Capacity Bounds For Multi-User Channels With Feedback, Relaying and Cooperation

Recent developments in communications are driven by the goal of achieving high data rates for wireless communication devices. To achieve this goal, several new phenomena need to be investigated from an information theoretic perspective. In this dissertation, we focus on three of these phenomena: feedback, relaying and cooperation. We study these phenomena for various multi-user channels from an information theoretic point of view. One of the aims of this dissertation is to study the performance limits of simple wireless networks, for various forms of feedback and cooperation. Consider an uplink communication system, where several users wish to transmit independent data to a base-station. If the base-station can send feedback to the users, one can expect to achieve higher data-rates since feedback can enable cooperation among the users. Another way to improve data-rates is to make use of the broadcast nature of the wireless medium, where the users can overhear each other's transmitted signals. This particular phenomenon has garnered much attention lately, where users can help in increasing each other's data-rates by utilizing the overheard information. This overheard information can be interpreted as a generalized form of feedback. To take these several models of feedback and cooperation into account, we study the two-user multiple access channel and the two-user interference channel with generalized feedback. For all these models, we derive new outer bounds on their capacity regions. We specialize these results for noiseless feedback, additive noisy feedback and user-cooperation models and show strict improvements over the previously known bounds. Next, we study state-dependent channels with rate-limited state information to the receiver or to the transmitter. This state-dependent channel models a practical situation of fading, where the fade information is partially available to the receiver or to the transmitter. We derive new bounds on the capacity of such channels and obtain capacity results for a special sub-class of such channels. We study the effect of relaying by considering the parallel relay network, also known as the diamond channel. The parallel relay network considered in this dissertation comprises of a cascade of a general broadcast channel to the relays and an orthogonal multiple access channel from the relays to the receiver. We characterize the capacity of the diamond channel, when the broadcast channel is deterministic. We also study the diamond channel with partially separated relays, and obtain capacity results when the broadcast channel is either semi-deterministic or physically degraded. Our results also demonstrate that feedback to the relays can strictly increase the capacity of the diamond channel. In several sensor network applications, distributed lossless compression of sources is of considerable interest. The presence of adversarial nodes makes it important to design compression schemes which serve the dual purpose of reliable source transmission to legitimate nodes while minimizing the information leakage to the adversarial nodes. Taking this constraint into account, we consider information theoretic secrecy, where our aim is to limit the information leakage to the eavesdropper. For this purpose, we study a secure source coding problem with coded side information from a helper to the legitimate user. We derive the rate-equivocation region for this problem. We show that the helper node serves the dual purpose of reducing the source transmission rate and increasing the uncertainty at the adversarial node. Next, we considered two different secure source coding models and provide the corresponding rate-equivocation regions

The Approximate Capacity of the Gaussian N-Relay Diamond Network

We consider the Gaussian "diamond" or parallel relay network, in which a source node transmits a message to a destination node with the help of N relays. Even for the symmetric setting, in which the channel gains to the relays are identical and the channel gains from the relays are identical, the capacity of this channel is unknown in general. The best known capacity approximation is up to an additive gap of order N bits and up to a multiplicative gap of order N^2, with both gaps independent of the channel gains. In this paper, we approximate the capacity of the symmetric Gaussian N-relay diamond network up to an additive gap of 1.8 bits and up to a multiplicative gap of a factor 14. Both gaps are independent of the channel gains and, unlike the best previously known result, are also independent of the number of relays N in the network. Achievability is based on bursty amplify-and-forward, showing that this simple scheme is uniformly approximately optimal, both in the low-rate as well as in the high-rate regimes. The upper bound on capacity is based on a careful evaluation of the cut-set bound. We also present approximation results for the asymmetric Gaussian N-relay diamond network. In particular, we show that bursty amplify-and-forward combined with optimal relay selection achieves a rate within a factor O(log^4(N)) of capacity with pre-constant in the order notation independent of the channel gains.Comment: 23 pages, to appear in IEEE Transactions on Information Theor

Wireless Network Information Flow: A Deterministic Approach

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

Cooperative Transmission for a Vector Gaussian Parallel Relay Network

In this paper, we consider a parallel relay network where two relays cooperatively help a source transmit to a destination. We assume the source and the destination nodes are equipped with multiple antennas. Three basic schemes and their achievable rates are studied: Decode-and-Forward (DF), Amplify-and-Forward (AF), and Compress-and-Forward (CF). For the DF scheme, the source transmits two private signals, one for each relay, where dirty paper coding (DPC) is used between the two private streams, and a common signal for both relays. The relays make efficient use of the common information to introduce a proper amount of correlation in the transmission to the destination. We show that the DF scheme achieves the capacity under certain conditions. We also show that the CF scheme is asymptotically optimal in the high relay power limit, regardless of channel ranks. It turns out that the AF scheme also achieves the asymptotic optimality but only when the relays-to-destination channel is full rank. The relative advantages of the three schemes are discussed with numerical results.Comment: 35 pages, 10 figures, submitted to IEEE Transactions on Information Theor

Degraded Broadcast Diamond Channels with Non-Causal State Information at the Source

A state-dependent degraded broadcast diamond channel is studied where the source-to-relays cut is modeled with two noiseless, finite-capacity digital links with a degraded broadcasting structure, while the relays-to-destination cut is a general multiple access channel controlled by a random state. It is assumed that the source has non-causal channel state information and the relays have no state information. Under this model, first, the capacity is characterized for the case where the destination has state information, i.e., has access to the state sequence. It is demonstrated that in this case, a joint message and state transmission scheme via binning is optimal. Next, the case where the destination does not have state information, i.e., the case with state information at the source only, is considered. For this scenario, lower and upper bounds on the capacity are derived for the general discrete memoryless model. Achievable rates are then computed for the case in which the relays-to-destination cut is affected by an additive Gaussian state. Numerical results are provided that illuminate the performance advantages that can be accrued by leveraging non-causal state information at the source.Comment: Submitted to IEEE Transactions on Information Theory, Feb. 201

The Gaussian Multiple Access Diamond Channel

In this paper, we study the capacity of the diamond channel. We focus on the special case where the channel between the source node and the two relay nodes are two separate links with finite capacities and the link from the two relay nodes to the destination node is a Gaussian multiple access channel. We call this model the Gaussian multiple access diamond channel. We first propose an upper bound on the capacity. This upper bound is a single-letterization of an $n$-letter upper bound proposed by Traskov and Kramer, and is tighter than the cut-set bound. As for the lower bound, we propose an achievability scheme based on sending correlated codes through the multiple access channel with superposition structure. We then specialize this achievable rate to the Gaussian multiple access diamond channel. Noting the similarity between the upper and lower bounds, we provide sufficient and necessary conditions that a Gaussian multiple access diamond channel has to satisfy such that the proposed upper and lower bounds meet. Thus, for a Gaussian multiple access diamond channel that satisfies these conditions, we have found its capacity.Comment: submitted to IEEE Transactions on Information Theor