15,166 research outputs found
Capacity Bounds for a Class of Diamond Networks
A class of diamond networks are studied where the broadcast component is
modelled by two independent bit-pipes. New upper and low bounds are derived on
the capacity which improve previous bounds. The upper bound is in the form of a
max-min problem, where the maximization is over a coding distribution and the
minimization is over an auxiliary channel. The proof technique generalizes
bounding techniques of Ozarow for the Gaussian multiple description problem
(1981), and Kang and Liu for the Gaussian diamond network (2011). The bounds
are evaluated for a Gaussian multiple access channel (MAC) and the binary adder
MAC, and the capacity is found for interesting ranges of the bit-pipe
capacities
The Approximate Capacity of the Gaussian N-Relay Diamond Network
We consider the Gaussian "diamond" or parallel relay network, in which a
source node transmits a message to a destination node with the help of N
relays. Even for the symmetric setting, in which the channel gains to the
relays are identical and the channel gains from the relays are identical, the
capacity of this channel is unknown in general. The best known capacity
approximation is up to an additive gap of order N bits and up to a
multiplicative gap of order N^2, with both gaps independent of the channel
gains.
In this paper, we approximate the capacity of the symmetric Gaussian N-relay
diamond network up to an additive gap of 1.8 bits and up to a multiplicative
gap of a factor 14. Both gaps are independent of the channel gains and, unlike
the best previously known result, are also independent of the number of relays
N in the network. Achievability is based on bursty amplify-and-forward, showing
that this simple scheme is uniformly approximately optimal, both in the
low-rate as well as in the high-rate regimes. The upper bound on capacity is
based on a careful evaluation of the cut-set bound. We also present
approximation results for the asymmetric Gaussian N-relay diamond network. In
particular, we show that bursty amplify-and-forward combined with optimal relay
selection achieves a rate within a factor O(log^4(N)) of capacity with
pre-constant in the order notation independent of the channel gains.Comment: 23 pages, to appear in IEEE Transactions on Information Theor
Analog network coding in general SNR regime: Performance of a greedy scheme
The problem of maximum rate achievable with analog network coding for a
unicast communication over a layered relay network with directed links is
considered. A relay node performing analog network coding scales and forwards
the signals received at its input. Recently this problem has been considered
under certain assumptions on per node scaling factor and received SNR.
Previously, we established a result that allows us to characterize the optimal
performance of analog network coding in network scenarios beyond those that can
be analyzed using the approaches based on such assumptions.
The key contribution of this work is a scheme to greedily compute a lower
bound to the optimal rate achievable with analog network coding in the general
layered networks. This scheme allows for exact computation of the optimal
achievable rates in a wider class of layered networks than those that can be
addressed using existing approaches. For the specific case of Gaussian N-relay
diamond network, to the best of our knowledge, the proposed scheme provides the
first exact characterization of the optimal rate achievable with analog network
coding. Further, for general layered networks, our scheme allows us to compute
optimal rates within a constant gap from the cut-set upper bound asymptotically
in the source power.Comment: 11 pages, 5 figures. Fixed an issue with the notation in the
statement and proof of Lemma 1. arXiv admin note: substantial text overlap
with arXiv:1204.2150 and arXiv:1202.037
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