Optimality of Network Coding in Packet Networks

We resolve the question of optimality for a well-studied packetized implementation of random linear network coding, called PNC. In PNC, in contrast to the classical memoryless setting, nodes store received information in memory to later produce coded packets that reflect this information. PNC is known to achieve order optimal stopping times for the many-to-all multicast problem in many settings. We give a reduction that captures exactly how PNC and other network coding protocols use the memory of the nodes. More precisely, we show that any such protocol implementation induces a transformation which maps an execution of the protocol to an instance of the classical memoryless setting. This allows us to prove that, for any (non-adaptive dynamic) network, PNC converges with high probability in optimal time. In other words, it stops at exactly the first time in which in hindsight it was possible to route information from the sources to each receiver individually. Our technique also applies to variants of PNC, in which each node uses only a finite buffer. We show that, even in this setting, PNC stops exactly within the time in which in hindsight it was possible to route packets given the memory constraint, i.e., that the memory used at each node never exceeds its buffer size. This shows that PNC, even without any feedback or explicit memory management, allows to keep minimal buffer sizes while maintaining its capacity achieving performance

Near Optimal Broadcast with Network Coding in Large Sensor Networks

We study efficient broadcasting for wireless sensor networks, with network coding. We address this issue for homogeneous sensor networks in the plane. Our results are based on a simple principle (IREN/IRON), which sets the same rate on most of the nodes (wireless links) of the network. With this rate selection, we give a value of the maximum achievable broadcast rate of the source: our central result is a proof of the value of the min-cut for such networks, viewed as hypergraphs. Our metric for efficiency is the number of transmissions necessary to transmit one packet from the source to every destination: we show that IREN/IRON achieves near optimality for large networks; that is, asymptotically, nearly every transmission brings new information from the source to the receiver. As a consequence, network coding asymptotically outperforms any scheme that does not use network coding.Comment: Dans First International Workshop on Information Theory for Sensor Netwoks (WITS 2007) (2007

Queue-Architecture and Stability Analysis in Cooperative Relay Networks

An abstraction of the physical layer coding using bit pipes that are coupled through data-rates is insufficient to capture notions such as node cooperation in cooperative relay networks. Consequently, network-stability analyses based on such abstractions are valid for non-cooperative schemes alone and meaningless for cooperative schemes. Motivated from this, this paper develops a framework that brings the information-theoretic coding scheme together with network-stability analysis. This framework does not constrain the system to any particular achievable scheme, i.e., the relays can use any cooperative coding strategy of its choice, be it amplify/compress/quantize or any alter-and-forward scheme. The paper focuses on the scenario when coherence duration is of the same order of the packet/codeword duration, the channel distribution is unknown and the fading state is only known causally. The main contributions of this paper are two-fold: first, it develops a low-complexity queue-architecture to enable stable operation of cooperative relay networks, and, second, it establishes the throughput optimality of a simple network algorithm that utilizes this queue-architecture.Comment: 16 pages, 1 figur

Communication Through Collisions: Opportunistic Utilization of Past Receptions

When several wireless users are sharing the spectrum, packet collision is a simple, yet widely used model for interference. Under this model, when transmitters cause interference at any of the receivers, their collided packets are discarded and need to be retransmitted. However, in reality, that receiver can still store its analog received signal and utilize it for decoding the packets in the future (for example, by successive interference cancellation techniques). In this work, we propose a physical layer model for wireless packet networks that allows for such flexibility at the receivers. We assume that the transmitters will be aware of the state of the channel (i.e. when and where collisions occur, or an unintended receiver overhears the signal) with some delay, and propose several coding opportunities that can be utilized by the transmitters to exploit the available signal at the receivers for interference management (as opposed to discarding them). We analyze the achievable throughput of our strategy in a canonical interference channel with two transmitter-receiver pairs, and demonstrate the gain over conventional schemes. By deriving an outer-bound, we also prove the optimality of our scheme for the corresponding model.Comment: Accepted to IEEE INFOCOM 2014. arXiv admin note: text overlap with arXiv:1301.530