In two-way networks, nodes act as both sources and destinations of messages. This allows for "adaptation" at or "interaction" between the nodes - a node's channel inputs may be functions of its message(s) and previously received signals. How to best adapt is key to two-way communication, rendering it challenging. However, examples exist of point-to-point channels where adaptation is not beneficial from a capacity perspective. We ask whether analogous examples exist for multi-user two-way networks. We first consider deterministic two-way channel models: the binary modulo-2 addition channel and a generalization thereof, and the linear deterministic channel. For these deterministic models we obtain the capacity region for the two-way multiple access broadcast channel, the two-way Z channel and the two-way interference channel (IC). In all cases we permit all nodes to adapt channel inputs to past outputs (except for portions of the linear deterministic two-way IC where we only permit 2 of the 4 nodes to fully adapt). However, we show that this adaptation is useless from a capacity region perspective and capacity is achieved by strategies where the channel inputs at each use do not adapt to previous inputs. Finally, we consider the Gaussian two-way IC, and show that partial adaptation is useless when the interference is very strong. In the strong and weak interference regimes, we show that the non-adaptive Han and Kobayashi scheme utilized in parallel in both directions achieves to within a constant gap for the symmetric rate of the fully (some regimes) or partially (remaining regimes) adaptive models. The central technical contribution is the derivation of new, computable outer bounds which allow for adaptation. Inner bounds follow from non-adaptive achievability schemes of the corresponding one-way channel models.
The second channel model we consider is the two-way Z channel, with 6 messages. The one-way Z channel (with 3 messages, rather than the Z Interference channel with 2 messages) was first studied in @cite_12 , in which a general outer bound, and a matching inner bound for a special class of degraded Z channels are obtained. The capacity region of the one-way deterministic Z channel with invertibility constraints similar in flavor to those in @cite_40 , is found in @cite_31 , which will be of use here.
@cite_40 @cite_31 @cite_12
2087258384 2137158410 2140960960
The capacity region of a class of deterministic discrete memoryless interference channels is established. In this class of channels the outputs Y_ 1 and Y_ 2 are (deterministic) functions of the inputs X_ 1 and X_ 2 such that H(Y_ 1 |X_ 1 )=H(V_ 2 ) and H(Y_ 2 |X_ 2 )=H(V_ l ) for all product probabiliW distributions on X_ 1 X_ 2 , where V_ 1 is a function of X_ 1 and V_ 2 a function of X_ 2 . The capacity, region for the case in which V_ 2 0 and Y_ 1 depends randomly on X_ 1 is also obtained and illustrated with an example. We characterize the capacity region of a class of the deterministic Z channels. We show that, interestingly, Han-Kobayashi type rate-splitting is not required in the optimal achievable scheme for the class of channels considered. A two transmitter two receiver channel where independent data is sent on each communication link of the system is considered. We consider a three-link system, termed the "Z" channel, in which one transmitter is connected to both receivers while the other transmitter is only connected to one of the receivers. Thus, the "Z" channel has a three dimensional capacity region. We characterize the capacity region of a special class of degraded "Z" channels and establish an achievable region for the Gaussian "Z" channels. Finally, we use genie-aided techniques previously used for the interference and broadcast channels to obtain an outer bound for general "Z" channels.