727 research outputs found
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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
Improved HAC Covariance Matrix Estimation Based on Forecast Errors
We propose computing HAC covariance matrix estimators based on one-stepahead forecasting errors. It is shown that this estimator is consistent and has smaller bias than other HAC estimators. Moreover, the tests that rely on this estimator have more accurate sizes without sacrificing its power.forecast error, HAC estimator, kernel estimator, recursive residual, robust test
Spatially Coupled Sparse Regression Codes: Design and State Evolution Analysis.
We consider the design and analysis of spatially coupled sparse regression
codes (SC-SPARCs), which were recently introduced by Barbier et al. for
efficient communication over the additive white Gaussian noise channel.
SC-SPARCs can be efficiently decoded using an Approximate Message Passing (AMP)
decoder, whose performance in each iteration can be predicted via a set of
equations called state evolution. In this paper, we give an asymptotic
characterization of the state evolution equations for SC-SPARCs. For any given
base matrix (that defines the coupling structure of the SC-SPARC) and rate,
this characterization can be used to predict whether or not AMP decoding will
succeed in the large system limit. We then consider a simple base matrix
defined by two parameters , and show that AMP decoding
succeeds in the large system limit for all rates . The
asymptotic result also indicates how the parameters of the base matrix affect
the decoding progression. Simulation results are presented to evaluate the
performance of SC-SPARCs defined with the proposed base matrix.Comment: 8 pages, 6 figures. A shorter version of this paper to appear in ISIT
201
Near-Optimal Coding for Many-user Multiple Access Channels
This paper considers the Gaussian multiple-access channel (MAC) in the
asymptotic regime where the number of users grows linearly with the code
length. We propose efficient coding schemes based on random linear models with
approximate message passing (AMP) decoding and derive the asymptotic error rate
achieved for a given user density, user payload (in bits), and user energy. The
tradeoff between energy-per-bit and achievable user density (for a fixed user
payload and target error rate) is studied, and it is demonstrated that in the
large system limit, a spatially coupled coding scheme with AMP decoding
achieves near-optimal tradeoffs for a wide range of user densities.
Furthermore, in the regime where the user payload is large, we also study the
spectral efficiency versus energy-per-bit tradeoff and discuss methods to
reduce decoding complexity at large payload sizes.Comment: 35 pages, 4 figures. A shorter version of this paper appeared in ISIT
202
Capacity-achieving Spatially Coupled Sparse Superposition Codes with AMP Decoding
Sparse superposition codes, also referred to as
sparse regression codes (SPARCs), are a class of codes for efficient
communication over the 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, while in a spatially coupled SPARC the design matrix has
a block-wise structure, where the variance of the Gaussian entries
can be varied across blocks. A well-designed spatial coupling
structure can significantly enhance the error performance of
iterative decoding algorithms such as Approximate Message
Passing (AMP).
In this paper, we obtain a non-asymptotic bound on the
probability of error of spatially coupled SPARCs with AMP
decoding. Applying this bound to a simple band-diagonal design
matrix, we prove that spatially coupled SPARCs with AMP
decoding achieve the capacity of the AWGN channel. The bound
also highlights how the decay of error probability depends on
each design parameter of the spatially coupled SPARC.
An attractive feature of AMP decoding is that its asymptotic
mean squared error (MSE) can be predicted via a deterministic
recursion called state evolution. Our result provides the first
proof that the MSE concentrates on the state evolution prediction
for spatially coupled designs. Combined with the state evolution
prediction, this result implies that spatially coupled SPARCs with
the proposed band-diagonal design are capacity-achieving. Using
the proof technique used to establish the main result, we also
obtain a concentration inequality for the MSE of AMP applied
to compressed sensing with spatially coupled design matrices.
Finally, we provide numerical simulation results that demonstrate
the finite length error performance of spatially coupled SPARCs.
The performance is compared with coded modulation schemes
that use LDPC codes from the DVB-S2 standard
Recommended from our members
Capacity-achieving Spatially Coupled Sparse Superposition Codes with AMP Decoding
Sparse superposition codes, also referred to as
sparse regression codes (SPARCs), are a class of codes for efficient
communication over the 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, while in a spatially coupled SPARC the design matrix has
a block-wise structure, where the variance of the Gaussian entries
can be varied across blocks. A well-designed spatial coupling
structure can significantly enhance the error performance of
iterative decoding algorithms such as Approximate Message
Passing (AMP).
In this paper, we obtain a non-asymptotic bound on the
probability of error of spatially coupled SPARCs with AMP
decoding. Applying this bound to a simple band-diagonal design
matrix, we prove that spatially coupled SPARCs with AMP
decoding achieve the capacity of the AWGN channel. The bound
also highlights how the decay of error probability depends on
each design parameter of the spatially coupled SPARC.
An attractive feature of AMP decoding is that its asymptotic
mean squared error (MSE) can be predicted via a deterministic
recursion called state evolution. Our result provides the first
proof that the MSE concentrates on the state evolution prediction
for spatially coupled designs. Combined with the state evolution
prediction, this result implies that spatially coupled SPARCs with
the proposed band-diagonal design are capacity-achieving. Using
the proof technique used to establish the main result, we also
obtain a concentration inequality for the MSE of AMP applied
to compressed sensing with spatially coupled design matrices.
Finally, we provide numerical simulation results that demonstrate
the finite length error performance of spatially coupled SPARCs.
The performance is compared with coded modulation schemes
that use LDPC codes from the DVB-S2 standard
Instrumentation of a high-sensitivity microwave vector detection system for low-temperature applications
We present the design and the circuit details of a high-sensitivity microwave
vector detection system, which is aiming for studying the low-dimensional
electron system embedded in the slots of a coplanar waveguide at low
temperatures. The coplanar waveguide sample is placed inside a phase-locked
loop; the phase change of the sample may cause a corresponding change in the
operation frequency, which can be measured precisely. We also employ a
double-pulse modulation on the microwave signals, which comprises a fast pulse
modulation for gated averaging and a slow pulse modulation for lock-in
detection. In measurements on real samples at low temperatures, this system
provides much better resolutions in both amplitude and phase than most of the
conventional vector analyzers at power levels below -65 dBm.Comment: 7 pages, 11 figures, 1 table, lette
Importance and performance analysis on the investorâs choice of an offshore mutual fund and a bank channel in Taiwan
Investors in Taiwan prefer to invest in offshore funds, and they are good customers in the eyes of the world's major fund companies. Funds are competing these investors through these 3,400 bank branches. Literature has indicated comprehensive selection criteria when investors choosing a fund, yet no study revealed the gap between what investorsâ expected and experienced. The current study conducted a survey among these investors with importance-performance analysis (IPA) to fill this gap. There were two parts in the questionnaire, first part was drawn from literature to measure funds, and the second part was summarized from several depth interviews based on SERVQUAL with senior investors. 240 valid responses from current fund investors. The factors investorâs preference in evaluating a fund may be different in terms of residence areas and age. Perceived importance of fund selection criteria is not significantly different in terms of gender, education, marriage, and income levels. Test results indicated that âinvestment performance recordâ, âmanagement feesâ and âadditional featuresâ of fund, and the âsympathyâ dimension of bank should be first improved by either fund or bank company respectively
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