The deterministic capacity of relay networks with relay private messages

Abstract

We study the capacity region of a deterministic 4node network, where 3 nodes can only communicate via the fourth one. However, the fourth node is not merely a relay since it can exchange private messages with all other nodes. This situation resembles the case where a base station relays messages between users and delivers messages between the backbone system and the users. We assume an asymmetric scenario where the channel between any two nodes is not reciprocal. First, an upper bound on the capacity region is obtained based on the notion of single sided genie. Subsequently, we construct an achievable scheme that achieves this upper bound using a superposition of broadcasting node 4 messages and an achievable "detour" scheme for a reduced 3-user relay network.

Using network coding to achieve the capacity of deterministic relay networks with relay messages

“…From the insights obtained from this work, [11] and [12], we can make a conjecture about the capacity region of the K-node relay network with relay messages, where we have K 1 users f1, 2, : : : , K 1g, each of them wishes to exchange messages with the remaining network nodes via the K-th node, which acts as a relay beside its interest to transmit its private messages to each user.…”

“…It can be observed from [8,9,11,12] that the achievability technique differs from one topology to another depending on the number of users; thus, a question rises, how we can achieve the capacity region of the K-user relay network. To answer this question, we consider a deterministic four-user multicast relay network with no direct links, where each user can exchange private messages with the other network nodes.…”

“…A distinguishing feature of this work is the assumption of non-reciprocal channels. In fact, one can see this work as a generalisation of the work in [11] and [12]. In contrast to [11], it considers four-user relay network with private messages and non-reciprocal channels, and in contrast to [12], it considers an extra user in the network.…”

“…In fact, one can see this work as a generalisation of the work in [11] and [12]. In contrast to [11], it considers four-user relay network with private messages and non-reciprocal channels, and in contrast to [12], it considers an extra user in the network. Therefore, results in [8,9,11,12] can be obtained from the results presented here with appropriate settings of system parameters.…”

“…Achievability of the capacity region was demonstrated via two detour schemes (DS), which are different from the ones used in [8] because of the different nature of the multicast network. After that, in [12], we studied the capacity of a three-user relay network where the relay node is interested in exchanging some private messages with the other network users. It was shown that, if all messages emanating from the 'relay node' are transmitted first, we obtain a reduced capacity region in the form of the capacity region of an asymmetric three-user relay network, the achievability of which was proven using a combination of the SOS and a DS.…”