245 research outputs found
Information Recovery from Pairwise Measurements
A variety of information processing tasks in practice involve recovering
objects from single-shot graph-based measurements, particularly those taken
over the edges of some measurement graph . This paper concerns the
situation where each object takes value over a group of different values,
and where one is interested to recover all these values based on observations
of certain pairwise relations over . The imperfection of
measurements presents two major challenges for information recovery: 1)
: a (dominant) portion of measurements are
corrupted; 2) : a significant fraction of pairs are
unobservable, i.e. can be highly sparse.
Under a natural random outlier model, we characterize the , that is, the critical threshold of non-corruption rate
below which exact information recovery is infeasible. This accommodates a very
general class of pairwise relations. For various homogeneous random graph
models (e.g. Erdos Renyi random graphs, random geometric graphs, small world
graphs), the minimax recovery rate depends almost exclusively on the edge
sparsity of the measurement graph irrespective of other graphical
metrics. This fundamental limit decays with the group size at a square root
rate before entering a connectivity-limited regime. Under the Erdos Renyi
random graph, a tractable combinatorial algorithm is proposed to approach the
limit for large (), while order-optimal recovery is
enabled by semidefinite programs in the small regime.
The extended (and most updated) version of this work can be found at
(http://arxiv.org/abs/1504.01369).Comment: This version is no longer updated -- please find the latest version
at (arXiv:1504.01369
The capacity region of broadcast channels with intersymbol interference and colored Gaussian noise
We derive the capacity region for a broadcast channel with intersymbol interference (ISI) and colored Gaussian noise under an input power constraint. The region is obtained by first defining a similar channel model, the circular broadcast channel, which can be decomposed into a set of parallel degraded broadcast channels. The capacity region for parallel degraded broadcast channels is known. We then show that the capacity region of the original broadcast channel equals that of the circular broadcast channel in the limit of infinite block length, and we obtain an explicit formula for the resulting capacity region. The coding strategy used to achieve each point on the convex hull of the capacity region uses superposition coding on some or all of the parallel channels and dedicated transmission on the others. The optimal power allocation for any point in the capacity region is obtained via a multilevel water-filling. We derive this optimal power allocation and the resulting capacity region for several broadcast channel models
The Impact of CSI and Power Allocation on Relay Channel Capacity and Cooperation Strategies
Capacity gains from transmitter and receiver cooperation are compared in a
relay network where the cooperating nodes are close together. Under
quasi-static phase fading, when all nodes have equal average transmit power
along with full channel state information (CSI), it is shown that transmitter
cooperation outperforms receiver cooperation, whereas the opposite is true when
power is optimally allocated among the cooperating nodes but only CSI at the
receiver (CSIR) is available. When the nodes have equal power with CSIR only,
cooperative schemes are shown to offer no capacity improvement over
non-cooperation under the same network power constraint. When the system is
under optimal power allocation with full CSI, the decode-and-forward
transmitter cooperation rate is close to its cut-set capacity upper bound, and
outperforms compress-and-forward receiver cooperation. Under fast Rayleigh
fading in the high SNR regime, similar conclusions follow. Cooperative systems
provide resilience to fading in channel magnitudes; however, capacity becomes
more sensitive to power allocation, and the cooperating nodes need to be closer
together for the decode-and-forward scheme to be capacity-achieving. Moreover,
to realize capacity improvement, full CSI is necessary in transmitter
cooperation, while in receiver cooperation optimal power allocation is
essential.Comment: Accepted for publication in IEEE Transactions on Wireless
Communication
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