1,205 research outputs found
Cluster-Aided Mobility Predictions
Predicting the future location of users in wireless net- works has numerous
applications, and can help service providers to improve the quality of service
perceived by their clients. The location predictors proposed so far estimate
the next location of a specific user by inspecting the past individual
trajectories of this user. As a consequence, when the training data collected
for a given user is limited, the resulting prediction is inaccurate. In this
paper, we develop cluster-aided predictors that exploit past trajectories
collected from all users to predict the next location of a given user. These
predictors rely on clustering techniques and extract from the training data
similarities among the mobility patterns of the various users to improve the
prediction accuracy. Specifically, we present CAMP (Cluster-Aided Mobility
Predictor), a cluster-aided predictor whose design is based on recent
non-parametric bayesian statistical tools. CAMP is robust and adaptive in the
sense that it exploits similarities in users' mobility only if such
similarities are really present in the training data. We analytically prove the
consistency of the predictions provided by CAMP, and investigate its
performance using two large-scale datasets. CAMP significantly outperforms
existing predictors, and in particular those that only exploit individual past
trajectories
Applications of Coding Theory to Massive Multiple Access and Big Data Problems
The broad theme of this dissertation is design of schemes that admit iterative algorithms
with low computational complexity to some new problems arising in massive
multiple access and big data. Although bipartite Tanner graphs and low-complexity
iterative algorithms such as peeling and message passing decoders are very popular
in the channel coding literature they are not as widely used in the respective areas
of study and this dissertation serves as an important step in that direction to bridge
that gap. The contributions of this dissertation can be categorized into the following
three parts.
In the first part of this dissertation, a timely and interesting multiple access
problem for a massive number of uncoordinated devices is considered wherein the
base station is interested only in recovering the list of messages without regard to the
identity of the respective sources. A coding scheme with polynomial encoding and
decoding complexities is proposed for this problem, the two main features of which
are (i) design of a close-to-optimal coding scheme for the T-user Gaussian multiple
access channel and (ii) successive interference cancellation decoder. The proposed
coding scheme not only improves on the performance of the previously best known
coding scheme by ≈ 13 dB but is only ≈ 6 dB away from the random Gaussian
coding information rate.
In the second part construction-D lattices are constructed where the underlying
linear codes are nested binary spatially-coupled low-density parity-check codes (SCLDPC)
codes with uniform left and right degrees. It is shown that the proposed
lattices achieve the Poltyrev limit under multistage belief propagation decoding.
Leveraging this result lattice codes constructed from these lattices are applied to the
three user symmetric interference channel. For channel gains within 0.39 dB from
the very strong interference regime, the proposed lattice coding scheme with the
iterative belief propagation decoder, for target error rates of ≈ 10^-5, is only 2:6 dB
away the Shannon limit.
The third part focuses on support recovery in compressed sensing and the nonadaptive
group testing (GT) problems. Prior to this work, sensing schemes based on
left-regular sparse bipartite graphs and iterative recovery algorithms based on peeling
decoder were proposed for the above problems. These schemes require O(K logN)
and Ω(K logK logN) measurements respectively to recover the sparse signal with
high probability (w.h.p), where N, K denote the dimension and sparsity of the signal
respectively (K (double backward arrow) N). Also the number of measurements required to recover
at least (1 - €) fraction of defective items w.h.p (approximate GT) is shown to be
cv€_K logN/K. In this dissertation, instead of the left-regular bipartite graphs, left-and-
right regular bipartite graph based sensing schemes are analyzed. It is shown
that this design strategy enables to achieve superior and sharper results. For the
support recovery problem, the number of measurements is reduced to the optimal
lower bound of
Ω (K log N/K). Similarly for the approximate GT, proposed scheme
only requires c€_K log N/
K measurements. For the probabilistic GT, proposed scheme
requires (K logK log vN/
K) measurements which is only log K factor away from the
best known lower bound of Ω (K log N/
K). Apart from the asymptotic regime, the proposed
schemes also demonstrate significant improvement in the required number of
measurements for finite values of K, N
Applications of Coding Theory to Massive Multiple Access and Big Data Problems
The broad theme of this dissertation is design of schemes that admit iterative algorithms
with low computational complexity to some new problems arising in massive
multiple access and big data. Although bipartite Tanner graphs and low-complexity
iterative algorithms such as peeling and message passing decoders are very popular
in the channel coding literature they are not as widely used in the respective areas
of study and this dissertation serves as an important step in that direction to bridge
that gap. The contributions of this dissertation can be categorized into the following
three parts.
In the first part of this dissertation, a timely and interesting multiple access
problem for a massive number of uncoordinated devices is considered wherein the
base station is interested only in recovering the list of messages without regard to the
identity of the respective sources. A coding scheme with polynomial encoding and
decoding complexities is proposed for this problem, the two main features of which
are (i) design of a close-to-optimal coding scheme for the T-user Gaussian multiple
access channel and (ii) successive interference cancellation decoder. The proposed
coding scheme not only improves on the performance of the previously best known
coding scheme by ≈ 13 dB but is only ≈ 6 dB away from the random Gaussian
coding information rate.
In the second part construction-D lattices are constructed where the underlying
linear codes are nested binary spatially-coupled low-density parity-check codes (SCLDPC)
codes with uniform left and right degrees. It is shown that the proposed
lattices achieve the Poltyrev limit under multistage belief propagation decoding.
Leveraging this result lattice codes constructed from these lattices are applied to the
three user symmetric interference channel. For channel gains within 0.39 dB from
the very strong interference regime, the proposed lattice coding scheme with the
iterative belief propagation decoder, for target error rates of ≈ 10^-5, is only 2:6 dB
away the Shannon limit.
The third part focuses on support recovery in compressed sensing and the nonadaptive
group testing (GT) problems. Prior to this work, sensing schemes based on
left-regular sparse bipartite graphs and iterative recovery algorithms based on peeling
decoder were proposed for the above problems. These schemes require O(K logN)
and Ω(K logK logN) measurements respectively to recover the sparse signal with
high probability (w.h.p), where N, K denote the dimension and sparsity of the signal
respectively (K (double backward arrow) N). Also the number of measurements required to recover
at least (1 - €) fraction of defective items w.h.p (approximate GT) is shown to be
cv€_K logN/K. In this dissertation, instead of the left-regular bipartite graphs, left-and-
right regular bipartite graph based sensing schemes are analyzed. It is shown
that this design strategy enables to achieve superior and sharper results. For the
support recovery problem, the number of measurements is reduced to the optimal
lower bound of
Ω (K log N/K). Similarly for the approximate GT, proposed scheme
only requires c€_K log N/
K measurements. For the probabilistic GT, proposed scheme
requires (K logK log vN/
K) measurements which is only log K factor away from the
best known lower bound of Ω (K log N/
K). Apart from the asymptotic regime, the proposed
schemes also demonstrate significant improvement in the required number of
measurements for finite values of K, N
Reed-Muller codes for random erasures and errors
This paper studies the parameters for which Reed-Muller (RM) codes over
can correct random erasures and random errors with high probability,
and in particular when can they achieve capacity for these two classical
channels. Necessarily, the paper also studies properties of evaluations of
multi-variate polynomials on random sets of inputs.
For erasures, we prove that RM codes achieve capacity both for very high rate
and very low rate regimes. For errors, we prove that RM codes achieve capacity
for very low rate regimes, and for very high rates, we show that they can
uniquely decode at about square root of the number of errors at capacity.
The proofs of these four results are based on different techniques, which we
find interesting in their own right. In particular, we study the following
questions about , the matrix whose rows are truth tables of all
monomials of degree in variables. What is the most (resp. least)
number of random columns in that define a submatrix having full column
rank (resp. full row rank) with high probability? We obtain tight bounds for
very small (resp. very large) degrees , which we use to show that RM codes
achieve capacity for erasures in these regimes.
Our decoding from random errors follows from the following novel reduction.
For every linear code of sufficiently high rate we construct a new code
, also of very high rate, such that for every subset of coordinates, if
can recover from erasures in , then can recover from errors in .
Specializing this to RM codes and using our results for erasures imply our
result on unique decoding of RM codes at high rate.
Finally, two of our capacity achieving results require tight bounds on the
weight distribution of RM codes. We obtain such bounds extending the recent
\cite{KLP} bounds from constant degree to linear degree polynomials
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