4 research outputs found
Interference management for Interference Channels: Performance improvement and lattice techniques
Get PDFThis thesis focuses on interference management methods for interference channels, in particular on interference alignment. The aim is to contribute to the understanding of issues such as the performance of the interference alignment scheme and lattice codes for interference channels. Interference alignment is studied from two perspectives. One is the signal space perspective where precoding methods are designed to align the interference in half of the received subspace. Cadambe and Jafar found precoding matrices to achieve the theoretical degrees of freedom. However, using an interference suppression technique over the Cadambe and Jafar scheme, yields poor performance. Thus, in this thesis precoding methods such as singular value decomposition and Tomlinson-Harashima precoding are proposed to improve performance. The second perspective is on the signal scale, where structured codes are used to align interference. For this, lattice codes are suitable. In this research, the problem was initially approached with a many-to-one interference channel. Using lattices, joint maximum-likelihood decoding of the desired signal and the sum of the interference signals is used, and the union bound of the error probability for user 1 is derived, in terms of the theta series. Later, a symmetric interference channel is studied. Jafar built a scheme for every level of interference, where interference was aligned and could be cancelled. In this thesis, Barnes-Wall lattices are used since they have a similar structure to the scheme proposed by Jafar, and it is shown to be possible to improve the performance of the technique using codes constructed with Barnes-Wall lattices. Finally, previous work has found the generalized degrees of freedom for a two-user symmetric interference channel using random codes. Here, we obtain the generalized degrees of freedom for that channel setting using lattice Gaussian distribution.Open Acces
Applications of Coding Theory to Massive Multiple Access and Big Data Problems
Get PDFThe 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
Get PDFThe 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
