5,012 research outputs found

    Using Network Coding to Achieve the Capacity of Deterministic Relay Networks with Relay Messages

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    In this paper, we derive the capacity of the deterministic relay networks with relay messages. We consider a network which consists of five nodes, four of which can only communicate via the fifth one. However, the fifth node is not merely a relay as it may exchange private messages with the other network nodes. First, we develop an upper bound on the capacity region based on the notion of a single sided genie. In the course of the achievability proof, we also derive the deterministic capacity of a 4-user relay network (without private messages at the relay). The capacity achieving schemes use a combination of two network coding techniques: the Simple Ordering Scheme (SOS) and Detour Schemes (DS). In the SOS, we order the transmitted bits at each user such that the bi-directional messages will be received at the same channel level at the relay, while the basic idea behind the DS is that some parts of the message follow an indirect path to their respective destinations. This paper, therefore, serves to show that user cooperation and network coding can enhance throughput, even when the users are not directly connected to each other.Comment: 12 pages, 5 figures, submitted to IEEE JSAC Network codin

    Wireless Network Information Flow: A Deterministic Approach

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    In a wireless network with a single source and a single destination and an arbitrary number of relay nodes, what is the maximum rate of information flow achievable? We make progress on this long standing problem through a two-step approach. First we propose a deterministic channel model which captures the key wireless properties of signal strength, broadcast and superposition. We obtain an exact characterization of the capacity of a network with nodes connected by such deterministic channels. This result is a natural generalization of the celebrated max-flow min-cut theorem for wired networks. Second, we use the insights obtained from the deterministic analysis to design a new quantize-map-and-forward scheme for Gaussian networks. In this scheme, each relay quantizes the received signal at the noise level and maps it to a random Gaussian codeword for forwarding, and the final destination decodes the source's message based on the received signal. We show that, in contrast to existing schemes, this scheme can achieve the cut-set upper bound to within a gap which is independent of the channel parameters. In the case of the relay channel with a single relay as well as the two-relay Gaussian diamond network, the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the relays need no knowledge of the values of the channel parameters to (approximately) achieve the rate supportable by the network. We also present extensions of the results to multicast networks, half-duplex networks and ergodic networks.Comment: To appear in IEEE transactions on Information Theory, Vol 57, No 4, April 201

    On the Capacity Region of the Deterministic Y-Channel with Common and Private Messages

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    In multi user Gaussian relay networks, it is desirable to transmit private information to each user as well as common information to all of them. However, the capacity region of such networks with both kinds of information is not easy to characterize. The prior art used simple linear deterministic models in order to approximate the capacities of these Gaussian networks. This paper discusses the capacity region of the deterministic Y-channel with private and common messages. In this channel, each user aims at delivering two private messages to the other two users in addition to a common message directed towards both of them. As there is no direct link between the users, all messages must pass through an intermediate relay. We present outer-bounds on the rate region using genie aided and cut-set bounds. Then, we develop a greedy scheme to define an achievable region and show that at a certain number of levels at the relay, our achievable region coincides with the upper bound. Finally, we argue that these bounds for this setup are not sufficient to characterize the capacity region.Comment: 4 figures, 7 page

    Computation Alignment: Capacity Approximation without Noise Accumulation

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    Consider several source nodes communicating across a wireless network to a destination node with the help of several layers of relay nodes. Recent work by Avestimehr et al. has approximated the capacity of this network up to an additive gap. The communication scheme achieving this capacity approximation is based on compress-and-forward, resulting in noise accumulation as the messages traverse the network. As a consequence, the approximation gap increases linearly with the network depth. This paper develops a computation alignment strategy that can approach the capacity of a class of layered, time-varying wireless relay networks up to an approximation gap that is independent of the network depth. This strategy is based on the compute-and-forward framework, which enables relays to decode deterministic functions of the transmitted messages. Alone, compute-and-forward is insufficient to approach the capacity as it incurs a penalty for approximating the wireless channel with complex-valued coefficients by a channel with integer coefficients. Here, this penalty is circumvented by carefully matching channel realizations across time slots to create integer-valued effective channels that are well-suited to compute-and-forward. Unlike prior constant gap results, the approximation gap obtained in this paper also depends closely on the fading statistics, which are assumed to be i.i.d. Rayleigh.Comment: 36 pages, to appear in IEEE Transactions on Information Theor
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