21,372 research outputs found
Synthesis of Gaussian Trees with Correlation Sign Ambiguity: An Information Theoretic Approach
In latent Gaussian trees the pairwise correlation signs between the variables
are intrinsically unrecoverable. Such information is vital since it completely
determines the direction in which two variables are associated. In this work,
we resort to information theoretical approaches to achieve two fundamental
goals: First, we quantify the amount of information loss due to unrecoverable
sign information. Second, we show the importance of such information in
determining the maximum achievable rate region, in which the observed output
vector can be synthesized, given its probability density function. In
particular, we model the graphical model as a communication channel and propose
a new layered encoding framework to synthesize observed data using upper layer
Gaussian inputs and independent Bernoulli correlation sign inputs from each
layer. We find the achievable rate region for the rate tuples of multi-layer
latent Gaussian messages to synthesize the desired observables.Comment: 14 pages, 9 figures, part of this work is submitted to Allerton 2016
conference, UIUC, IL, US
A Progressive Universal Noiseless Coder
The authors combine pruned tree-structured vector quantization (pruned TSVQ) with Itoh's (1987) universal noiseless coder. By combining pruned TSVQ with universal noiseless coding, they benefit from the “successive approximation” capabilities of TSVQ, thereby allowing progressive transmission of images, while retaining the ability to noiselessly encode images of unknown statistics in a provably asymptotically optimal fashion. Noiseless compression results are comparable to Ziv-Lempel and arithmetic coding for both images and finely quantized Gaussian sources
Cooperative Lattice Coding and Decoding
A novel lattice coding framework is proposed for outage-limited cooperative
channels. This framework provides practical implementations for the optimal
cooperation protocols proposed by Azarian et al. In particular, for the relay
channel we implement a variant of the dynamic decode and forward protocol,
which uses orthogonal constellations to reduce the channel seen by the
destination to a single-input single-output time-selective one, while
inheriting the same diversity-multiplexing tradeoff. This simplification allows
for building the receiver using traditional belief propagation or tree search
architectures. Our framework also generalizes the coding scheme of Yang and
Belfiore in the context of amplify and forward cooperation. For the cooperative
multiple access channel, a tree coding approach, matched to the optimal linear
cooperation protocol of Azarain et al, is developed. For this scenario, the
MMSE-DFE Fano decoder is shown to enjoy an excellent tradeoff between
performance and complexity. Finally, the utility of the proposed schemes is
established via a comprehensive simulation study.Comment: 25 pages, 8 figure
A Lattice Coding Scheme for Secret Key Generation from Gaussian Markov Tree Sources
In this article, we study the problem of secret key generation in the
multiterminal source model, where the terminals have access to correlated
Gaussian sources. We assume that the sources form a Markov chain on a tree. We
give a nested lattice-based key generation scheme whose computational
complexity is polynomial in the number, N , of independent and identically
distributed samples observed by each source. We also compute the achievable
secret key rate and give a class of examples where our scheme is optimal in the
fine quantization limit. However, we also give examples that show that our
scheme is not always optimal in the limit of fine quantization.Comment: 10 pages, 3 figures. A 5-page version of this article has been
submitted to the 2016 IEEE International Symposium on Information Theory
(ISIT
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