Capacity bounds for the discrete superposition model of the Gaussian multiple-access channel

Abstract

Abstract-Recently, it has been shown that the capacity of certain Gaussian networks can be approximated by the capacity of the corresponding network in the discrete superposition model (DSM) [1], [2]. The gap between the capacities is an additive constant only depending on the number of nodes in the network. Hence, the capacity in the DSM is a good approximation in the high SNR regime. Finding this capacity involves optimizing over a finite set of coding strategies. However, the problem space grows with both the number of nodes and with SNR, rendering the optimization infeasible.In this paper we find upper and lower bounds on the capacity in the DSM. We start with the point-to-point channel, and we extend our strategy to the multiple-access channel. We show that the gap between our bounds is at most an additive constant independent of the channel gains. Hence, combining our results with the results of [1], [2], we find closed form bounds on the Gaussian capacity to within an additive constant.

Approximating the capacity of wireless multiple unicast networks by discrete superposition model

“…where the first inequality is due to our result in [8]. Hence, we can achieve the polynomial rates ρ in and ρ out on the BC and MAC components, which yields step (a), R DSM ach ⊇ R poly ach , by using decode-and-forward in the multiple-unicast network.…”

“…Due to [8], the sum-rate achieved by a subset S of cooperating transmitters in the DSM MAC is upper bounded as …”

Approximate capacity of the general gaussian parallel relay network

“…The capacity in the DSM was shown to be an additive capacity approximation for relay networks and the interference channel [9]. We find an additive approximation for the capacity of the PRN in the DSM by using our previous results on the capacity region of the multiple-access channel in the DSM presented in [10]. Since the PRN is a relay network, our approximation is also an additive approximation for the Gaussian capacity.…”

“…Like in the previous section we derive upper and lower bounds partly relying on results we presented in [10]. Proof: Consider the separation of relays into sets S and S. We allow joint processing within each of the sets, that is we create two super-relays having multiple receptions and multiple transmissions.…”