1,685 research outputs found
Nomographic Functions: Efficient Computation in Clustered Gaussian Sensor Networks
In this paper, a clustered wireless sensor network is considered that is
modeled as a set of coupled Gaussian multiple-access channels. The objective of
the network is not to reconstruct individual sensor readings at designated
fusion centers but rather to reliably compute some functions thereof. Our
particular attention is on real-valued functions that can be represented as a
post-processed sum of pre-processed sensor readings. Such functions are called
nomographic functions and their special structure permits the utilization of
the interference property of the Gaussian multiple-access channel to reliably
compute many linear and nonlinear functions at significantly higher rates than
those achievable with standard schemes that combat interference. Motivated by
this observation, a computation scheme is proposed that combines a suitable
data pre- and post-processing strategy with a nested lattice code designed to
protect the sum of pre-processed sensor readings against the channel noise.
After analyzing its computation rate performance, it is shown that at the cost
of a reduced rate, the scheme can be extended to compute every continuous
function of the sensor readings in a finite succession of steps, where in each
step a different nomographic function is computed. This demonstrates the
fundamental role of nomographic representations.Comment: to appear in IEEE Transactions on Wireless Communication
Secure Compute-and-Forward in a Bidirectional Relay
We consider the basic bidirectional relaying problem, in which two users in a
wireless network wish to exchange messages through an intermediate relay node.
In the compute-and-forward strategy, the relay computes a function of the two
messages using the naturally-occurring sum of symbols simultaneously
transmitted by user nodes in a Gaussian multiple access (MAC) channel, and the
computed function value is forwarded to the user nodes in an ensuing broadcast
phase. In this paper, we study the problem under an additional security
constraint, which requires that each user's message be kept secure from the
relay. We consider two types of security constraints: perfect secrecy, in which
the MAC channel output seen by the relay is independent of each user's message;
and strong secrecy, which is a form of asymptotic independence. We propose a
coding scheme based on nested lattices, the main feature of which is that given
a pair of nested lattices that satisfy certain "goodness" properties, we can
explicitly specify probability distributions for randomization at the encoders
to achieve the desired security criteria. In particular, our coding scheme
guarantees perfect or strong secrecy even in the absence of channel noise. The
noise in the channel only affects reliability of computation at the relay, and
for Gaussian noise, we derive achievable rates for reliable and secure
computation. We also present an application of our methods to the multi-hop
line network in which a source needs to transmit messages to a destination
through a series of intermediate relays.Comment: v1 is a much expanded and updated version of arXiv:1204.6350; v2 is a
minor revision to fix some notational issues; v3 is a much expanded and
updated version of v2, and contains results on both perfect secrecy and
strong secrecy; v3 is a revised manuscript submitted to the IEEE Transactions
on Information Theory in April 201
Integer-Forcing Source Coding
Integer-Forcing (IF) is a new framework, based on compute-and-forward, for
decoding multiple integer linear combinations from the output of a Gaussian
multiple-input multiple-output channel. This work applies the IF approach to
arrive at a new low-complexity scheme, IF source coding, for distributed lossy
compression of correlated Gaussian sources under a minimum mean squared error
distortion measure. All encoders use the same nested lattice codebook. Each
encoder quantizes its observation using the fine lattice as a quantizer and
reduces the result modulo the coarse lattice, which plays the role of binning.
Rather than directly recovering the individual quantized signals, the decoder
first recovers a full-rank set of judiciously chosen integer linear
combinations of the quantized signals, and then inverts it. In general, the
linear combinations have smaller average powers than the original signals. This
allows to increase the density of the coarse lattice, which in turn translates
to smaller compression rates. We also propose and analyze a one-shot version of
IF source coding, that is simple enough to potentially lead to a new design
principle for analog-to-digital converters that can exploit spatial
correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor
Zero-rate feedback can achieve the empirical capacity
The utility of limited feedback for coding over an individual sequence of
DMCs is investigated. This study complements recent results showing how limited
or noisy feedback can boost the reliability of communication. A strategy with
fixed input distribution is given that asymptotically achieves rates
arbitrarily close to the mutual information induced by and the
state-averaged channel. When the capacity achieving input distribution is the
same over all channel states, this achieves rates at least as large as the
capacity of the state averaged channel, sometimes called the empirical
capacity.Comment: Revised version of paper originally submitted to IEEE Transactions on
Information Theory, Nov. 2007. This version contains further revisions and
clarification
- …