971 research outputs found
Universal Compression of Power-Law Distributions
English words and the outputs of many other natural processes are well-known
to follow a Zipf distribution. Yet this thoroughly-established property has
never been shown to help compress or predict these important processes. We show
that the expected redundancy of Zipf distributions of order is
roughly the power of the expected redundancy of unrestricted
distributions. Hence for these orders, Zipf distributions can be better
compressed and predicted than was previously known. Unlike the expected case,
we show that worst-case redundancy is roughly the same for Zipf and for
unrestricted distributions. Hence Zipf distributions have significantly
different worst-case and expected redundancies, making them the first natural
distribution class shown to have such a difference.Comment: 20 page
Graph-based Algorithm Unfolding for Energy-aware Power Allocation in Wireless Networks
We develop a novel graph-based trainable framework to maximize the weighted
sum energy efficiency (WSEE) for power allocation in wireless communication
networks. To address the non-convex nature of the problem, the proposed method
consists of modular structures inspired by a classical iterative suboptimal
approach and enhanced with learnable components. More precisely, we propose a
deep unfolding of the successive concave approximation (SCA) method. In our
unfolded SCA (USCA) framework, the originally preset parameters are now
learnable via graph convolutional neural networks (GCNs) that directly exploit
multi-user channel state information as the underlying graph adjacency matrix.
We show the permutation equivariance of the proposed architecture, which is a
desirable property for models applied to wireless network data. The USCA
framework is trained through a stochastic gradient descent approach using a
progressive training strategy. The unsupervised loss is carefully devised to
feature the monotonic property of the objective under maximum power
constraints. Comprehensive numerical results demonstrate its generalizability
across different network topologies of varying size, density, and channel
distribution. Thorough comparisons illustrate the improved performance and
robustness of USCA over state-of-the-art benchmarks.Comment: Published in IEEE Transactions on Wireless Communication
Information content based model for the topological properties of the gene regulatory network of Escherichia coli
Gene regulatory networks (GRN) are being studied with increasingly precise
quantitative tools and can provide a testing ground for ideas regarding the
emergence and evolution of complex biological networks. We analyze the global
statistical properties of the transcriptional regulatory network of the
prokaryote Escherichia coli, identifying each operon with a node of the
network. We propose a null model for this network using the content-based
approach applied earlier to the eukaryote Saccharomyces cerevisiae. (Balcan et
al., 2007) Random sequences that represent promoter regions and binding
sequences are associated with the nodes. The length distributions of these
sequences are extracted from the relevant databases. The network is constructed
by testing for the occurrence of binding sequences within the promoter regions.
The ensemble of emergent networks yields an exponentially decaying in-degree
distribution and a putative power law dependence for the out-degree
distribution with a flat tail, in agreement with the data. The clustering
coefficient, degree-degree correlation, rich club coefficient and k-core
visualization all agree qualitatively with the empirical network to an extent
not yet achieved by any other computational model, to our knowledge. The
significant statistical differences can point the way to further research into
non-adaptive and adaptive processes in the evolution of the E. coli GRN.Comment: 58 pages, 3 tables, 22 figures. In press, Journal of Theoretical
Biology (2009)
Second-Order Coding Rates for Conditional Rate-Distortion
This paper characterizes the second-order coding rates for lossy source
coding with side information available at both the encoder and the decoder. We
first provide non-asymptotic bounds for this problem and then specialize the
non-asymptotic bounds for three different scenarios: discrete memoryless
sources, Gaussian sources, and Markov sources. We obtain the second-order
coding rates for these settings. It is interesting to observe that the
second-order coding rate for Gaussian source coding with Gaussian side
information available at both the encoder and the decoder is the same as that
for Gaussian source coding without side information. Furthermore, regardless of
the variance of the side information, the dispersion is nats squared per
source symbol.Comment: 20 pages, 2 figures, second-order coding rates, finite blocklength,
network information theor
Adaptive scalar quantization without side information
In this paper, we introduce a novel technique for adaptive scalar quantization. Adaptivity is useful in applica- tions, including image compression, where the statistics of the source are either not known a priori or will change over time. Our algorithm uses previously quantized samples to estimate the distribution of the source, and does not require that side information be sent in order to adapt to changing source statistics. Our quantization scheme is thus backward adaptive. We propose that an adaptive quantizer can be separated into two building blocks, namely, model estimation and quantizer design. The model estimation produces an estimate of the changing source probability density function, which is then used to redesign the quantizer using standard techniques. We introduce non- parametric estimation techniques that only assume smoothness of the input distribution. We discuss the various sources of error in our estimation and argue that, for a wide class of sources with a smooth probability density function (pdf), we provide a good approximation to a “universal” quantizer, with the approximation becoming better as the rate increases. We study the performance of our scheme and show how the loss due to adaptivity is minimal in typical scenarios. In particular, we provide examples and show how our technique can achieve signal- to-noise ratios (SNR’s) within 0.05 dB of the optimal Lloyd–Max quantizer (LMQ) for a memoryless source, while achieving over 1.5 dB gain over a fixed quantizer for a bimodal source
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