-likelihood (ML) decoding often reduces to finding the closest (skewed) lattice point in N-dimensions to a given point x ϵ C^N. Sphere decoding is an algorithm that does this. We modify the sphere decoder to reduce the computational complexity of decoding while maintaining near-ML performance

On the Achievable Throughput in Two-Scale Wireless Networks

We propose a new model of wireless networks which we refer to as "two-scale networks". At a local scale, characterized by nodes being within a distance r, channel strengths are drawn independently and identically from a distance-independent distribution. At a global scale, characterized by nodes being further apart from each other than a distance r, channel connections are governed by a Rayleigh distribution, with the power satisfying a distance-based decay law. Thus, at a local scale, channel strengths are determined primarily by random effects such as obstacles and scatterers whereas at the global scale channel strengths depend on distance. For such networks, we propose a hybrid communications scheme, combining elements of P. Gupta et al. (2000) (for distance-dependent networks) and R. Gowaikar et al. (2006) (for random networks). For a particular class of two-scale networks with N nodes, we show that an aggregate throughput of the form N^(1/(t-1)) / (log^2 N) is achievable, where t > 2 is a parameter that depends on the distribution of the connection at the local scale and is independent of the decay law that operates at a global scale. For t < 3, this offers a significant improvement over the O(√N) results of P. Gupta et al. (2000)

A Practical Scheme for Wireless Network Operation

In many problems in wireline networks, it is known that achieving capacity on each link or subnetwork is optimal for the entire network operation. In this paper, we present examples of wireless networks in which decoding and achieving capacity on certain links or subnetworks gives us lower rates than other simple schemes, like forwarding. This implies that the separation of channel and network coding that holds for many classes of wireline networks does not, in general, hold for wireless networks. Next, we consider Gaussian and erasure wireless networks where nodes are permitted only two possible operations: nodes can either decode what they receive (and then re-encode and transmit the message) or simply forward it. We present a simple greedy algorithm that returns the optimal scheme from the exponential-sized set of possible schemes. This algorithm will go over each node at most once to determine its operation, and hence, is very efficient. We also present a decentralized algorithm whose performance can approach the optimum arbitrarily closely in an iterative fashion

An achievability result for random networks

We analyze a network of nodes in which pairs communicate over a shared wireless medium. We are interested in the maximum total aggregate traffic flow that is possible through the network. Our model differs substantially from the many existing approaches in that the channel connections in our network are entirely random: we assume that, rather than being governed by geometry and a decay law, the strength of the connections between nodes is drawn independently from a common distribution. Such a model is appropriate for environments where the first order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. We show that the aggregate traffic flow is a strong function of the channel distribution. In particular, we show that for certain distributions, the aggregate traffic flow scales at least as n/((log n)^v) for some fixed v > 0, which is significantly larger than the O(√n) results obtained for many geometric models

Capacity of wireless erasure networks

In this paper, a special class of wireless networks, called wireless erasure networks, is considered. In these networks, each node is connected to a set of nodes by possibly correlated erasure channels. The network model incorporates the broadcast nature of the wireless environment by requiring each node to send the same signal on all outgoing channels. However, we assume there is no interference in reception. Such models are therefore appropriate for wireless networks where all information transmission is packetized and where some mechanism for interference avoidance is already built in. This paper looks at multicast problems over these networks. The capacity under the assumption that erasure locations on all the links of the network are provided to the destinations is obtained. It turns out that the capacity region has a nice max-flow min-cut interpretation. The definition of cut-capacity in these networks incorporates the broadcast property of the wireless medium. It is further shown that linear coding at nodes in the network suffices to achieve the capacity region. Finally, the performance of different coding schemes in these networks when no side information is available to the destinations is analyzed

On the capacity of wireless erasure networks

We determine the capacity of a certain class of wireless erasure relay networks. We first find a suitable definition for the "cut-capacity" of erasure networks with broadcast at transmission and no interference at reception. With this definition, a maxflow mincut capacity result holds for the capacity of these networks