On Network Coding of Independent and Dependent Sources in Line Networks

We investigate the network coding capacity for line networks. For independent sources and a special class of dependent sources, we fully characterize the capacity region of line networks for all possible demand structures (e.g., multiple unicast, mixtures of unicasts and multicasts, etc.) Our achievability bound is derived by first decomposing a line network into single-demand components and then adding the component rate regions to get rates for the parent network. For general dependent sources, we give an achievability result and provide examples where the result is and is not tight

Dynamic algorithms for multicast with intra-session network coding

The problem of multiple multicast sessions with intra-session network coding in time-varying networks is considered. The network-layer capacity region of input rates that can be stably supported is established. Dynamic algorithms for multicast routing, network coding, power allocation, session scheduling, and rate allocation across correlated sources, which achieve stability for rates within the capacity region, are presented. This work builds on the back-pressure approach introduced by Tassiulas et al., extending it to network coding and correlated sources. In the proposed algorithms, decisions on routing, network coding, and scheduling between different sessions at a node are made locally at each node based on virtual queues for different sinks. For correlated sources, the sinks locally determine and control transmission rates across the sources. The proposed approach yields a completely distributed algorithm for wired networks. In the wireless case, power control among different transmitters is centralized while routing, network coding, and scheduling between different sessions at a given node are distributed

Capacity of Sum-networks for Different Message Alphabets

A sum-network is a directed acyclic network in which all terminal nodes demand the `sum' of the independent information observed at the source nodes. Many characteristics of the well-studied multiple-unicast network communication problem also hold for sum-networks due to a known reduction between instances of these two problems. Our main result is that unlike a multiple unicast network, the coding capacity of a sum-network is dependent on the message alphabet. We demonstrate this using a construction procedure and show that the choice of a message alphabet can reduce the coding capacity of a sum-network from $1$ to close to $0$

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

Adaptive Resonance: An Emerging Neural Theory of Cognition

Adaptive resonance is a theory of cognitive information processing which has been realized as a family of neural network models. In recent years, these models have evolved to incorporate new capabilities in the cognitive, neural, computational, and technological domains. Minimal models provide a conceptual framework, for formulating questions about the nature of cognition; an architectural framework, for mapping cognitive functions to cortical regions; a semantic framework, for precisely defining terms; and a computational framework, for testing hypotheses. These systems are here exemplified by the distributed ART (dART) model, which generalizes localist ART systems to allow arbitrarily distributed code representations, while retaining basic capabilities such as stable fast learning and scalability. Since each component is placed in the context of a unified real-time system, analysis can move from the level of neural processes, including learning laws and rules of synaptic transmission, to cognitive processes, including attention and consciousness. Local design is driven by global functional constraints, with each network synthesizing a dynamic balance of opposing tendencies. The self-contained working ART and dART models can also be transferred to technology, in areas that include remote sensing, sensor fusion, and content-addressable information retrieval from large databases.Office of Naval Research and the defense Advanced Research Projects Agency (N00014-95-1-0409, N00014-1-95-0657); National Institutes of Health (20-316-4304-5

Network vector quantization

We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples

Networked Slepian-Wolf: theory, algorithms, and scaling laws

Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed