51,020 research outputs found
Computation Over Gaussian Networks With Orthogonal Components
Function computation of arbitrarily correlated discrete sources over Gaussian
networks with orthogonal components is studied. Two classes of functions are
considered: the arithmetic sum function and the type function. The arithmetic
sum function in this paper is defined as a set of multiple weighted arithmetic
sums, which includes averaging of the sources and estimating each of the
sources as special cases. The type or frequency histogram function counts the
number of occurrences of each argument, which yields many important statistics
such as mean, variance, maximum, minimum, median, and so on. The proposed
computation coding first abstracts Gaussian networks into the corresponding
modulo sum multiple-access channels via nested lattice codes and linear network
coding and then computes the desired function by using linear Slepian-Wolf
source coding. For orthogonal Gaussian networks (with no broadcast and
multiple-access components), the computation capacity is characterized for a
class of networks. For Gaussian networks with multiple-access components (but
no broadcast), an approximate computation capacity is characterized for a class
of networks.Comment: 30 pages, 12 figures, submitted to IEEE Transactions on Information
Theor
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
On the Convergence Speed of Turbo Demodulation with Turbo Decoding
Iterative processing is widely adopted nowadays in modern wireless receivers
for advanced channel codes like turbo and LDPC codes. Extension of this
principle with an additional iterative feedback loop to the demapping function
has proven to provide substantial error performance gain. However, the adoption
of iterative demodulation with turbo decoding is constrained by the additional
implied implementation complexity, heavily impacting latency and power
consumption. In this paper, we analyze the convergence speed of these combined
two iterative processes in order to determine the exact required number of
iterations at each level. Extrinsic information transfer (EXIT) charts are used
for a thorough analysis at different modulation orders and code rates. An
original iteration scheduling is proposed reducing two demapping iterations
with reasonable performance loss of less than 0.15 dB. Analyzing and
normalizing the computational and memory access complexity, which directly
impact latency and power consumption, demonstrates the considerable gains of
the proposed scheduling and the promising contributions of the proposed
analysis.Comment: Submitted to IEEE Transactions on Signal Processing on April 27, 201
Analysing Astronomy Algorithms for GPUs and Beyond
Astronomy depends on ever increasing computing power. Processor clock-rates
have plateaued, and increased performance is now appearing in the form of
additional processor cores on a single chip. This poses significant challenges
to the astronomy software community. Graphics Processing Units (GPUs), now
capable of general-purpose computation, exemplify both the difficult
learning-curve and the significant speedups exhibited by massively-parallel
hardware architectures. We present a generalised approach to tackling this
paradigm shift, based on the analysis of algorithms. We describe a small
collection of foundation algorithms relevant to astronomy and explain how they
may be used to ease the transition to massively-parallel computing
architectures. We demonstrate the effectiveness of our approach by applying it
to four well-known astronomy problems: Hogbom CLEAN, inverse ray-shooting for
gravitational lensing, pulsar dedispersion and volume rendering. Algorithms
with well-defined memory access patterns and high arithmetic intensity stand to
receive the greatest performance boost from massively-parallel architectures,
while those that involve a significant amount of decision-making may struggle
to take advantage of the available processing power.Comment: 10 pages, 3 figures, accepted for publication in MNRA
Evaluating critical bits in arithmetic operations due to timing violations
Various error models are being used in simulation of voltage-scaled arithmetic units to examine application-level tolerance of timing violations. The selection of an error model needs further consideration, as differences in error models drastically affect the performance of the application. Specifically, floating point arithmetic units (FPUs) have architectural characteristics that characterize its behavior. We examine the architecture of FPUs and design a new error model, which we call Critical Bit. We run selected benchmark applications with Critical Bit and other widely used error injection models to demonstrate the differences
Network Coding for Computing: Cut-Set Bounds
The following \textit{network computing} problem is considered. Source nodes
in a directed acyclic network generate independent messages and a single
receiver node computes a target function of the messages. The objective is
to maximize the average number of times can be computed per network usage,
i.e., the ``computing capacity''. The \textit{network coding} problem for a
single-receiver network is a special case of the network computing problem in
which all of the source messages must be reproduced at the receiver. For
network coding with a single receiver, routing is known to achieve the capacity
by achieving the network \textit{min-cut} upper bound. We extend the definition
of min-cut to the network computing problem and show that the min-cut is still
an upper bound on the maximum achievable rate and is tight for computing (using
coding) any target function in multi-edge tree networks and for computing
linear target functions in any network. We also study the bound's tightness for
different classes of target functions. In particular, we give a lower bound on
the computing capacity in terms of the Steiner tree packing number and a
different bound for symmetric functions. We also show that for certain networks
and target functions, the computing capacity can be less than an arbitrarily
small fraction of the min-cut bound.Comment: Submitted to the IEEE Transactions on Information Theory (Special
Issue on Facets of Coding Theory: from Algorithms to Networks); Revised on
Aug 9, 201
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