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

The Capacity of Wireless Channels: A Physical Approach

In this paper, the capacity of wireless channels is characterized based on electromagnetic and antenna theories with only minimal assumptions. We assume the transmitter can generate an arbitrary current distribution inside a spherical region and the receive antennas are uniformly distributed on a bigger sphere surrounding the transmitter. The capacity is shown to be $(\alpha P/N_0) \log e$ [bits/sec] in the limit of large number of receive antennas, where $P$ is the transmit power constraint, $\alpha$ is the normalized density of the receive antennas and $N_0$ is the noise power spectral density. Although this result may look trivial, it is surprising in two ways. First, this result holds regardless of the bandwidth (bandwidth can even be negligibly small). Second, this result shows that the capacity is irrespective of the size of the region containing the transmitter. This is against some previous results that claimed the maximum degrees of freedom is proportional to the surface area containing the transmitter normalized by the square of the wavelength. Our result has important practical implications since it shows that even a compact antenna array with negligible bandwidth and antenna spacing well below the wavelength can provide a huge throughput as if the array was big enough so that the antenna spacing is on the order of the wavelength.Comment: 5 pages, to appear in proceedings of 2013 IEEE ISI

A Unified Approach for Network Information Theory

In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter expression has a very simple form, which was made possible by many novel elements such as a unified framework that represents various network problems in a simple and unified way, a unified coding strategy that consists of a few basic ingredients but can emulate many known coding techniques if needed, and new proof techniques beyond the use of standard covering and packing lemmas. For example, in our framework, sources, channels, states and side information are treated in a unified way and various constraints such as cost and distortion constraints are unified as a single joint-typicality constraint. Our theorem can be useful in proving many new achievability results easily and in some cases gives simpler rate expressions than those obtained using conventional approaches. Furthermore, our unified coding can strictly outperform existing schemes. For example, we obtain a generalized decode-compress-amplify-and-forward bound as a simple corollary of our main theorem and show it strictly outperforms previously known coding schemes. Using our unified framework, we formally define and characterize three types of network duality based on channel input-output reversal and network flow reversal combined with packing-covering duality.Comment: 52 pages, 7 figures, submitted to IEEE Transactions on Information theory, a shorter version will appear in Proc. IEEE ISIT 201