77,968 research outputs found
Low-Complexity OFDM Spectral Precoding
This paper proposes a new large-scale mask-compliant spectral precoder
(LS-MSP) for orthogonal frequency division multiplexing systems. In this paper,
we first consider a previously proposed mask-compliant spectral precoding
scheme that utilizes a generic convex optimization solver which suffers from
high computational complexity, notably in large-scale systems. To mitigate the
complexity of computing the LS-MSP, we propose a divide-and-conquer approach
that breaks the original problem into smaller rank 1 quadratic-constraint
problems and each small problem yields closed-form solution. Based on these
solutions, we develop three specialized first-order low-complexity algorithms,
based on 1) projection on convex sets and 2) the alternating direction method
of multipliers. We also develop an algorithm that capitalizes on the
closed-form solutions for the rank 1 quadratic constraints, which is referred
to as 3) semi-analytical spectral precoding. Numerical results show that the
proposed LS-MSP techniques outperform previously proposed techniques in terms
of the computational burden while complying with the spectrum mask. The results
also indicate that 3) typically needs 3 iterations to achieve similar results
as 1) and 2) at the expense of a slightly increased computational complexity.Comment: Accepted in IEEE International Workshop on Signal Processing Advances
in Wireless Communications (SPAWC), 201
Low-complexity distributed issue queue
As technology evolves, power density significantly increases and cooling systems become more complex and expensive. The issue logic is one of the processor hotspots and, at the same time, its latency is crucial for the processor performance. We present a low-complexity FP issue logic (MB/spl I.bar/distr) that achieves high performance with small energy requirements. The MB/spl I.bar/distr scheme is based on classifying instructions and dispatching them into a set of queues depending on their data dependences. These instructions are selected for issuing based on an estimation of when their operands will be available, so the conventional wakeup activity is not required. Additionally, the functional units are distributed across the different queues. The energy required by the proposed scheme is substantially lower than that required by a conventional issue design, even if the latter has the ability of waking-up only unready operands. MB/spl I.bar/distr scheme reduces the energy-delay product by 35% and the energy-delay product by 18% with respect to a state-of-the-art approach.Peer ReviewedPostprint (published version
Testing Low Complexity Affine-Invariant Properties
Invariance with respect to linear or affine transformations of the domain is
arguably the most common symmetry exhibited by natural algebraic properties. In
this work, we show that any low complexity affine-invariant property of
multivariate functions over finite fields is testable with a constant number of
queries. This immediately reproves, for instance, that the Reed-Muller code
over F_p of degree d < p is testable, with an argument that uses no detailed
algebraic information about polynomials except that low degree is preserved by
composition with affine maps.
The complexity of an affine-invariant property P refers to the maximum
complexity, as defined by Green and Tao (Ann. Math. 2008), of the sets of
linear forms used to characterize P. A more precise statement of our main
result is that for any fixed prime p >=2 and fixed integer R >= 2, any
affine-invariant property P of functions f: F_p^n -> [R] is testable, assuming
the complexity of the property is less than p. Our proof involves developing
analogs of graph-theoretic techniques in an algebraic setting, using tools from
higher-order Fourier analysis.Comment: 38 pages, appears in SODA '1
Low Complexity Algorithms for Linear Recurrences
We consider two kinds of problems: the computation of polynomial and rational
solutions of linear recurrences with coefficients that are polynomials with
integer coefficients; indefinite and definite summation of sequences that are
hypergeometric over the rational numbers. The algorithms for these tasks all
involve as an intermediate quantity an integer (dispersion or root of an
indicial polynomial) that is potentially exponential in the bit size of their
input. Previous algorithms have a bit complexity that is at least quadratic in
. We revisit them and propose variants that exploit the structure of
solutions and avoid expanding polynomials of degree . We give two
algorithms: a probabilistic one that detects the existence or absence of
nonzero polynomial and rational solutions in bit
operations; a deterministic one that computes a compact representation of the
solution in bit operations. Similar speed-ups are obtained in
indefinite and definite hypergeometric summation. We describe the results of an
implementation.Comment: This is the author's version of the work. It is posted here by
permission of ACM for your personal use. Not for redistributio
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