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

Abstract

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 twoway 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 twoway channels which approximate their Gaussian counterparts at high SNR, which include the two-way MAC/BC channel, the twoway 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.

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

“…As we see, little work has emerged on multi-user two-way channel models, and as such we first consider simple modulo 2 adder channel models. Since the submission of this work, we have extended our results to the corresponding linear deterministic channel models that model Gaussian channels at high SNR [17], where we show that adaptation is useless in the MAC/BC and Z channels, and partial adaptation (defined in [17]) is useless for the two-way IC.…”

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

“…Due to adaptation, the inputs X 2m−1 , m ∈ {1, 2, ..., K} may be correlated, but even if all users are fully correlated and all the transmitters meet the power constraint P , H(Y n 4 ) ≤ n(log P + o(log P )) as correlation only induces a power gain inside the logarithm for a single antenna receiver. 4 Here f (x) = o(φ(x)) denotes the Landau little-O notation, i.e. that lim x→∞…”

“…To extend our understanding of the impact of full-duplex operation to two-way networks with interference, the two-way interference channel (TWIC) has been studied in [4]- [7], in which there are 4 independent messages: two-messages to be transmitted over an interference channel (IC) in the → direction simultaneously with two-messages to be transmitted over an in-band IC in the ← direction. All 4 nodes in this network act as both sources and destinations of messages.…”

“…Here, we seek to extend our understanding of the DoF to two-way networks, whose study is motivated by the fact that full-duplex operation is becoming practically realizable. Some progress has already been made: the DoF of the full-duplex TWIC has been shown to be 2 [4], [6]. This is interesting, because the capacity of any network with interaction at nodes is no smaller than that of the same network where interaction is not possible (interaction can mimic non-interaction).…”

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

“…To extend our understanding of the impact of full-duplex operation to two-way networks with interference, the two-way interference channel (TWIC) has been studied in [10]- [13], in which there are 4 independent messages: two-messages to be transmitted over an interference channel (IC) in the → direction simultaneously with two-messages to be transmitted over an in-band IC in the ← direction. In wireless communications, the TWIC has been used in [14] to model an inter-cell interference scenario where a base station in one cell suffers interference signal from a user in an adjacent cell and vice versa.…”