40 research outputs found
Distributed Functional Scalar Quantization Simplified
Distributed functional scalar quantization (DFSQ) theory provides optimality
conditions and predicts performance of data acquisition systems in which a
computation on acquired data is desired. We address two limitations of previous
works: prohibitively expensive decoder design and a restriction to sources with
bounded distributions. We rigorously show that a much simpler decoder has
equivalent asymptotic performance as the conditional expectation estimator
previously explored, thus reducing decoder design complexity. The simpler
decoder has the feature of decoupled communication and computation blocks.
Moreover, we extend the DFSQ framework with the simpler decoder to acquire
sources with infinite-support distributions such as Gaussian or exponential
distributions. Finally, through simulation results we demonstrate that
performance at moderate coding rates is well predicted by the asymptotic
analysis, and we give new insight on the rate of convergence
Linear Precoding with Low-Resolution DACs for Massive MU-MIMO-OFDM Downlink
We consider the downlink of a massive multiuser (MU) multiple-input
multiple-output (MIMO) system in which the base station (BS) is equipped with
low-resolution digital-to-analog converters (DACs). In contrast to most
existing results, we assume that the system operates over a frequency-selective
wideband channel and uses orthogonal frequency division multiplexing (OFDM) to
simplify equalization at the user equipments (UEs). Furthermore, we consider
the practically relevant case of oversampling DACs. We theoretically analyze
the uncoded bit error rate (BER) performance with linear precoders (e.g., zero
forcing) and quadrature phase-shift keying using Bussgang's theorem. We also
develop a lower bound on the information-theoretic sum-rate throughput
achievable with Gaussian inputs, which can be evaluated in closed form for the
case of 1-bit DACs. For the case of multi-bit DACs, we derive approximate, yet
accurate, expressions for the distortion caused by low-precision DACs, which
can be used to establish lower bounds on the corresponding sum-rate throughput.
Our results demonstrate that, for a massive MU-MIMO-OFDM system with a
128-antenna BS serving 16 UEs, only 3--4 DAC bits are required to achieve an
uncoded BER of 10^-4 with a negligible performance loss compared to the
infinite-resolution case at the cost of additional out-of-band emissions.
Furthermore, our results highlight the importance of taking into account the
inherent spatial and temporal correlations caused by low-precision DACs
Multiple Description Quantization via Gram-Schmidt Orthogonalization
The multiple description (MD) problem has received considerable attention as
a model of information transmission over unreliable channels. A general
framework for designing efficient multiple description quantization schemes is
proposed in this paper. We provide a systematic treatment of the El Gamal-Cover
(EGC) achievable MD rate-distortion region, and show that any point in the EGC
region can be achieved via a successive quantization scheme along with
quantization splitting. For the quadratic Gaussian case, the proposed scheme
has an intrinsic connection with the Gram-Schmidt orthogonalization, which
implies that the whole Gaussian MD rate-distortion region is achievable with a
sequential dithered lattice-based quantization scheme as the dimension of the
(optimal) lattice quantizers becomes large. Moreover, this scheme is shown to
be universal for all i.i.d. smooth sources with performance no worse than that
for an i.i.d. Gaussian source with the same variance and asymptotically optimal
at high resolution. A class of low-complexity MD scalar quantizers in the
proposed general framework also is constructed and is illustrated
geometrically; the performance is analyzed in the high resolution regime, which
exhibits a noticeable improvement over the existing MD scalar quantization
schemes.Comment: 48 pages; submitted to IEEE Transactions on Information Theor
Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions
Communication of quantized information is frequently followed by a
computation. We consider situations of \emph{distributed functional scalar
quantization}: distributed scalar quantization of (possibly correlated) sources
followed by centralized computation of a function. Under smoothness conditions
on the sources and function, companding scalar quantizer designs are developed
to minimize mean-squared error (MSE) of the computed function as the quantizer
resolution is allowed to grow. Striking improvements over quantizers designed
without consideration of the function are possible and are larger in the
entropy-constrained setting than in the fixed-rate setting. As extensions to
the basic analysis, we characterize a large class of functions for which
regular quantization suffices, consider certain functions for which asymptotic
optimality is achieved without arbitrarily fine quantization, and allow limited
collaboration between source encoders. In the entropy-constrained setting, a
single bit per sample communicated between encoders can have an
arbitrarily-large effect on functional distortion. In contrast, such
communication has very little effect in the fixed-rate setting.Comment: 36 pages, 10 figure
Message-Passing Estimation from Quantized Samples
Estimation of a vector from quantized linear measurements is a common problem
for which simple linear techniques are suboptimal -- sometimes greatly so. This
paper develops generalized approximate message passing (GAMP) algorithms for
minimum mean-squared error estimation of a random vector from quantized linear
measurements, notably allowing the linear expansion to be overcomplete or
undercomplete and the scalar quantization to be regular or non-regular. GAMP is
a recently-developed class of algorithms that uses Gaussian approximations in
belief propagation and allows arbitrary separable input and output channels.
Scalar quantization of measurements is incorporated into the output channel
formalism, leading to the first tractable and effective method for
high-dimensional estimation problems involving non-regular scalar quantization.
Non-regular quantization is empirically demonstrated to greatly improve
rate-distortion performance in some problems with oversampling or with
undersampling combined with a sparsity-inducing prior. Under the assumption of
a Gaussian measurement matrix with i.i.d. entries, the asymptotic error
performance of GAMP can be accurately predicted and tracked through the state
evolution formalism. We additionally use state evolution to design MSE-optimal
scalar quantizers for GAMP signal reconstruction and empirically demonstrate
the superior error performance of the resulting quantizers.Comment: 12 pages, 8 figure
Adaptive Quantizers for Estimation
In this paper, adaptive estimation based on noisy quantized observations is
studied. A low complexity adaptive algorithm using a quantizer with adjustable
input gain and offset is presented. Three possible scalar models for the
parameter to be estimated are considered: constant, Wiener process and Wiener
process with deterministic drift. After showing that the algorithm is
asymptotically unbiased for estimating a constant, it is shown, in the three
cases, that the asymptotic mean squared error depends on the Fisher information
for the quantized measurements. It is also shown that the loss of performance
due to quantization depends approximately on the ratio of the Fisher
information for quantized and continuous measurements. At the end of the paper
the theoretical results are validated through simulation under two different
classes of noise, generalized Gaussian noise and Student's-t noise
Differential encoding techniques applied to speech signals
The increasing use of digital communication systems has
produced a continuous search for efficient methods of speech
encoding.
This thesis describes investigations of novel differential
encoding systems. Initially Linear First Order DPCM systems
employing a simple delayed encoding algorithm are examined.
The systems detect an overload condition in the encoder, and
through a simple algorithm reduce the overload noise at the
expense of some increase in the quantization (granular) noise.
The signal-to-noise ratio (snr) performance of such d codec has
1 to 2 dB's advantage compared to the First Order Linear DPCM
system.
In order to obtain a large improvement in snr the high
correlation between successive pitch periods as well as the
correlation between successive samples in the voiced speech
waveform is exploited. A system called "Pitch Synchronous
First Order DPCM" (PSFOD) has been developed. Here the difference
Sequence formed between the samples of the input sequence in the
current pitch period and the samples of the stored decoded
sequence from the previous pitch period are encoded. This
difference sequence has a smaller dynamic range than the original
input speech sequence enabling a quantizer with better resolution
to be used for the same transmission bit rate. The snr is increased
by 6 dB compared with the peak snr of a First Order DPCM codea.
A development of the PSFOD system called a Pitch Synchronous
Differential Predictive Encoding system (PSDPE) is next investigated.
The principle of its operation is to predict the next sample in
the voiced-speech waveform, and form the prediction error which
is then subtracted from the corresponding decoded prediction
error in the previous pitch period. The difference is then
encoded and transmitted. The improvement in snr is approximately
8 dB compared to an ADPCM codea, when the PSDPE system uses an
adaptive PCM encoder. The snr of the system increases further
when the efficiency of the predictors used improve. However,
the performance of a predictor in any differential system is
closely related to the quantizer used. The better the quantization
the more information is available to the predictor and the better
the prediction of the incoming speech samples. This leads
automatically to the investigation in techniques of efficient
quantization. A novel adaptive quantization technique called
Dynamic Ratio quantizer (DRQ) is then considered and its theory
presented. The quantizer uses an adaptive non-linear element
which transforms the input samples of any amplitude to samples
within a defined amplitude range. A fixed uniform quantizer
quantizes the transformed signal. The snr for this quantizer
is almost constant over a range of input power limited in practice
by the dynamia range of the adaptive non-linear element, and it
is 2 to 3 dB's better than the snr of a One Word Memory adaptive
quantizer.
Digital computer simulation techniques have been used widely
in the above investigations and provide the necessary experimental
flexibility. Their use is described in the text
Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems
Stabilization of non-stationary linear systems over noisy communication
channels is considered. Stochastically stable sources, and unstable but
noise-free or bounded-noise systems have been extensively studied in
information theory and control theory literature since 1970s, with a renewed
interest in the past decade. There have also been studies on non-causal and
causal coding of unstable/non-stationary linear Gaussian sources. In this
paper, tight necessary and sufficient conditions for stochastic stabilizability
of unstable (non-stationary) possibly multi-dimensional linear systems driven
by Gaussian noise over discrete channels (possibly with memory and feedback)
are presented. Stochastic stability notions include recurrence, asymptotic mean
stationarity and sample path ergodicity, and the existence of finite second
moments. Our constructive proof uses random-time state-dependent stochastic
drift criteria for stabilization of Markov chains. For asymptotic mean
stationarity (and thus sample path ergodicity), it is sufficient that the
capacity of a channel is (strictly) greater than the sum of the logarithms of
the unstable pole magnitudes for memoryless channels and a class of channels
with memory. This condition is also necessary under a mild technical condition.
Sufficient conditions for the existence of finite average second moments for
such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor