Aleksandra Z. Jovanovic

Multidimensional Optical Transport Based on Optimized Vector-Quantization-Inspired Signal Constellation Design

An optimized vector-quantization-inspired signal constellation design (OVQ-SCD) suitable for multidimensional optical transport is proposed, in which signal constellation radii transformation function is optimized and near-uniform distribution of points is achieved. The proposed OVQ-SCD is used in a tandem with a hybrid multidimensional coded-modulation scheme employing Slepian sequences as electrical discrete-time basis functions, orthogonal prolate spheroidal wave functions as impulse responses of optical filters in orthogonal-division multiplexing, and spatial modes as optical continuous-time basis functions. It has been shown that the proposed multidimensional coded-modulation schemes based on OVQ-SCDs outperform corresponding counterparts and can be used to enable beyond 10 Pb/s serial optical transport over spatial division multiplexing (SDM) fibers as well as beyond 1 Pb/s transport over SMFs. The proposed OVQ-SCD-based hybrid multidimensional coded modulation scheme can simultaneously solve the problems related to the limited bandwidth of information-infrastructure, high energy consumption, and heterogeneity of network segments; while enabling elastic and dynamic bandwidth allocation.

Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks

In this paper, we propose a hybrid multidimensional coded-modulation (CM) scheme based on a new multidimensional signal constellation design as a solution to limited bandwidth and high energy consumption of information infrastructure. This multidimensional signal constellation, herewith called vector-quantization-based signal constellation design (VQ-SCD), is based on the vector quantization theory. The proposed scheme employs both the electrical basis functions (in the form of the prolate spheroidal wave functions) and the optical basis functions (in the form of polarization and spatial mode states) as optical basis functions. The proposed coded VQ-SCD scheme is the enabling technology for optical serial transport with bit rates exceeding 1000 Tb/s (1 Pb/s). In addition, the CM scheme we proposed allows for the adaptive, elastic, and dynamic allocation of the bandwidth. This fine granularity bandwidth manipulation is envisioned as a part of future software-defined optical networking.

Two forward adaptive dual-mode companding scalar quantizers for Gaussian source

In this paper we propose a novel model of piecewise linear companding scalar quantizer (PLCSQ) having the piecewise linear compressor function determined by minimizing the mean-squared error between the optimal compressor function and the piecewise linear compressor function for the Gaussian source subject to the constraint of the equal number of cells per segments. We show that with the increase of the number of segments, the difference between the optimal compressor function and the novel piecewise linear compressor function decreases, which implies that the novel PLCSQ, having a simpler design and implementation procedure compared to the one of optimal companding scalar quantizer (OCSQ), can be used as a good alternative for OCSQ. We also consider the implementation of these two quantizers in the forward adaptive dual-mode quantization scheme. The numerical results presented in the paper indicate that the proposed quantizers are worth implementing not only in view of flexibility in the bit rate choice, but also in view of the significant gain in signal to quantization noise ratio (SQNR) achieved over the one forward adaptive unrestricted companding scalar quantizer. Also, the numerical results indicate great possibilities for application of the proposed quantizers in high-quality quantization of Gaussian source signals. We propose the novel model of piecewise linear companding scalar quantizer.We compare performances of two forward adaptive dual-mode quantizers.The results indicate great possibilities for application of the proposed quantizers.We show that the proposed quantizers are worth implementing not only in view of flexibility in the bit rate choice, but also in view of the significant gain in SQNR achieved over the one forward adaptive unrestricted companding scalar quantizer.The numerical results indicate great possibilities for application of the proposed quantizers in high-quality quantization of Gaussian source signals.

Variance Mismatch Analysis of Unrestricted Polar Quantization for Gaussian Source

In this letter, asymptotic formulas are derived for signal to quantization noise ratio (SQNR) of two unrestricted polar quantizers (UPQs) for the case where designed-for and applied-to Gaussian sources have different variances. It is shown that the limitation in the variance mismatch analysis observed in one of the UPQs can be overcome by the constrained application of asymptotic approximations and by optimizing the last magnitude reconstruction level subsequently. The derived formulas are a useful analytical tool for determining the effect of variance mismatch on SQNR in unrestricted polar quantization for Gaussian source.

Adaptive nonuniform polar quantization application to high quality speech compression

The logarithmic companding technique has shown to be extremely useful in speech quantization with rate of 8 bits/sample. However, for lower bit rates it is not the ideal solution for high quality speech coding. Because of that, in this paper we establish source coding scheme which enables better spectrum efficiency for input that has a large dynamic range. Since our wish is also to improve signal quality in comparison with quality defined with standards G.711 and G.712, we opt for adaptive technique application to the speech coding. Our research shows that proper design of forward gain-adaptive polar quantization can enable compression of about 1 bit/sample as well as significantly better quality than in case of using coder designed according to standard G.711. Furthermore, performances can be sustained over the whole speech dynamic range. Also, if the requisite speech quality is not supposed to be lower than G.712 standard quality, the achieved compression can be almost 1.5 bits/sample. Besides, we propose knew simple encoding rule which can additionally reduce bit rate for 0.1 bit/sample.

Optimal log-polar image sampling

In order to achieve better image compression simultaneously maintaining the high signal quality, the image sampling has become very important. Also, since the human eye sensitivity has circularly symmetric distribution, in recent years it is usual to apply log-polar image sampling. In this paper, we perform optimization of log-polar image sampling and show the significant improvement in comparison with the product log-polar sampling. Namely, for equal numbers of sensors optimal model gives higher signal-to-noise ratio (SNR) up to 2.5 dB, i.e., it is possible to decrease the number of required sensors by 45% for the same SNR. Furthermore, research shows that in optimal log-polar image sampling, the middle region of image, which is not sampled, can be made to be smaller than in the case of product sampling.

Optimal Piecewise Uniform Vector Quantization of the Memoryless Two Dimensional Laplacian Source

In this paper we will present a simple and complete asymptotical analysis of an optimal piecewise uniform quantization (PUQ) of two-dimensional memoryless Laplacian source with the respect to distortion (D) i.e. the mean-square error (MSE). PUQ is based on uniform vector quantizers. PUQ consists of L different uniform vector quantizers. Uniform quantizer optimality conditions and all main equations for number of optimum number of output points and optimal number of levels for each partition are presented. These systems, although not optimal, may have asymptotic performance arbitrary close to the optimum. Furthermore, their analysis and implementation can be simpler than those of optimal systems. PUQ has complexity implementation between optimal nonuniform quantization (NQ) and uniform quantization (UQ). We derive the optimal granular distortion Dg opt (i) for each partition in a closed form. The two- dimensional space is partitioned using rectangular cells.

Design of piecewise uniform scalar quantizer for the backward adaptive algorithm

This paper proposes a novel piecewise uniform scalar quantizer model built on the bases of the Jayants quantizer model. The novel model utilizes the Jayants manner of maximum amplitude adaptation, which means according to the one word memory and with the use of the backward adaptive technique. Particularly, the proposed model is equal to the Jayants quantizer model when the step size multiplier, introduced by the novel model, has the unit value. Therefore, we actually propose more general model of a quantizer that, as we will demonstrate, provides overreaching of the Jayants average signal to quantization noise ratio for about 9 dB.

Support region estimation of the product polar companded quantizer for Gaussian source

Abstract This paper describes two approaches to optimization of the key design parameters, the support region threshold and the number of magnitude representation levels, of product polar companded quantizer (PPCQ) for Gaussian source of unit variance. The first approach is based on the exact performance analysis of PPCQ and on distortion optimization with respect to the key design parameters. Due to the optimization problem complexity we encountered with the first approach, some suitable approximations are introduced with the second one. As a result, much simpler asymptotic closed-form formula for distortion of PPCQ is derived as a function of the support region threshold. Although with this approach the closed-form formula for the support region threshold cannot be derived, the results of this approach indicate the useful support region threshold form. By combining the results of both approaches we propose, the worthy closed-form formulas for the support region threshold and signal to quantization noise ratio of a nearly optimal PPCQ are provided. Moreover, from the results of both analyses the lower and upper bound expressions for the number of magnitude representation levels are provided. The analysis presented in the paper is useful for designing PPCQ and is of great theoretical and practical importance.