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

Capacity Bounds for a Class of Diamond Networks

A class of diamond networks are studied where the broadcast component is modelled by two independent bit-pipes. New upper and low bounds are derived on the capacity which improve previous bounds. The upper bound is in the form of a max-min problem, where the maximization is over a coding distribution and the minimization is over an auxiliary channel. The proof technique generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981), and Kang and Liu for the Gaussian diamond network (2011). The bounds are evaluated for a Gaussian multiple access channel (MAC) and the binary adder MAC, and the capacity is found for interesting ranges of the bit-pipe capacities

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

Switched Local Schedules for Diamond Networks

We consider a Gaussian diamond network where a source communicates with the destination through $n$ non-interfering half-duplex relays. We focus on half-duplex schedules that utilize only local channel state information, i.e., each relay has access to its incoming and outgoing channel realizations. We demonstrate that random independent switching, resulting in multiple listen-transmit sub cycles at each relay, while still respecting the overall locally optimal listen-transmit fractions, enables to approximately achieve at least $3/4$ of the capacity of the $2$-relay diamond network. With a single listen-transmit cycle, this fraction drops from $3/4$ to $1/2$. We also provide simulation results that point to the same fractions of capacity being retained over networks with more than $2$ relays

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