19 research outputs found
Quickest Sequence Phase Detection
A phase detection sequence is a length- cyclic sequence, such that the
location of any length- contiguous subsequence can be determined from a
noisy observation of that subsequence. In this paper, we derive bounds on the
minimal possible in the limit of , and describe some sequence
constructions. We further consider multiple phase detection sequences, where
the location of any length- contiguous subsequence of each sequence can be
determined simultaneously from a noisy mixture of those subsequences. We study
the optimal trade-offs between the lengths of the sequences, and describe some
sequence constructions. We compare these phase detection problems to their
natural channel coding counterparts, and show a strict separation between the
fundamental limits in the multiple sequence case. Both adversarial and
probabilistic noise models are addressed.Comment: To appear in the IEEE Transactions on Information Theor
A Novel Power Allocation Scheme for Two-User GMAC with Finite Input Constellations
Constellation Constrained (CC) capacity regions of two-user Gaussian Multiple
Access Channels (GMAC) have been recently reported, wherein an appropriate
angle of rotation between the constellations of the two users is shown to
enlarge the CC capacity region. We refer to such a scheme as the Constellation
Rotation (CR) scheme. In this paper, we propose a novel scheme called the
Constellation Power Allocation (CPA) scheme, wherein the instantaneous transmit
power of the two users are varied by maintaining their average power
constraints. We show that the CPA scheme offers CC sum capacities equal (at low
SNR values) or close (at high SNR values) to those offered by the CR scheme
with reduced decoding complexity for QAM constellations. We study the
robustness of the CPA scheme for random phase offsets in the channel and
unequal average power constraints for the two users. With random phase offsets
in the channel, we show that the CC sum capacity offered by the CPA scheme is
more than the CR scheme at high SNR values. With unequal average power
constraints, we show that the CPA scheme provides maximum gain when the power
levels are close, and the advantage diminishes with the increase in the power
difference.Comment: To appear in IEEE Transactions on Wireless Communications, 10 pages
and 7 figure
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
Superposition Mapping & Related Coding Techniques
Since Shannon's landmark paper in 1948, it has been known that the capacity of a
Gaussian channel can be achieved if and only if the channel outputs are Gaussian. In the low signal-to-noise ratio (SNR) regime, conventional mapping schemes suffice for approaching the Shannon limit, while in the high SNR regime, these mapping schemes, which produce uniformly distributed symbols, are insufficient to achieve the capacity. To solve this problem, researchers commonly resort to the technique of signal shaping that mends the symbol distribution, which is originally uniform, into a Gaussian-like one.
Superposition mapping (SM) refers to a class of mapping techniques which use linear superposition to load binary digits onto finite-alphabet symbols that are suitable for waveform transmission. Different from conventional mapping schemes, the output symbols of a superposition mapper can easily be made Gaussian-like, which effectively eliminates the necessity of active signal shaping. For this reason, superposition mapping is of great interest for theoretical research as well as for practical implementations. It is an attractive alternative to signal shaping for approaching the channel capacity in the high SNR regime.
This thesis aims to provide a deep insight into the principles of superposition
mapping and to derive guidelines for systems adopting it. Particularly, the influence of power allocation to the system performance, both w.r.t the achievable power efficiency and supportable bandwidth efficiency, is made clear. Considerable effort is spent on finding code structures that are matched to SM. It is shown that currently prevalent code design concepts, which are mostly derived for coded transmission with bijective uniform mapping, do not really fit with
superposition mapping, which is often non-bijective and nonuniform. As the main
contribution, a novel coding strategy called low-density hybrid-check (LDHC) coding is proposed. LDHC codes are optimal and universally applicable for SM with arbitrary type of power allocation
High Capacity CDMA and Collaborative Techniques
The thesis investigates new approaches to increase the user capacity and improve the error
performance of Code Division Multiple Access (CDMA) by employing adaptive interference cancellation
and collaborative spreading and space diversity techniques. Collaborative Coding Multiple
Access (CCMA) is also investigated as a separate technique and combined with CDMA. The
advantages and shortcomings of CDMA and CCMA are analysed and new techniques for both the
uplink and downlink are proposed and evaluated.
Multiple access interference (MAI) problem in the uplink of CDMA is investigated first. The
practical issues of multiuser detection (MUD) techniques are reviewed and a novel blind adaptive
approach to interference cancellation (IC) is proposed. It exploits the constant modulus (CM)
property of digital signals to blindly suppress interference during the despreading process and obtain
amplitude estimation with minimum mean squared error for use in cancellation stages. Two
new blind adaptive receiver designs employing successive and parallel interference cancellation
architectures using the CM algorithm (CMA) referred to as ‘CMA-SIC’ and ‘BA-PIC’, respectively,
are presented. These techniques have shown to offer near single user performance for large
number of users. It is shown to increase the user capacity by approximately two fold compared
with conventional IC receivers. The spectral efficiency analysis of the techniques based on output
signal-to interference-and-noise ratio (SINR) also shows significant gain in data rate. Furthermore,
an effective and low complexity blind adaptive subcarrier combining (BASC) technique using a
simple gradient descent based algorithm is proposed for Multicarrier-CDMA. It suppresses MAI
without any knowledge of channel amplitudes and allows large number of users compared with
equal gain and maximum ratio combining techniques normally used in practice.
New user collaborative schemes are proposed and analysed theoretically and by simulations
in different channel conditions to achieve spatial diversity for uplink of CCMA and CDMA. First,
a simple transmitter diversity and its equivalent user collaborative diversity techniques for CCMA
are designed and analysed. Next, a new user collaborative scheme with successive interference
cancellation for uplink of CDMA referred to as collaborative SIC (C-SIC) is investigated to reduce
MAI and achieve improved diversity. To further improve the performance of C-SIC under high
system loading conditions, Collaborative Blind Adaptive SIC (C-BASIC) scheme is proposed.
It is shown to minimize the residual MAI, leading to improved user capacity and a more robust
system. It is known that collaborative diversity schemes incur loss in throughput due to the need of
orthogonal time/frequency slots for relaying source’s data. To address this problem, finally a novel
near-unity-rate scheme also referred to as bandwidth efficient collaborative diversity (BECD) is proposed and evaluated for CDMA. Under this scheme, pairs of users share a single spreading sequence to exchange and forward their data employing a simple superposition or space-time
encoding methods. At the receiver collaborative joint detection is performed to separate each
paired users’ data. It is shown that the scheme can achieve full diversity gain at no extra bandwidth
as inter-user channel SNR becomes high.
A novel approach of ‘User Collaboration’ is introduced to increase the user capacity of CDMA
for both the downlink and uplink. First, collaborative group spreading technique for the downlink
of overloaded CDMA system is introduced. It allows the sharing of the same single spreading
sequence for more than one user belonging to the same group. This technique is referred to as
Collaborative Spreading CDMA downlink (CS-CDMA-DL). In this technique T-user collaborative
coding is used for each group to form a composite codeword signal of the users and then a
single orthogonal sequence is used for the group. At each user’s receiver, decoding of composite
codeword is carried out to extract the user’s own information while maintaining a high SINR performance.
To improve the bit error performance of CS-CDMA-DL in Rayleigh fading conditions,
Collaborative Space-time Spreading (C-STS) technique is proposed by combining the collaborative
coding multiple access and space-time coding principles. A new scheme for uplink of CDMA
using the ‘User Collaboration’ approach, referred to as CS-CDMA-UL is presented next. When
users’ channels are independent (uncorrelated), significantly higher user capacity can be achieved
by grouping multiple users to share the same spreading sequence and performing MUD on per
group basis followed by a low complexity ML decoding at the receiver. This approach has shown
to support much higher number of users than the available sequences while also maintaining the
low receiver complexity. For improved performance under highly correlated channel conditions,
T-user collaborative coding is also investigated within the CS-CDMA-UL system
Reliable Software for Unreliable Hardware - A Cross-Layer Approach
A novel cross-layer reliability analysis, modeling, and optimization approach is proposed in this thesis that leverages multiple layers in the system design abstraction (i.e. hardware, compiler, system software, and application program) to exploit the available reliability enhancing potential at each system layer and to exchange this information across multiple system layers
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Coding; Communications; Engineering; Networks; Information Theory; Algorithm
Network information theory for classical-quantum channels
Network information theory is the study of communication problems involving
multiple senders, multiple receivers and intermediate relay stations. The
purpose of this thesis is to extend the main ideas of classical network
information theory to the study of classical-quantum channels. We prove coding
theorems for quantum multiple access channels, quantum interference channels,
quantum broadcast channels and quantum relay channels.
A quantum model for a communication channel describes more accurately the
channel's ability to transmit information. By using physically faithful models
for the channel outputs and the detection procedure, we obtain better
communication rates than would be possible using a classical strategy. In this
thesis, we are interested in the transmission of classical information, so we
restrict our attention to the study of classical-quantum channels. These are
channels with classical inputs and quantum outputs, and so the coding theorems
we present will use classical encoding and quantum decoding. We study the
asymptotic regime where many copies of the channel are used in parallel, and
the uses are assumed to be independent. In this context, we can exploit
information-theoretic techniques to calculate the maximum rates for error-free
communication for any channel, given the statistics of the noise on that
channel. These theoretical bounds can be used as a benchmark to evaluate the
rates achieved by practical communication protocols.
Most of the results in this thesis consider classical-quantum channels with
finite dimensional output systems, which are analogous to classical discrete
memoryless channels. In the last chapter, we will show some applications of our
results to a practical optical communication scenario, in which the information
is encoded in continuous quantum degrees of freedom, which are analogous to
classical channels with Gaussian noise.Comment: Ph.D. Thesis, McGill University, School of Computer Science, July
2012, 223 pages, 18 figures, 36 TikZ diagram