In this paper, we study causal discrete memoryless relay networks. The network consists of multiple nodes, each of which can be a source, a relay, and/or a destination. In the network, there are two types of relays: 1) relays with one sample delay (strictly causal) and 2) relays without delay (causal) whose transmit signals depend not only on the past received symbols but also on the current received symbols. For this network, we derive two new cut-set bounds, one when every node has a message and the other when only the strictly causal relays have messages. Using the examples of a causal vector Gaussian two-way relay channel and a causal vector Gaussian relay channel, we show that the new cut-set bounds can be achieved by a simple amplify-and-forward type relaying. Our result for the causal relay channel strengthens the previously known capacity result for the same channel by El Gamal, Hassanpour, and Mammen.

In this paper, we consider causal discrete-memoryless relay networks (DMRNs) with causal side information. The networks consist of multiple nodes, each of which can be a source, relay, and/or destination. There are two types of relays in the network, i.e., relays with one sample delay (strictly causal relays) and relays without delay (causal relays) whose transmit signal depends not only on the past received symbols but also on the current received symbol. Also, we assume that some nodes can causally use channel state information (CSI) as side information. For the network, we derive a new cut-set bound, which recovers the classical cut-set bound and our previous cut-set bound for causal DMRNs without side information. Using an example of a fading relay channel, we show that the new cut-set bound can be achieved by a simple amplify-and-forward type relaying.

This paper considers a Gaussian multiple-input single-output (MISO) broadcast channel with a per-antenna peak power constraint (or simply peak power constraint). It is more realistic to consider the peak power constraint on each transmit antenna because in many practical implementations each antenna is equipped with its own power amplifier. Assuming the perfect knowledge of the channel state information (CSI) at the transmitter, we propose an achievable scheme using dirty-tape coding (DTC). The ideal dirty-paper coding (DPC), which is a capacity-achieving scheme for the Gaussian multiple-input multiple-output (MIMO) broadcast channel, cannot be used for our model because its optimal input distribution is Gaussian and thus the peak power constraint is violated. On the other hand, the channel input of DTC is uniformly distributed in a fixed range, which helps to control the peak power of the transmit signal easily. We also present an algorithm that finds capacity-achieving beamforming vectors and power allocation factors under a per-antenna average power constraint and use the optimized parameters in the proposed scheme. Simulation results show that the proposed scheme provides gains of 2.7dB over a non-DTC scheme based on minimum mean square error (MMSE) beamforming at high signal-to-noise ratio (SNR) when there are three receivers and the transmitter has three antennas.

This paper considers a two user Gaussian multiple-input single-output (MISO) broadcast channel with a per-antenna peak power constraint (or simply peak power constraint). It is more realistic to consider the peak power constraint on each transmit antenna because each antenna is equipped with its own power amplifier in many practical implementations. Assuming the perfect channel state information (CSI) at the transmitter, we propose an achievable scheme using a dirty-tape coding (DTC). The uniform input in a fixed range of the DTC scheme helps to control the peak power of the transmit signal easily. We also present an optimization algorithm that finds the capacity achieving beamforming vectors and power allocations under a per-antenna average power constraint used in our achievable scheme. Simulation results show that as the transmit power increases, the achievable rate region under the peak power constraint is getting close to the capacity region under the reduced per-antenna average power constraint by 1/3. Compared to a non-DTC scheme based on minimum mean square error (MMSE) beamforming, the proposed scheme performs better.

In this paper, we propose a network coding using a lattice for the two-way relay channel with two nodes communicating bidirectionally through a relay, which we call modulo-and- forward (MF). Our scheme extends the network coding in the binary channel to the Gaussian channel case, where XOR in the binary case is replaced by mod Lambda for the Gaussian case, where Lambda is a high-dimensional lattice whose shaping gain is close to optimal. If the relay node re-transmits the received signal after the mod Lambda operation, we can reduce the complexity compared to decode-and-forward (DF) and can get a better power efficiency compared to amplify-and-forward (AF). When the transmission powers of two nodes are different, we use superposition coding and partial decoding at the relay node. Finally, we plot and compare the sum rates of three different schemes, i.e., AF, DF, and MF. We show that by applying the proposed scheme, we can get better performance than AF and DF schemes under some conditions.

We construct lattices with high coding gains based on nested low-density parity-check (LDPC) codes by Construction D′.We generalize the LDPC lattices [1] to have irregular degrees and call them irregular LDPC lattices. To construct good irregular LDPC lattices, we optimize the degree distributions by using density evolution and a modified sequential quadratic programming (SQP) and show our optimized irregular LDPC lattice has a threshold 0.48dB from the capacity, which is about 0.6dB better than the regular one in [1]. To construct a Tanner graph corresponding to LDPC lattices, we generalize the progressive-edge growth (PEG) algorithm and show a lower bound on the girth of the graph. Simulation is performed using the sum-product algorithm. Also, we compare the performance of joint decoding and multi-stage decoding [2] and show the advantage of joint decoding.