We study a wireless broadcast network, where a single source reliably communicates independent messages to multiple destinations, with the potential aid of relays and cooperation between destinations. The wireless nature of the medium is captured by the broadcast nature of transmissions as well as the superposition of transmitted signals plus independent Gaussian noise at the received signal at any radio. We propose a scheme that can achieve rate tuples within a constant gap away from the cut-set bound, where the constant is independent of channel coefficients and power constraints. First, for a deterministic broadcast network, we propose a new coding scheme, constructed by adopting a “receiver-centric” viewpoint, that uses quantize-and-forward relaying as an inner code concatenated with an outer Marton code for the induced deterministic broadcast channel. This scheme is shown to achieve the cut-set bound evaluated with product form distributions. This result is then lifted to the Gaussian network by using a deterministic network called the discrete superposition network as a formal quantization interface. This two-stage construction circumvents the difficulty involved in working with a vector nonlinear non-Gaussian broadcast channel that arises if we construct a similar scheme directly for the Gaussian network.

Abstract Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks. This paper proposes a novel approach for wireless communication, which embraces collisions rather than avoiding them, over an additive channel. It introduces a coding technique called Bounded-Contention Coding (BCC) that allows collisions to be successfully decoded by the receiving nodes into the original transmissions and whose complexity depends on a bound on the contention among the transmitters. BCC enables deterministic local broadcast in a network with n nodes and at most a transmitters with information of bits each within O(a log n + a ) bits of communication with full-duplex radios, and O((a log n + a )(log n)) bits, with high probability, with half-duplex radios. When combined with random linear network coding, BCC gives global broadcast within O((D + a + log n)(a log n + )) bits, with high probability. This also holds in dynamic networks that can change arbitrarily over time by a worst-case adversary. When no bound on the contention is given, it is shown how to probabilistically estimate it and obtain global broadcast that is adaptive to the true contention in the network.

Abstract—It is well known that transfer polynomials play an important role in the network code design problem. In this paper we provide a graph theoretical description of the terms of such polynomials. We consider acyclic networks with arbitrary number of receivers and min-cut h between each source-receiver pair. We show that the associated polynomial can be described in terms of certain subgraphs of the network. 1 I.

A classical result in undirected wireline networks is the near optimality of routing (flow) for multiple-unicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In this paper we “extend” the wireline result to the wireless context. Our main result is the approximate optimality of a simple layering principle: local physical-layer schemes combined with global routing. We use the reciprocity of the wireless channel critically in this result. Our formal result is in the context of channel models for which “good ” local schemes, that achieve the cut-set bound, exist (such as Gaussian MAC and broadcast channels, broadcast erasure networks, fast fading Gaussian networks). Layered architectures, common in the engineering-design of wireless networks, can have near-optimal performance if the locality over which physical-layer schemes should operate is carefully designed. Feedback is shown to play a critical role in enabling the separation between the physical and the network layers. The key technical idea is the modeling of a wireless network by an undirected “polymatroidal” network, for which we establish a max-flow min-cut approximation theorem.

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