Cooperative Strategies for Simultaneous and Broadcast Relay Channels

Consider the \emph{simultaneous relay channel} (SRC) which consists of a set of relay channels where the source wishes to transmit common and private information to each of the destinations. This problem is recognized as being equivalent to that of sending common and private information to several destinations in presence of helper relays where each channel outcome becomes a branch of the \emph{broadcast relay channel} (BRC). Cooperative schemes and capacity region for a set with two memoryless relay channels are investigated. The proposed coding schemes, based on \emph{Decode-and-Forward} (DF) and \emph{Compress-and-Forward} (CF) must be capable of transmitting information simultaneously to all destinations in such set. Depending on the quality of source-to-relay and relay-to-destination channels, inner bounds on the capacity of the general BRC are derived. Three cases of particular interest are considered: cooperation is based on DF strategy for both users --referred to as DF-DF region--, cooperation is based on CF strategy for both users --referred to as CF-CF region--, and cooperation is based on DF strategy for one destination and CF for the other --referred to as DF-CF region--. These results can be seen as a generalization and hence unification of previous works. An outer-bound on the capacity of the general BRC is also derived. Capacity results are obtained for the specific cases of semi-degraded and degraded Gaussian simultaneous relay channels. Rates are evaluated for Gaussian models where the source must guarantee a minimum amount of information to both users while additional information is sent to each of them.Comment: 32 pages, 7 figures, To appear in IEEE Trans. on Information Theor

GDoF of the MISO BC: Bridging the gap between finite precision CSIT and perfect CSIT

This work bridges the gap between sharply contrasting results on the degrees of freedom of the K user broadcast channel where the transmitter is equipped with K transmit antennas and each of the K receivers is equipped with a single antenna. This channel has K DoF when channel state information at the transmitter (CSIT) is perfect, but as shown recently, it has only 1 DoF when the CSIT is limited to finite precision. By considering the full range of partial CSIT assumptions parameterized by β ⋯ [0,1], such that the strength of the channel estimation error terms scales as ∼ SNR-β relative to the channel strengths which scale as ∼ SNR, it is shown that this channel has 1 - β + Kβ DoF. For K = 2 users with arbitrary βij parameters, the DoF are shown to be 1 + mini,j βij. To explore diversity of channel strengths, the results are further extended to the symmetric Generalized Degrees of Freedom setting where the direct channel strengths scale as ∼ SNR and the cross channel strengths scale as ∼ SNRα, α ⋯ [0,1], β ⋯ [0,α]. Here, the roles of α and β are shown to counter each other on equal terms, so that the sum GDoF value in the K user setting is (α - β) + K(1 - (α-β )) and for the 2 user setting with arbitrary βij, is 2 - α + mini,j βij

Cooperative Compute-and-Forward

We examine the benefits of user cooperation under compute-and-forward. Much like in network coding, receivers in a compute-and-forward network recover finite-field linear combinations of transmitters' messages. Recovery is enabled by linear codes: transmitters map messages to a linear codebook, and receivers attempt to decode the incoming superposition of signals to an integer combination of codewords. However, the achievable computation rates are low if channel gains do not correspond to a suitable linear combination. In response to this challenge, we propose a cooperative approach to compute-and-forward. We devise a lattice-coding approach to block Markov encoding with which we construct a decode-and-forward style computation strategy. Transmitters broadcast lattice codewords, decode each other's messages, and then cooperatively transmit resolution information to aid receivers in decoding the integer combinations. Using our strategy, we show that cooperation offers a significant improvement both in the achievable computation rate and in the diversity-multiplexing tradeoff.Comment: submitted to IEEE Transactions on Information Theor

On the Vector Broadcast Channel with Alternating CSIT: A Topological Perspective

In many wireless networks, link strengths are affected by many topological factors such as different distances, shadowing and inter-cell interference, thus resulting in some links being generally stronger than other links. From an information theoretic point of view, accounting for such topological aspects has remained largely unexplored, despite strong indications that such aspects can crucially affect transceiver and feedback design, as well as the overall performance. The work here takes a step in exploring this interplay between topology, feedback and performance. This is done for the two user broadcast channel with random fading, in the presence of a simple two-state topological setting of statistically strong vs. weaker links, and in the presence of a practical ternary feedback setting of alternating channel state information at the transmitter (alternating CSIT) where for each channel realization, this CSIT can be perfect, delayed, or not available. In this setting, the work derives generalized degrees-of-freedom bounds and exact expressions, that capture performance as a function of feedback statistics and topology statistics. The results are based on novel topological signal management (TSM) schemes that account for topology in order to fully utilize feedback. This is achieved for different classes of feedback mechanisms of practical importance, from which we identify specific feedback mechanisms that are best suited for different topologies. This approach offers further insight on how to split the effort --- of channel learning and feeding back CSIT --- for the strong versus for the weaker link. Further intuition is provided on the possible gains from topological spatio-temporal diversity, where topology changes in time and across users.Comment: Shorter version will be presented at ISIT 201