40 research outputs found
High-resolution distributed sampling of bandlimited fields with low-precision sensors
The problem of sampling a discrete-time sequence of spatially bandlimited
fields with a bounded dynamic range, in a distributed,
communication-constrained, processing environment is addressed. A central unit,
having access to the data gathered by a dense network of fixed-precision
sensors, operating under stringent inter-node communication constraints, is
required to reconstruct the field snapshots to maximum accuracy. Both
deterministic and stochastic field models are considered. For stochastic
fields, results are established in the almost-sure sense. The feasibility of
having a flexible tradeoff between the oversampling rate (sensor density) and
the analog-to-digital converter (ADC) precision, while achieving an exponential
accuracy in the number of bits per Nyquist-interval per snapshot is
demonstrated. This exposes an underlying ``conservation of bits'' principle:
the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed
along the amplitude axis (sensor-precision) and space (sensor density) in an
almost arbitrary discrete-valued manner, while retaining the same (exponential)
distortion-rate characteristics. Achievable information scaling laws for field
reconstruction over a bounded region are also derived: With N one-bit sensors
per Nyquist-interval, Nyquist-intervals, and total network
bitrate (per-sensor bitrate ), the maximum pointwise distortion goes to zero as
or . This is shown to be possible
with only nearest-neighbor communication, distributed coding, and appropriate
interpolation algorithms. For a fixed, nonzero target distortion, the number of
fixed-precision sensors and the network rate needed is always finite.Comment: 17 pages, 6 figures; paper withdrawn from IEEE Transactions on Signal
Processing and re-submitted to the IEEE Transactions on Information Theor
Sampling versus Random Binning for Multiple Descriptions of a Bandlimited Source
Random binning is an efficient, yet complex, coding technique for the
symmetric L-description source coding problem. We propose an alternative
approach, that uses the quantized samples of a bandlimited source as
"descriptions". By the Nyquist condition, the source can be reconstructed if
enough samples are received. We examine a coding scheme that combines sampling
and noise-shaped quantization for a scenario in which only K < L descriptions
or all L descriptions are received. Some of the received K-sets of descriptions
correspond to uniform sampling while others to non-uniform sampling. This
scheme achieves the optimum rate-distortion performance for uniform-sampling
K-sets, but suffers noise amplification for nonuniform-sampling K-sets. We then
show that by increasing the sampling rate and adding a random-binning stage,
the optimal operation point is achieved for any K-set.Comment: Presented at the ITW'13. 5 pages, two-column mode, 3 figure
Results on lattice vector quantization with dithering
The statistical properties of the error in uniform scalar quantization have been analyzed by a number of authors in the past, and is a well-understood topic today. The analysis has also been extended to the case of dithered quantizers, and the advantages and limitations of dithering have been studied and well documented in the literature. Lattice vector quantization is a natural extension into multiple dimensions of the uniform scalar quantization. Accordingly, there is a natural extension of the analysis of the quantization error. It is the purpose of this paper to present this extension and to elaborate on some of the new aspects that come with multiple dimensions. We show that, analogous to the one-dimensional case, the quantization error vector can be rendered independent of the input in subtractive vector-dithering. In this case, the total mean square error is a function of only the underlying lattice and there are lattices that minimize this error. We give a necessary condition on such lattices. In nonsubtractive vector dithering, we show how to render moments of the error vector independent of the input by using appropriate dither random vectors. These results can readily be applied for the case of wide sense stationary (WSS) vector random processes, by use of iid dither sequences. We consider the problem of pre- and post-filtering around a dithered lattice quantifier, and show how these filters should be designed in order to minimize the overall quantization error in the mean square sense. For the special case where the WSS vector process is obtained by blocking a WSS scalar process, the optimum prefilter matrix reduces to the blocked version of the well-known scalar half-whitening filter
Hardware-Limited Task-Based Quantization
Quantization plays a critical role in digital signal processing systems.
Quantizers are typically designed to obtain an accurate digital representation
of the input signal, operating independently of the system task, and are
commonly implemented using serial scalar analog-to-digital converters (ADCs).
In this work, we study hardware-limited task-based quantization, where a system
utilizing a serial scalar ADC is designed to provide a suitable representation
in order to allow the recovery of a parameter vector underlying the input
signal. We propose hardware-limited task-based quantization systems for a fixed
and finite quantization resolution, and characterize their achievable
distortion. We then apply the analysis to the practical setups of channel
estimation and eigen-spectrum recovery from quantized measurements. Our results
illustrate that properly designed hardware-limited systems can approach the
optimal performance achievable with vector quantizers, and that by taking the
underlying task into account, the quantization error can be made negligible
with a relatively small number of bits
Asymptotic Task-Based Quantization with Application to Massive MIMO
Quantizers take part in nearly every digital signal processing system which
operates on physical signals. They are commonly designed to accurately
represent the underlying signal, regardless of the specific task to be
performed on the quantized data. In systems working with high-dimensional
signals, such as massive multiple-input multiple-output (MIMO) systems, it is
beneficial to utilize low-resolution quantizers, due to cost, power, and memory
constraints. In this work we study quantization of high-dimensional inputs,
aiming at improving performance under resolution constraints by accounting for
the system task in the quantizers design. We focus on the task of recovering a
desired signal statistically related to the high-dimensional input, and analyze
two quantization approaches: We first consider vector quantization, which is
typically computationally infeasible, and characterize the optimal performance
achievable with this approach. Next, we focus on practical systems which
utilize hardware-limited scalar uniform analog-to-digital converters (ADCs),
and design a task-based quantizer under this model. The resulting system
accounts for the task by linearly combining the observed signal into a lower
dimension prior to quantization. We then apply our proposed technique to
channel estimation in massive MIMO networks. Our results demonstrate that a
system utilizing low-resolution scalar ADCs can approach the optimal channel
estimation performance by properly accounting for the task in the system
design