arXiv subjects
Publications and source records attributed to Gerhard Kramer.
Outer bounds on the admissible source region for broadcast channels with dependent sources are developed and used to prove capacity results for several classes of sources and channels.
This paper considers an interference network composed of K half-duplex single-antenna pairs of users who wish to establish bi-directional communication with the aid of a multi-input-multi-output (MIMO) half-duplex relay node. This channel is referred to as the "MIMO Wireless Switch" since, for the sake of simplicity, our model assumes no direct link between the two end nodes of each pair implying that all communication must go through the relay node (i.e., the MIMO switch). Assuming a delay-limited scenario, the fundamental limits in the high signal-to-noise ratio (SNR) regime is analyzed using the diversity multiplexing tradeoff (DMT) framework. Our results sheds light on the structure of optimal transmission schemes and the gain offered by the relay node in two distinct cases, namely reciprocal and non-reciprocal channels (between the relay and end-users). In particular, the existence of a relay node, equipped with a sufficient number of antennas, is shown to increase the multiplexing gain; as compared with the traditional fully connected K-pair interference channel. To the best of our knowledge, this is the first known example where adding a relay node results in enlarging the pre-log factor of the sum rate. Moreover, for the case of reciprocal channels, it is shown that, when the relay has a number of antennas at least equal to the sum of antennas of all the users, static time allocation of decode and forward (DF) type schemes is optimal. On the other hand, in the non-reciprocal scenario, we establish the optimality of dynamic decode and forward in certain relevant scenarios.
The Marton-Gelfand-Pinsker inner bound on the capacity region of broadcast channels was extended by Han-Costa to include arbitrarily correlated sources where the capacity region is replaced by an admissible source region. The main arguments of Han-Costa are correct but unfortunately the authors overlooked an inequality in their derivation. The corrected region is presented and the absence of the omitted inequality is shown to sometimes admit sources that are not admissible.
The capacity region of a multiple-input-multiple-output interference channel (MIMO IC) where the channel matrices are square and invertible is studied. The capacity region for strong interference is established where the definition of strong interference parallels that of scalar channels. Moreover, the sum-rate capacity for Z interference, noisy interference, and mixed interference is established. These results generalize known results for the scalar Gaussian IC.
The performance of user-cooperation in a multi-access network is compared to that of using a wireless relay. Using the total transmit and processing power consumed at all nodes as a cost metric, the outage probabilities achieved by dynamic decode-and-forward (DDF) and amplify-and-forward (AF) are compared for the two networks. A geometry-inclusive high signal-to-noise ratio (SNR) outage analysis in conjunction with area-averaged numerical simulations shows that user and relay cooperation achieve a maximum diversity of K and 2 respectively for a K-user multiaccess network under both DDF and AF. However, when accounting for energy costs of processing and communication, relay cooperation can be more energy efficient than user cooperation, i.e., relay cooperation achieves coding (SNR) gains, particularly in the low SNR regime, that override the diversity advantage of user cooperation.
Recent outer bounds on the capacity region of Gaussian interference channels are generalized to $m$-user channels with $m>2$ and asymmetric powers and crosstalk coefficients. The bounds are again shown to give the sum-rate capacity for Gaussian interference channels with low powers and crosstalk coefficients. The capacity is achieved by using single-user detection at each receiver, i.e., treating the interference as noise incurs no loss in performance.
A new outer bound on the capacity region of Gaussian interference channels is developed. The bound combines and improves existing genie-aided methods and is shown to give the sum-rate capacity for noisy interference as defined in this paper. Specifically, it is shown that if the channel coefficients and power constraints satisfy a simple condition then single-user detection at each receiver is sum-rate optimal, i.e., treating the interference as noise incurs no loss in performance. This is the first concrete (finite signal-to-noise ratio) capacity result for the Gaussian interference channel with weak to moderate interference. Furthermore, for certain mixed (weak and strong) interference scenarios, the new outer bounds give a corner point of the capacity region.
A partially cooperative relay broadcast channel (RBC) is a three-node network with one source node and two destination nodes (destinations 1 and 2) where destination 1 can act as a relay to assist destination 2. Inner and outer bounds on the capacity region of the discrete memoryless partially cooperative RBC are obtained. When the relay function is disabled, the inner and outer bounds reduce to new bounds on the capacity region of broadcast channels. Four classes of RBCs are studied in detail. For the partially cooperative RBC with degraded message sets, inner and outer bounds are obtained. For the semideterministic partially cooperative RBC and the orthogonal partially cooperative RBC, the capacity regions are established. For the parallel partially cooperative RBC with unmatched degraded subchannels, the capacity region is established for the case of degraded message sets. The capacity is also established when the source node has only a private message for destination 2, i.e., the channel reduces to a parallel relay channel with unmatched degraded subchannels.
We provide a rate distortion interpretation of the problem of quantum data compression of ensembles of mixed states with commuting density operators. There are two versions of this problem. In the visible case the sequence of states is available to the encoder and in the blind or hidden case the encoder may access only a sequence of measurements. We find the exact optimal compression rates for both the visible and hidden cases. Our analysis includes the scenario in which asymptotic reconstruction is imperfect.