Sum Of Distortion Research Articles

Optimizing Low-Complexity Analog Mappings for Low-Power Sensors With Energy Scheduling Capabilities

Power consumption is a major challenge for a massive deployment of wireless sensors in Internet of Things (IoT) networks. This article studies the use of analog joint source-channel coding (AJSCC) mappings in low-power sensing schemes. In particular, we propose a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">triangular</i> mapping geometry as a low-complexity dimension reduction mapping. The proposed triangular mapping is employed for analog compression of multiple sensor readings into one signal and, thus, limits the need for power-hungry analog-to-digital conversion and processing at the sensing nodes. A comprehensive performance analysis of the proposed triangular mapping in terms of the mean squared error (MSE) performance is provided analytically and verified numerically. The problem of mapping adaptation to different source distributions is also studied. Moreover, the proposed triangular mapping is adopted in an energy scheduling problem in which the sensing nodes schedule their use of the received powers at different time instants and adjust the mapping parameters accordingly with the goal of minimizing the sum distortion at the receiver. We present a fast low-complexity algorithm for optimal energy scheduling and verify its performance in comparison with commercial convex optimization solvers. It is shown that the proposed mapping provides a very good MSE performance compared to the AJSCC benchmarks despite having a much lower complexity circuit implementation.

Design of General Entropy-Constrained Successively Refinable Unrestricted Polar Quantizer

This paper presents an algorithm for the optimal design of general entropy-constrained successively refinable unrestricted polar quantizer, i.e., with arbitrary number $L$ of refinement levels, for bivariate circularly symmetric sources. The optimization problem is formulated as the minimization of a weighted sum of distortions and entropies for the scenario where the magnitude quantizers’ thresholds are confined to a predefined finite set. The proposed solution algorithm is globally optimal. It involves $L$ stages, where each stage corresponds to an unrestricted polar quantizer (UPQ) level, and includes solving the minimum-weight path problem for multiple node pairs in a series of weighted directed acyclic graphs. Additionally, we derive an upper bound $P^{(l)}_{\max }, l\in [1:L]$ , on the possible number of phase levels in any phase quantizer of the $l$ -th level UPQ, which grows linearly with $l$ . The time complexity of the proposed approach is $O(L^{2}K^{3} P^{(1)}_{\max })$ , where $K$ is the cardinality of the predefined set of possible magnitude thresholds. Finally, the experimental results for $L=3$ demonstrate the effectiveness in practice of the proposed scheme.

Design of Optimal Scalar Quantizer for Sequential Coding of Correlated Sources

This paper addresses the design of a sequential scalar quantizer (SSQ) for finite-alphabet correlated sources in the fixed-rate (FR) and entropy-constrained (EC) cases. The optimization problem is formulated as the minimization of a weighted sum of distortions and rates. The proposed solution is globally optimal for the class of SSQs with convex cells and is based on solving the minimum-weight path (MWP) problem in the EC case, respectively, a length-constrained MWP problem in the FR case, in a series of weighted directed acyclic graphs. The asymptotic time complexity is $O(K_{1}^{2}K_{2}^{2})$ , where $K_{1}$ and $K_{2}$ are the respective sizes of the alphabets of the two sources. Additionally, it is proved that, by applying the proposed algorithms to discretizations of correlated sources with continuous joint probability density function, the performance approaches that of the optimal EC-SSQ, respectively, FR-SSQ, with convex cells for the original sources as the accuracy of the discretization increases. Extensive experiments performed with correlated Gaussian sources validate the effectiveness in practice of the proposed approach in approximating the optimal SSQ for the case of continuous-alphabet sources.

Energy Efficient Power Allocation for Distributed MIMO System

The rapid increasing demands of multi-media applications have busted the improvement of video transmission. By the increase of multimedia transmission, quality of experience (QoE) has become the hot topic of the wireless networks’ research. This paper proposes a QoE-aware resource allocation algorithm in MIMO-OFDM Networks. The power allocation estimation is formulated to maximize according to QoE by considering the video transmission rate and the subcarrier schemes under the constraint of minimum power. In this paper, we will analyses the the performance of video transmission from transmission rate at the application layer to the power allocation at the physical layer. From simulation results, we can see that the proposed subcarrier allocation algorithm maximizes the video QoE by minimizing the sum distortion of multi-users in MIMO networks with power constraints.

Two-Level Scheduling for Video Transmission over Downlink OFDMA Networks.

This paper presents a two-level scheduling scheme for video transmission over downlink orthogonal frequency-division multiple access (OFDMA) networks. It aims to maximize the aggregate quality of the video users subject to the playback delay and resource constraints, by exploiting the multiuser diversity and the video characteristics. The upper level schedules the transmission of video packets among multiple users based on an overall target bit-error-rate (BER), the importance level of packet and resource consumption efficiency factor. Instead, the lower level renders unequal error protection (UEP) in terms of target BER among the scheduled packets by solving a weighted sum distortion minimization problem, where each user weight reflects the total importance level of the packets that has been scheduled for that user. Frequency-selective power is then water-filled over all the assigned subcarriers in order to leverage the potential channel coding gain. Realistic simulation results demonstrate that the proposed scheme significantly outperforms the state-of-the-art scheduling scheme by up to 6.8 dB in terms of peak-signal-to-noise-ratio (PSNR). Further test evaluates the suitability of equal power allocation which is the common assumption in the literature.

Evaluation of Analog Joint Source-Channel Coding Systems for Multiple Access Channels

We address the evaluation of low-complexity analog Joint Source Channel Coding (JSCC) methods for the transmission of discrete-time analog symbols over Multiple-Input Multiple-Output (MIMO) Multiple Access Channels (MAC). Analog JSCC is employed to encode the source information at each transmitter prior to be directly input to the MAC access scheme. Three channel access methods are considered to ensure the receiver is able to recover the user information: Code Division Multiple Access (CDMA), linear MMSE access codes and opportunistic access. CDMA allows the orthogonal transmission of the user data requiring only Channel State Information (CSI) at reception. On the other hand, linear MMSE access codes exploit CSI knowledge at transmission and exhibit better performance. Finally, opportunistic access also exploits CSI at transmission and allocates all MAC resources to the user with the strongest channel. This latter access scheme exhibits the best performance in terms of sum distortion although it may lead to unfair rate distributions among users.

Rate Allocation for Transmission of Two Gaussian Sources over Multiple Access Fading Channels

We perform optimal rate allocation of two independent Gaussian sources on a two-user multiple access Rayleigh fading channel by minimizing the sum distortion at the common receiver. We first consider the case of fast fading, where we use the ergodic capacity region, and analytically solve for the optimal pair of rates. We then address the case of slow fading, where we determine the optimal pair of rates that minimizes the sum distortion, using outage probabilities. Results show that the sum distortion for slow fading is larger than for fast fading and that the use of individual outage probabilities outperforms the use of common outage probability. The higher variance source requires higher rates in both fast and slow fading.

Drawing Road Networks with Focus Regions

Mobile users of maps typically need detailed information about their surroundings plus some context information about remote places. In order to avoid that the map partly gets too dense, cartographers have designed mapping functions that enlarge a user-defined focus region--such functions are sometimes called fish-eye projections. The extra map space occupied by the enlarged focus region is compensated by distorting other parts of the map. We argue that, in a map showing a network of roads relevant to the user, distortion should preferably take place in those areas where the network is sparse. Therefore, we do not apply a predefined mapping function. Instead, we consider the road network as a graph whose edges are the road segments. We compute a new spatial mapping with a graph-based optimization approach, minimizing the square sum of distortions at edges. Our optimization method is based on a convex quadratic program (CQP); CQPs can be solved in polynomial time. Important requirements on the output map are expressed as linear inequalities. In particular, we show how to forbid edge crossings. We have implemented our method in a prototype tool. For instances of different sizes, our method generated output maps that were far less distorted than those generated with a predefined fish-eye projection. Future work is needed to automate the selection of roads relevant to the user. Furthermore, we aim at fast heuristics for application in real-time systems.

Distortion component analysis of outer hair cell motility-related gating charge.

The underlying Boltzmann characteristics of motility-related gating currents of the outer hair cell (OHC) are predicted to generate distortion components in response to sinusoidal transmembrane voltages. We studied this distortion since it reflects the mechanical activity of the cell that may contribute to peripheral auditory system distortion. Distortion components in the OHC electrical response were analyzed using the whole-cell voltage clamp technique, under conditions where ionic conductances were blocked. Single or double-sinusoidal transmembrane voltage stimulation was delivered at various holding voltages, and distortion components of the current responses were detected by Fourier analysis. Current response magnitude and phase of each distortion component as a function of membrane potential were compared with characteristics of the voltage-dependent capacitance, obtained by voltage stair-step transient analysis or dual-frequency admittance analysis. The sum distortion was most prominent among the distortion components at all holding voltages. Notches in the sum (f1+f2), difference (f2-f1) and second harmonic (2f) components occur at the voltage where peak voltage-dependent capacitance resides (VpkCm). Rapid phase reversals also occurred at VpkCm, but phase remained fairly stable at more depolarized and hyperpolarized potentials. Thus, it is possible to extract Boltzmann parameters of the motility-related charge movement from these distortion components. In fact, we have developed a technique to follow changes in the voltage dependence of OHC motility and charge movement by tracking the voltage at phase reversal of the f2-f1 product. When intracellular turgor pressure was changed, VpkCm and distortion notch voltages shifted in the same direction. These data have important implications for understanding cochlear nonlinearity, and more generally, indicate the usefulness of distortion analysis to study displacement currents.

One-dimensional maps and Poincare metric

Invertible compositions of one-dimensional maps are studied which are assumed to include maps with a non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, the author shows that the joint distortion of the composition is bounded. On the other hand, if all maps with possibly non-negative Schwarzian derivatives are almost linear-fractional and their nonlinearities tend to cancel leaving only a small total, then they can all be replaced with affine maps with the same domains and images and the resulting composition is a very good approximation of the original one. These technical tools are then applied to prove a theorem about critical circle maps.

Root‐power sums and spectral slope distortion measures for all‐pole models of speech

Distortion measures for use in speech processing are presented with emphasis on improvement of efficiency and recognition performance for noisy speech. Good results have been obtained from measures calculated from differences of root‐power sums (i.e., differences of index‐weighted cepstral coefficients: k *ck). This type of distortion measure can be derived as an approximation to the spectral slope distortion measure, which expresses slope differences between test and reference logarithmic spectra. However, when used on all‐pole model spectra, the root‐power sum distortion is computationally more efficient. It is well‐suited for use with both linear predictive (LP) analysis and the recently proposed perceptually based LP [H. Hermansky, B. A. Hanson, and H. Wakita, IEEE Proc. ICASSP 85, 509–512 (1985)]. The proposed distortion measures are shown to provide equal or better recognition scores compared to standard LP‐cepstral matching in low noise conditions and substantial improvements in noisy conditions.

Perspective Pictures and Visual Perception

The author analyzes the possibilities of developing a system of scientific perceptual perspective by means of interior pictures. Analysis shows that many different perspective pictures of one interior viewed from the same point may exist, all of them being equivalent (i.e. containing an equal sum of distortions of visual perception). The author believes that Renaissance perspective cannot set the aesthetic standard for a ‘correct’ perspective because it is only one of the possible variants.