Zhiyu Cheng

Two-Way Networks: When Adaptation is Useless

Most wireless communication networks are two-way, where nodes act as both sources and destinations of messages. This allows for adaptation at or interaction between the nodes-a nodes channel inputs may be functions of its message(s) and previously received signals allowing for potentially larger rates than those achievable in feedback-free one-way channels where inputs are functions of messages only. However, examples exist of channels where adaptation is not beneficial from a capacity perspective. We ask whether analogous results hold for several multiuser two-way networks. We first consider deterministic two-way channel models: the binary modulo-2 addition channel and a generalization of this, and the linear deterministic channel, which models Gaussian channels at high SNR. For these deterministic models, we obtain the capacity region for the two-way multiple access/broadcast channel (MAC/BC), the two-way Z channel, and the two-way interference channel (under certain partial adaptation constraints in some regimes). We permit all nodes to adapt their channel inputs to past outputs (except for portions of the linear high-SNR two-way interference channel where we only permit two of the four nodes to fully adapt). However, we show that the two-way fully or partially adaptive capacity region consists of two parallel one-way regions operating simultaneously in opposite directions, i.e., adaptation is useless. We next consider two noisy channel models: 1) the Gaussian two-way MAC/BC, where we show that adaptation can at most increase the sum-rate by (1/2) bit in each direction and 2) the two-way interference channel, where partial adaptation is shown to be useless when the interference is very strong. In the strong and weak interference regimes, we show that the nonadaptive Han and Kobayashi scheme utilized in parallel in both directions achieves to within a constant gap for the symmetric rate of the fully (for some regimes) or partially (for the remaining regimes) adaptive models. The central technical contribution is the derivation of new, computable outer bounds which allow for adaptation.

The Degrees of Freedom of Full-Duplex Bidirectional Interference Networks With and Without a MIMO Relay

In a full-duplex bidirectional interference network with 2K transceivers, there are K communication pairs: each user transmits a message to and receives a message from one intended user and interferes with and experiences interference from all other users. All nodes may interact, or adapt inputs to past received signals, and may thus co-operate with each other. We derive a new outer bound, and use interference alignment to demonstrate that the optimal degrees of freedom (DoF, also known as the multiplexing gain) is K: full-duplex operation doubles the DoF, but interaction and co-operation does not further increase the DoF. We next characterize the DoF of a full-duplex bidirectional interference network with a MIMO full-duplex relay. If the relay is noncausal/instantaneous (at time k forwards a function of its received signals up to time k) and has 2K antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free 2K DoF. In contrast, if the relay is causal (at time k forwards a function of its received signals up to time k - 1), we show that a full-duplex MIMO relay cannot increase the DoF of the full-duplex bidirectional interference network beyond K, as if no relay or interaction is present.

On the capacity of multi-user two-way linear deterministic channels

In multi-user two-way channels nodes are both sources and destinations of messages. This allows for “adaptation” at or “interaction” between the nodes - the next channel inputs may be a function of the past received signals at a particular node. How to best adapt is key to two-way communication problems, rendering them complex and challenging. However, examples exist of channels where adaptation is not beneficial from a capacity perspective; it is known that for the point-to-point two-way modulo 2 adder and Gaussian channels, adaptation does not increase capacity. Recently, it was shown that the two-way modulo-2 additive versions of the multiple-access / broadcast (MAC/BC respectively, in the two directions), the Z channel and the interference channel also have capacity regions equal to two parallel one-way versions of the channels. In this work we show that the same is true for the linear deterministic multi-user two-way channels which approximate their Gaussian counterparts at high SNR, which include the two-way MAC/BC channel, the two-way Z channel, and the two-way interference channel under some adaptation constraints. For all three channel models we obtain the capacity region, which is that of two one-way channels in each direction, which may be achieved without the use of adaptation.

On constant gaps for the two-way Gaussian interference channel

We introduce the two-way Gaussian interference channel in which there are four nodes with four independent messages: two-messages to be transmitted over a Gaussian interference channel in the → direction, simultaneously with two-messages to be transmitted over an interference channel (in-band, full-duplex) in the ← direction. In such a two-way network, all nodes are transmitters and receivers of messages, allowing them to adapt current channel inputs to previously received channel outputs. We propose two new outer bounds on the symmetric sum-rate for the two-way Gaussian interference channel with complex channel gains: one under full adaptation (all 4 nodes are permitted to adapt inputs to previous outputs), and one under partial adaptation (only 2 nodes are permitted to adapt, the other 2 are restricted). We show that simple non-adaptive schemes such as the Han and Kobayashi scheme, where inputs are functions of messages only and not past outputs, utilized in each direction are sufficient to achieve within a constant gap of these fully or partially adaptive outer bounds for all channel regimes.

The degrees of freedom of the K-pair-user full-duplex two-way interference channel with a MIMO relay

In a K-pair-user two-way interference channel (TWIC), 2K messages and 2K transmitters/receivers form a K-user IC in the forward direction (K messages) and another K-user IC in the backward direction which operate in full-duplex. All nodes may interact, or adapt inputs to past received signals. The optimal degrees of freedom (DoF, also known as the multiplexing gain) is known to be K [1]: full-duplex operation doubles the DoF, but interaction does not further increase the DoF. In this paper, we characterize the DoF of the K-pair-user TWIC with a MIMO, full-duplex relay. If the relay is noncausal/ instantaneous (at time k forwards a function of its received signals up to time k) and has 2K antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free 2K DoF. In contrast, if the relay is causal (at time k forwards a function of its received signals up to time k - 1), we show that a full-duplex MIMO relay cannot increase the DoF of the K-pair-user TWIC beyond K, as if no relay or interaction is present.

On constant gaps for the K-pair user two-way Gaussian interference channel with interaction

In a K-pair-user two-way Gaussian interference channel (IC), 2K messages and 2K transmitters/receivers form a Gaussian K-user IC in the forward direction (K messages) and another Gaussian K-user IC in the backward direction (K messages) which operate simultaneously in full-duplex mode. All nodes are permitted to interact, i.e. adapt current channel inputs to past received signals. We derive a new sum-rate outer bound for linear deterministic and Gaussian noise channels allowing for interaction, but show that for symmetric scenarios and certain interference regimes (moderately weak and strong), non-interactive schemes achieve to within a constant gap of this outer bound. That is, interaction for symmetric channels in certain interference regimes may only improve the sum-rate by a constant number of bits per channel use.

An outer bound region for the parallel two-way channel with interference

The classical interference channel models the communication limits of two independent, interfering streams of one-way data. In this paper we extend the classical interference channel model to a new channel model in which two streams of two-way data interfere with each other. In the absence of interference, this model would result in two parallel two-way channels (a four node channel); in the presence of interference it encompasses two-way, interference, and cooperation tradeoffs. The discrete memoryless “parallel two-way channel with interference” is considered, in which each of the four nodes is the source of one message, the receiver of another, and experiences interference from yet another transmitter. The nodes may adapt their transmissions to the past received signals in a fully two-way fashion. We present an outer bound to the four dimensional capacity region which utilizes four auxiliary random variables to constrain the input distributions, and present a looser outer bound with a single auxiliary random variable which is computable as we place bounds on this variables alphabet size.

Multi-user two-way deterministic modulo 2 adder channels — When adaptation is useless

In two-way channels nodes are both sources and destinations of messages, allowing them to “adapt” or “interact” in the sense that their next channel input may be a function of their past received signals. This “adaptation” and how to best exploit it lies at the heart of two-way communication problems, rendering them particularly complex and challenging. It would be useful to know when adaptation is not beneficial from a capacity perspective. Certain examples exist: it is known that for the point-to-point two-way modulo 2 adder channel, and the point-to-point Gaussian two-way channel, adaptation does not increase capacity. In this work we show that the same is true for certain classes of deterministic multi-user two-way channels. In particular, we consider a class of multi-user two-way modulo 2 adder channels, which include the two-way modulo 2 adder MAC/BC channel, the two-way modulo 2 adder interference channel, and the two-way modulo 2 adder Z channel. For all three channel models we obtain the capacity region, which may be achieved using simple time-sharing.

Waveform scheduling via directed information in cognitive radar

The objective of waveform scheduling is to achieve maximal information extraction of the radar scene, which typically changes from one measurement to the next, by exploiting prior statistics and waveform diversity. In this paper waveform scheduling is addressed using information theoretic concepts. A pre-defined waveform library is assumed to be given, or designed a priori. To keep the analysis simple, we constrain ourselves to a library comprised of two waveforms scheduled over two consecutive time intervals. We propose selecting the waveforms to maximize the directed information, a metric not previously considered in this context, which directly incorporates the feedback present in the radar system. Analog and discrete models are discussed; the former allows for a spectral domain interpretation, whereas, the latter permits analogies to Bayesian error metrics.

Degrees of freedom of the two-way interference channel with a non causal multi-antenna relay

We characterize the degrees of freedom (DoF) of the full-duplex two-way interference channel with a non causal multi-antenna relay and time-varying channels. In a two-way interference channel (IC), 4 messages and 4 transmitters/receivers form an IC in the forward direction (2 messages) and another IC in the backward direction (2 messages) which operate simultaneously in full-duplex mode. Furthermore, all nodes are permitted to interact, i.e. adapt current channel inputs to past received signals. We propose a novel block Markov coding scheme combining the ideas of interference alignment and successive decoding to achieve the full, maximal, 4 degrees of freedom asymptotically. All source/destination nodes have a single antenna while 4 antennas at the relay are sufficient to achieve the full DoF. Interestingly, this implies that the non causal relay is able to effectively mitigate interference in this two way setting - i.e. each user in the two-way interference channel is able to exchange information with its desired user at interference-free rates thanks to the relay.