6,892 research outputs found
Information Spectrum Approach to the Source Channel Separation Theorem
A source-channel separation theorem for a general channel has recently been
shown by Aggrawal et. al. This theorem states that if there exist a coding
scheme that achieves a maximum distortion level d_{max} over a general channel
W, then reliable communication can be accomplished over this channel at rates
less then R(d_{max}), where R(.) is the rate distortion function of the source.
The source, however, is essentially constrained to be discrete and memoryless
(DMS). In this work we prove a stronger claim where the source is general,
satisfying only a "sphere packing optimality" feature, and the channel is
completely general. Furthermore, we show that if the channel satisfies the
strong converse property as define by Han & verdu, then the same statement can
be made with d_{avg}, the average distortion level, replacing d_{max}. Unlike
the proofs there, we use information spectrum methods to prove the statements
and the results can be quite easily extended to other situations
Computation in Multicast Networks: Function Alignment and Converse Theorems
The classical problem in network coding theory considers communication over
multicast networks. Multiple transmitters send independent messages to multiple
receivers which decode the same set of messages. In this work, computation over
multicast networks is considered: each receiver decodes an identical function
of the original messages. For a countably infinite class of two-transmitter
two-receiver single-hop linear deterministic networks, the computing capacity
is characterized for a linear function (modulo-2 sum) of Bernoulli sources.
Inspired by the geometric concept of interference alignment in networks, a new
achievable coding scheme called function alignment is introduced. A new
converse theorem is established that is tighter than cut-set based and
genie-aided bounds. Computation (vs. communication) over multicast networks
requires additional analysis to account for multiple receivers sharing a
network's computational resources. We also develop a network decomposition
theorem which identifies elementary parallel subnetworks that can constitute an
original network without loss of optimality. The decomposition theorem provides
a conceptually-simpler algebraic proof of achievability that generalizes to
-transmitter -receiver networks.Comment: to appear in the IEEE Transactions on Information Theor
Q-CSMA: Queue-Length Based CSMA/CA Algorithms for Achieving Maximum Throughput and Low Delay in Wireless Networks
Recently, it has been shown that CSMA-type random access algorithms can
achieve the maximum possible throughput in ad hoc wireless networks. However,
these algorithms assume an idealized continuous-time CSMA protocol where
collisions can never occur. In addition, simulation results indicate that the
delay performance of these algorithms can be quite bad. On the other hand,
although some simple heuristics (such as distributed approximations of greedy
maximal scheduling) can yield much better delay performance for a large set of
arrival rates, they may only achieve a fraction of the capacity region in
general. In this paper, we propose a discrete-time version of the CSMA
algorithm. Central to our results is a discrete-time distributed randomized
algorithm which is based on a generalization of the so-called Glauber dynamics
from statistical physics, where multiple links are allowed to update their
states in a single time slot. The algorithm generates collision-free
transmission schedules while explicitly taking collisions into account during
the control phase of the protocol, thus relaxing the perfect CSMA assumption.
More importantly, the algorithm allows us to incorporate mechanisms which lead
to very good delay performance while retaining the throughput-optimality
property. It also resolves the hidden and exposed terminal problems associated
with wireless networks.Comment: 12 page
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