# On the Sum-Capacity of Degraded Gaussian Multiaccess Relay Channels - Computer Science > Information Theory

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Abstract: The sum-capacity is studied for a K-user degraded Gaussian multiaccess relaychannel MARC where the multiaccess signal received at the destination fromthe K sources and relay is a degraded version of the signal received at therelay from all sources, given the transmit signal at the relay. An outer boundon the capacity region is developed using cutset bounds. An achievable rateregion is obtained for the decode-and-forward DF strategy. It is shown thatfor every choice of input distribution, the rate regions for the inner DF andouter bounds are given by the intersection of two K-dimensional polymatroids,one resulting from the multiaccess link at the relay and the other from that atthe destination. Although the inner and outer bound rate regions are notidentical in general, for both cases, a classical result on the intersection oftwo polymatroids is used to show that the intersection belongs to either theset of active cases or inactive cases, where the two bounds on the K-usersum-rate are active or inactive, respectively. It is shown that DF achieves thecapacity region for a class of degraded Gaussian MARCs in which the relay has ahigh SNR link to the destination relative to the multiaccess link from thesources to the relay. Otherwise, DF is shown to achieve the sum-capacity for anactive class of degraded Gaussian MARCs for which the DF sum-rate is maximizedby a polymatroid intersection belonging to the set of active cases. This classis shown to include the class of symmetric Gaussian MARCs where all userstransmit at the same power.

Author: ** Lalitha Sankar, Narayan B. Mandayam, H. Vincent Poor**

Source: https://arxiv.org/