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Spatially Coupled Sparse Regression Codes for Single- and Multi-user Communications
Sparse regression codes (SPARCs) are a class of channel codes for efficient communication over the single-user additive white Gaussian noise (AWGN) channel at rates approaching the channel capacity. In a standard SPARC, codewords are sparse linear combinations of columns of an i.i.d. Gaussian design matrix, and the user message is encoded in the indices of those columns. Techniques such as power allocation and spatial coupling have been proposed to improve the performance of low-complexity iterative decoding algorithms such as approximate message passing (AMP).
In this thesis we investigate spatially coupled SPARCs, where the design matrix has a block- wise band-diagonal structure, and modulated SPARCs, which generalise standard SPARCs by introducing modulation to the encoding of user messages. We introduce a base matrix framework which provides a unified way to construct power allocated and spatially coupled design matrices, and propose AMP decoders for modulated SPARCs constructed using base matrices.
We prove that phase shift keying modulated and spatially coupled SPARCs with AMP decoding asymptotically achieve the capacity of the (complex) AWGN channel. We also show via numerical simulations that they can achieve lower error rates than standard coded modulation schemes at finite code lengths. A sliding window AMP decoder is proposed for spatially coupled SPARCs that significantly reduces the decoding latency and complexity.
We then investigate coding schemes based on random linear models and AMP decoding for the multi-user Gaussian multiple access channel in the asymptotic regime where the number of users grows linearly with the code length. For a fixed target error rate and message size per user (in bits), we obtain the exact trade-off between energy-per-bit and the user density achievable in the large system limit. We show that a coding scheme based on spatially coupled Gaussian matrices and AMP decoding achieves near-optimal trade-off for a large range of user densities. To the best of our knowledge, this is the first efficient coding scheme to do so in this multiple access regime. Moreover, the spatially coupled coding scheme has a practical interpretation: it can be viewed as block-wise time-division with overlap.Funded by a Doctoral Training Partnership Award from the Engineering and Physical Sciences Research Council
Legibility of machine readable codes used for gas turbine part tracking
Gas turbines are comprised of many parts, which are often expensive and required to
survive a harsh environment for significant periods (with or without reconditioning). To
differentiate between parts, and facilitate keeping accurate historical records, they are
often given a unique identification number. However, manually recording and tracking
these is difficult. This has led to increased adoption of machine readable codes to help
reduce or eliminate many of the issues currently faced (mostly human error). The harsh
environment of a gas turbine means that typical methods of applying machine readable
codes, such as printed adhesive labels, are simply not durable enough. Direct part marking
(DPM) is necessary to ensure the desired longevity of the code over the part's useful life.
The research presented in this thesis was approached in two main phases. Firstly, the
author sought to investigate the technical solutions available for the elements required
of a part tracking system (encoding, marking and scanning). This included identifying
the characteristics of each and their compatibility with one other (across elements). In
conjunction with Alstom, criteria were identified that were used as a basis for comparison
so that the preferred technical solutions could be determined. The outcome of this process
was enhanced by the author developing a number of industrial contacts experienced in
implementing part tracking systems.
The second phase related to the legibility of the codes. The harsh environment of a
gas turbine results in surface degradation that may in turn reduce the legibility of any
machine readable codes present. To better understand why read failures occur, the author
_rst looked to the scanning process. Data Matrix symbols (marked via dot peen) require
the scanner to capture an image for processing. Image capture is typically achieved using
a charge-coupled device (CCD), each pixel of which induces a charge proportional to the
incident illumination. This illumination is received via reflection from the surface of the
part and hence the Data Matrix marked on it. Several surface features were identified that
govern the way in which the part surface will reflect light back to the scanner: surface
roughness, dot geometry and surface colour. These parameters are important because
they link the degradation mechanisms occurring { broadly categorised as deposition,
erosion or corrosion { with the scanning process. Whilst the degradation mechanisms
are distinctly different in their behaviour, their effect on surface reflectivity is common
in that they can all be characterised via the surface parameters identified. This was
deduced theoretically and so the author completed tests (utilising shot blasting to change
the surface roughness and oxidation to change its colour, independently) to show that
these surface parameters do indeed change with the introduction of surface degradation
and that there is a commensurate change in symbol legibility.
Based on the learning derived with respect to Data Matrix legibility, the author has
proposed a framework for developing a tool referred to as a Risk Matrix System. This
tool is intended to enhance the application of part tracking to gas turbine engines by
enabling symbol durability to be assessed based on the expected operating conditions.
The research presented is the first step in fully understanding the issues that affect the
legibility of symbols applied to gas turbine parts. The author's main contribution to
learning has been the identification of knowledge from various other sources applicable to
this situation and to present it in a coherent and complete manner. From this foundation,
others will be able to pursue relevant issues further; the author has made a number of
recommendations to this effect
Eficiência energética avançada para sistema OFDMA CoMP coordenação multiponto
Doutoramento em Engenharia EletrotécnicaThe ever-growing energy consumption in mobile networks stimulated by
the expected growth in data tra ffic has provided the impetus for mobile
operators to refocus network design, planning and deployment towards reducing
the cost per bit, whilst at the same time providing a signifi cant step
towards reducing their operational expenditure. As a step towards incorporating
cost-eff ective mobile system, 3GPP LTE-Advanced has adopted the
coordinated multi-point (CoMP) transmission technique due to its ability
to mitigate and manage inter-cell interference (ICI). Using CoMP the cell
average and cell edge throughput are boosted. However, there is room for
reducing energy consumption further by exploiting the inherent
exibility of
dynamic resource allocation protocols. To this end packet scheduler plays
the central role in determining the overall performance of the 3GPP longterm
evolution (LTE) based on packet-switching operation and provide a
potential research playground for optimizing energy consumption in future
networks. In this thesis we investigate the baseline performance for down
link CoMP using traditional scheduling approaches, and subsequently go
beyond and propose novel energy e fficient scheduling (EES) strategies that
can achieve power-e fficient transmission to the UEs whilst enabling both
system energy effi ciency gain and fairness improvement. However, ICI can
still be prominent when multiple nodes use common resources with di fferent
power levels inside the cell, as in the so called heterogeneous networks (Het-
Net) environment. HetNets are comprised of two or more tiers of cells. The
rst, or higher tier, is a traditional deployment of cell sites, often referred
to in this context as macrocells. The lower tiers are termed small cells, and
can appear as microcell, picocells or femtocells. The HetNet has attracted
signiffi cant interest by key manufacturers as one of the enablers for high
speed data at low cost. Research until now has revealed several key hurdles
that must be overcome before HetNets can achieve their full potential:
bottlenecks in the backhaul must be alleviated, as well as their seamless
interworking with CoMP. In this thesis we explore exactly the latter hurdle,
and present innovative ideas on advancing CoMP to work in synergy with
HetNet deployment, complemented by a novel resource allocation policy
for HetNet tighter interference management. As system level simulator has
been used to analyze the proposed algorithm/protocols, and results have
concluded that up to 20% energy gain can be observed.O aumento do consumo de energia nas TICs e em particular nas redes de
comunicação móveis, estimulado por um crescimento esperado do tráfego de
dados, tem servido de impulso aos operadores m oveis para reorientarem os
seus projectos de rede, planeamento e implementa ção no sentido de reduzir
o custo por bit, o que ao mesmo tempo possibilita um passo signicativo no
sentido de reduzir as despesas operacionais. Como um passo no sentido de
uma incorporação eficaz em termos destes custos, o sistema móvel 3GPP
LTE-Advanced adoptou a técnica de transmissão Coordenação Multi-Ponto
(identificada na literatura com a sigla CoMP) devido à sua capacidade de
mitigar e gerir Interferência entre Células (sigla ICI na literatura). No entanto
a ICI pode ainda ser mais proeminente quando v arios n os no interior
da célula utilizam recursos comuns com diferentes níveis de energia,
como acontece nos chamados ambientes de redes heterogéneas (sigla Het-
Net na literatura). As HetNets são constituídas por duas ou mais camadas
de células. A primeira, ou camada superiora, constitui uma implantação
tradicional de sítios de célula, muitas vezes referidas neste contexto como
macrocells. Os níveis mais baixos são designados por células pequenas, e
podem aparecer como microcells, picocells ou femtocells. A HetNet tem
atra do grande interesse por parte dos principais fabricantes como sendo
facilitador para transmissões de dados de alta velocidade a baixo custo. A
investigação tem revelado at e a data, vários dos principais obstáculos que
devem ser superados para que as HetNets possam atingir todo o seu potencial:
(i) os estrangulamentos no backhaul devem ser aliviados; (ii) bem
como sua perfeita interoperabilidade com CoMP. Nesta tese exploramos
este ultimo constrangimento e apresentamos ideias inovadoras em como a
t ecnica CoMP poder a ser aperfeiçoada por forma a trabalhar em sinergia
com a implementação da HetNet, complementado ainda com uma nova
perspectiva na alocação de recursos rádio para um controlo e gestão mais
apertado de interferência nas HetNets. Com recurso a simulação a níível de
sistema para analisar o desempenho dos algoritmos e protocolos propostos,
os resultados obtidos concluíram que ganhos at e a ordem dos 20% poderão
ser atingidos em termos de eficiência energética
Optimization of high-throughput real-time processes in physics reconstruction
La presente tesis se ha desarrollado en colaboración entre
la Universidad de Sevilla y la Organización Europea para la
Investigación Nuclear, CERN.
El detector LHCb es uno de los cuatro grandes detectores
situados en el Gran Colisionador de Hadrones, LHC. En LHCb,
se colisionan partículas a altas energías para comprender la
diferencia existente entre la materia y la antimateria. Debido a la
cantidad ingente de datos generada por el detector, es necesario
realizar un filtrado de datos en tiempo real, fundamentado en
los conocimientos actuales recogidos en el Modelo Estándar de
física de partículas. El filtrado, también conocido como High
Level Trigger, deberá procesar un throughput de 40 Tb/s de datos,
y realizar un filtrado de aproximadamente 1 000:1, reduciendo
el throughput a unos 40 Gb/s de salida, que se almacenan para
posterior análisis.
El proceso del High Level Trigger se subdivide a su vez en
dos etapas: High Level Trigger 1 (HLT1) y High Level Trigger
2 (HLT2). El HLT1 transcurre en tiempo real, y realiza una reducción de datos de aproximadamente 30:1. El HLT1 consiste
en una serie de procesos software que reconstruyen lo que ha
sucedido en la colisión de partículas. En la reconstrucción del
HLT1 únicamente se analizan las trayectorias de las partículas
producidas fruto de la colisión, en un problema conocido como
reconstrucción de trazas, para dictaminar el interés de las colisiones.
Por contra, el proceso HLT2 es más fino, requiriendo más
tiempo en realizarse y reconstruyendo todos los subdetectores
que componen LHCb.
Hacia 2020, el detector LHCb, así como todos los componentes
del sistema de adquisici´on de datos, serán actualizados acorde
a los últimos desarrollos técnicos. Como parte del sistema
de adquisición de datos, los servidores que procesan HLT1 y
HLT2 también sufrirán una actualización. Al mismo tiempo, el
acelerador LHC será también actualizado, de manera que la
cantidad de datos generada en cada cruce de grupo de partículas
aumentare en aproxidamente 5 veces la actual. Debido a
las actualizaciones tanto del acelerador como del detector, se
prevé que la cantidad de datos que deberá procesar el HLT en
su totalidad sea unas 40 veces mayor a la actual.
La previsión de la escalabilidad del software actual a 2020
subestim´ó los recursos necesarios para hacer frente al incremento
en throughput. Esto produjo que se pusiera en marcha un
estudio de todos los algoritmos tanto del HLT1 como del HLT2,
así como una actualización del código a nuevos estándares, para
mejorar su rendimiento y ser capaz de procesar la cantidad de
datos esperada.
En esta tesis, se exploran varios algoritmos de la reconstrucción de LHCb. El problema de reconstrucción de trazas se analiza
en profundidad y se proponen nuevos algoritmos para su
resolución. Ya que los problemas analizados exhiben un paralelismo
masivo, estos algoritmos se implementan en lenguajes
especializados para tarjetas gráficas modernas (GPUs), dada su
arquitectura inherentemente paralela. En este trabajo se dise ˜nan
dos algoritmos de reconstrucción de trazas. Además, se diseñan
adicionalmente cuatro algoritmos de decodificación y un algoritmo
de clustering, problemas también encontrados en el HLT1.
Por otra parte, se diseña un algoritmo para el filtrado de Kalman,
que puede ser utilizado en ambas etapas.
Los algoritmos desarrollados cumplen con los requisitos esperados
por la colaboración LHCb para el año 2020. Para poder
ejecutar los algoritmos eficientemente en tarjetas gráficas, se
desarrolla un framework especializado para GPUs, que permite
la ejecución paralela de secuencias de reconstrucción en GPUs.
Combinando los algoritmos desarrollados con el framework, se
completa una secuencia de ejecución que asienta las bases para
un HLT1 ejecutable en GPU.
Durante la investigación llevada a cabo en esta tesis, y gracias
a los desarrollos arriba mencionados y a la colaboración de
un pequeño equipo de personas coordinado por el autor, se
completa un HLT1 ejecutable en GPUs. El rendimiento obtenido
en GPUs, producto de esta tesis, permite hacer frente al reto de
ejecutar una secuencia de reconstrucción en tiempo real, bajo
las condiciones actualizadas de LHCb previstas para 2020. As´ı
mismo, se completa por primera vez para cualquier experimento
del LHC un High Level Trigger que se ejecuta únicamente en
GPUs. Finalmente, se detallan varias posibles configuraciones
para incluir tarjetas gr´aficas en el sistema de adquisición de
datos de LHCb.The current thesis has been developed in collaboration between
Universidad de Sevilla and the European Organization for Nuclear
Research, CERN.
The LHCb detector is one of four big detectors placed alongside
the Large Hadron Collider, LHC. In LHCb, particles are
collided at high energies in order to understand the difference
between matter and antimatter. Due to the massive quantity
of data generated by the detector, it is necessary to filter data
in real-time. The filtering, also known as High Level Trigger,
processes a throughput of 40 Tb/s of data and performs a selection
of approximately 1 000:1. The throughput is thus reduced
to roughly 40 Gb/s of data output, which is then stored for
posterior analysis.
The High Level Trigger process is subdivided into two stages:
High Level Trigger 1 (HLT1) and High Level Trigger 2 (HLT2).
HLT1 occurs in real-time, and yields a reduction of data of approximately
30:1. HLT1 consists in a series of software processes
that reconstruct particle collisions. The HLT1 reconstruction only
analyzes the trajectories of particles produced at the collision,
solving a problem known as track reconstruction, that determines
whether the collision data is kept or discarded. In contrast,
HLT2 is a finer process, which requires more time to execute
and reconstructs all subdetectors composing LHCb.
Towards 2020, the LHCb detector and all the components
composing the data acquisition system will be upgraded. As
part of the data acquisition system, the servers that process
HLT1 and HLT2 will also be upgraded. In addition, the LHC
accelerator will also be updated, increasing the data generated in
every bunch crossing by roughly 5 times. Due to the accelerator
and detector upgrades, the amount of data that the HLT will
require to process is expected to increase by 40 times.
The foreseen scalability of the software through 2020 underestimated
the required resources to face the increase in data
throughput. As a consequence, studies of all algorithms composing
HLT1 and HLT2 and code modernizations were carried
out, in order to obtain a better performance and increase the
processing capability of the foreseen hardware resources in the
upgrade.
In this thesis, several algorithms of the LHCb recontruction
are explored. The track reconstruction problem is analyzed
in depth, and new algorithms are proposed. Since the analyzed
problems are massively parallel, these algorithms are implemented
in specialized languages for modern graphics cards
(GPUs), due to their inherently parallel architecture. From this
work stem two algorithm designs. Furthermore, four additional
decoding algorithms and a clustering algorithms have been designed
and implemented, which are also part of HLT1. Apart
from that, an parallel Kalman filter algorithm has been designed
and implemented, which can be used in both HLT stages.
The developed algorithms satisfy the requirements of the
LHCb collaboration for the LHCb upgrade. In order to execute
the algorithms efficiently on GPUs, a software framework specialized
for GPUs is developed, which allows executing GPU
reconstruction sequences in parallel. Combining the developed
algorithms with the framework, an execution sequence is completed
as the foundations of a GPU HLT1.
During the research carried out in this thesis, the aforementioned
developments and a small group of collaborators coordinated
by the author lead to the completion of a full GPU
HLT1 sequence. The performance obtained on GPUs allows
executing a reconstruction sequence in real-time, under LHCb
upgrade conditions. The developed GPU HLT1 constitutes the
first GPU high level trigger ever developed for an LHC experiment.
Finally, various possible realizations of the GPU HLT1 to
integrate in a production GPU-equipped data acquisition system
are detailed
Mobility Analysis and Management for Heterogeneous Networks
The global mobile data traffic has increased tremendously in the last decade due to the technological advancement in smartphones. Their endless usage and bandwidth-intensive applications will saturate current 4G technologies and has motivated the need for concrete research in order to sustain the mounting data traffic demand. In this regard, the network densification has shown to be a promising direction to cope with the capacity demands in future 5G wireless networks. The basic idea is to deploy several low power radio access nodes called small cells closer to the users on the existing large radio foot print of macrocells, and this constitutes a heterogeneous network (HetNet).
However, there are many challenges that operators face with the dense HetNet deployment. The mobility management becomes a challenging task due to triggering of frequent handovers when a user moves across the network coverage areas. When there are fewer users associated in certain small cells, this can lead to significant increase in the energy consumption. Intelligently switching them to low energy consumption modes or turning them off without seriously degrading user performance is desirable in order to improve the energy savings in HetNets. This dynamic power level switching in the small cells, however, may cause unnecessary handovers, and it becomes important to ensure energy savings without compromising handover performance. Finally, it is important to evaluate mobility management schemes in real network deployments, in order to find any problems affecting the quality of service (QoS) of the users. The research presented in this dissertation aims to address these challenges.
First, to tackle the mobility management issue, we develop a closed form, analytical model to study the handover and ping-pong performance as a function of network parameters in the small cells, and verify its performance using simulations. Secondly, we incorporate fuzzy logic based game-theoretic framework to address and examine the energy efficiency improvements in HetNets. In addition, we design fuzzy inference rules for handover decisions and target base station selection is performed through a fuzzy ranking technique in order to enhance the mobility robustness, while also considering energy/spectral efficiency. Finally, we evaluate the mobility performance by carrying out drive test in an existing 4G long term evolution (LTE) network deployment using software defined radios (SDR). This helps to obtain network quality information in order to find any problems affecting the QoS of the users
Spectral-energy efficiency trade-off for next-generation wireless communication systems
The data traffic in cellular networks has had and will experience a rapid exponential
rise. Therefore, it is essential to innovate a new cellular architecture with
advanced wireless technologies that can offer more capacity and enhanced spectral
efficiency to manage the exponential data traffic growth. Managing such mass
data traffic, however, brings up another challenge of increasing energy consumption.
This is because it contributes into a growing fraction of the carbon dioxide
(CO2) emission which is a global concern today due to its negative impact on
the environment. This has resulted in creating a new paradigm shift towards both
spectral and energy efficient orientated design for the next-generation wireless access
networks. Acquiring both improved energy efficiency and spectral efficiency
has, nonetheless, shown to be a difficult goal to achieve as it seems improving one
is at the detriment to the other. Therefore, the trade-off between the spectral and
energy efficiency is of paramount importance to assess the energy consumption in
a wireless communication system required to attain a specific spectral efficiency.
This thesis looks into this problem. It studies the spectral-energy efficiency tradeoff
for some of the emerging wireless communication technologies which are seen
as potential candidates for the fifth generation (5G) mobile cellular system. The
focus is on the orthogonal frequency division multiple access (OFDMA), mobile
femtocell (MFemtocell), cognitive radio (CR), and the spatial modulation (SM).
Firstly, the energy-efficient resource allocation scheme for multi-user OFDMA
(MU-OFDMA) system is studied. The spectral-energy efficiency trade-off is
analysed under the constraint of maintaining the fairness among users. The
energy-efficient optimisation problem has been formulated as integer fractional
programming. We then apply an iterative method to simplify the problem to an
integer linear programming (ILP) problem.
Secondly, the spectral and energy efficiency for a cellular system with MFemtocell
deployment is investigated using different resource partitioning schemes.
Femtocells are low range, low power base stations (BSs) that improve the coverage
inside a home or office building. MFemtocell adopts the femtocell solution to be deployed in public transport and emergency vehicles. Closed-form expressions
for the relationships between the spectral and energy efficiency are derived for
a single-user (SU) MFemtocell network. We also study the spectral efficiency
for MU-MFemtocells with two opportunistic scheduling schemes.
Thirdly, the spectral-energy efficiency trade-off for CR networks is analysed at
both SU and MU CR systems against varying signal-to-noise ratio (SNR) values.
CR is an innovative radio device that aims to utilise the spectrum more efficiently
by opportunistically exploiting underutilised licensed spectrum. For the SU system,
we study the required energy to achieve a specific spectral efficiency for a
CR channel under two different types of power constraints in different fading environments.
In this scenario, interference constraint at the primary receiver (PR)
is also considered to protect the PR from harmful interference. At the system
level, we study the spectral and energy efficiency for a CR network that shares
the spectrum with an indoor network. Adopting the extreme-value theory, we
are able to derive the average spectral efficiency of the CR network.
Finally, we propose two innovative schemes to enhance the capability of (SM). SM
is a recently developed technique that is employed for a low complexity multipleinput
multiple-output (MIMO) transmission. The first scheme can be applied for
SU MIMO (SU-MIMO) to offer more degrees of freedom than SM. Whereas the
second scheme introduces a transmission structure by which the SM is adopted
into a downlink MU-MIMO system. Unlike SM, both proposed schemes do not
involve any restriction into the number of transmit antennas when transmitting
signals. The spectral-energy efficiency trade-off for the MU-SM in the massive
MIMO system is studied. In this context, we develop an iterative energy-efficient
water-filling algorithm to optimises the transmit power and achieve the maximum
energy efficiency for a given spectral efficiency.
In summary, the research presented in this thesis reveals mathematical tools to
analysis the spectral and energy efficiency for wireless communications technologies.
It also offers insight to solve optimisation problems that belong to a class
of problems with objectives of enhancing the energy efficiency
Low-Complexity Voronoi Shaping for the Gaussian Channel
Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up version of the coding lattice. In this paper, we design low-complexity VCs with a cubic coding lattice of up to 32 dimensions, in which pseudo-Gray labeling is applied to minimize the bit error rate. The designed VCs have considerable shaping gains of up to 1.03 dB and finer choices of spectral efficiencies in practice compared with conventional VCs. A mutual information estimation method and a log-likelihood approximation method based on importance sampling for very large constellations are proposed and applied to the designed VCs. With error-control coding, the proposed VCs can have higher information rates than the conventional scaled VCs because of their inherently good pseudo-Gray labeling feature, with a lower decoding complexity
The Deep Space Network: A Radio Communications Instrument for Deep Space Exploration
The primary purpose of the Deep Space Network (DSN) is to serve as a communications instrument for deep space exploration, providing communications between the spacecraft and the ground facilities. The uplink communications channel provides instructions or commands to the spacecraft. The downlink communications channel provides command verification and spacecraft engineering and science instrument payload data
Low-Density Graph Codes for slow fading Relay Channels
We study Low-Density Parity-Check (LDPC) codes with iterative decoding on
block-fading (BF) Relay Channels. We consider two users that employ coded
cooperation, a variant of decode-and-forward with a smaller outage probability
than the latter. An outage probability analysis for discrete constellations
shows that full diversity can be achieved only when the coding rate does not
exceed a maximum value that depends on the level of cooperation. We derive a
new code structure by extending the previously published full-diversity
root-LDPC code, designed for the BF point-to-point channel, to exhibit a
rate-compatibility property which is necessary for coded cooperation. We
estimate the asymptotic performance through a new density evolution analysis
and the word error rate performance is determined for finite length codes. We
show that our code construction exhibits near-outage limit performance for all
block lengths and for a range of coding rates up to 0.5, which is the highest
possible coding rate for two cooperating users.Comment: Accepted for publication in IEEE Transactions on Information Theor
A digital signal processing system developed for the optimal use of high density magnetic storage media
High density data recording has traditionally been an essential factor in the development of communication and transmission systems. However, recently more sophisticated applications, including video recording, have necessitated refinements of this technology. This study concentrates on the signal processing techniques used to inhance the packing density of stored data. A comparison of the spectral mapping characteristics of different codes illustrates that the need for equalization can be eliminated and that significant bandwidth reduction can be achieved. Secondly, consideration is given to the deleterious effects of flutter, its associated effects on high density data recording, and the constraints imposed on the development of a time base corrector. An analysis is made of the bandlimiting effect which results when the incoming data is convolved with the head impulse response. The bandwidth of the channel, the size of the head gap, and the velocity of the media are seen from this analysis to be intrinsically related. These signal processing techniques are implemented, the channel capacity computed, and a significant channel efficiency achieved
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