Analysis of Energy Quantization Effects on Single-Electron Transistor Circuits

In this paper, the effects of energy quantization on different single-electron transistor (SET) circuits (logic inverter, current-biased circuits, and hybrid MOS-SET circuits) are analyzed through analytical modeling and Monte Carlo simulations. It is shown that energy quantizationmainly increases the Coulomb blockade area and Coulomb blockade oscillation periodicity, and thus, affects the SET circuit performance. A new model for the noise margin of the SET inverter is proposed, which includes the energy quantization effects. Using the noise margin as a metric, the robustness of the SET inverter is studied against the effects of energy quantization. An analytical expression is developed, which explicitly defines the maximum energy quantization (termed as ``quantization threshold'') that an SET inverter can withstand before its noise margin falls below a specified tolerance level. The effects of energy quantization are further studiedfor the current-biased negative differential resistance (NDR) circuitand hybrid SETMOS circuit. A new model for the conductance of NDR characteristics is also formulated that explains the energy quantization effects.

Sequential split vector quantization of LSF parameters using conditional PDF

A better performing product code vector quantization (VQ) method is proposed for coding the line spectrum frequency (LSF) parameters; the method is referred to as sequential split vector quantization (SeSVQ). The split sub-vectors of the full LSF vector are quantized in sequence and thus uses conditional distribution derived from the previous quantized sub-vectors. Unlike the traditional split vector quantization (SVQ) method, SeSVQ exploits the inter sub-vector correlation and thus provides improved rate-distortion performance, but at the expense of higher memory. We investigate the quantization performance of SeSVQ over traditional SVQ and transform domain split VQ (TrSVQ) methods. Compared to SVQ, SeSVQ saves 1 bit and nearly 3 bits, for telephone-band and wide-band speech coding applications respectively.

A mixed-split scheme for 2-D DPCM based LSF quantization

In this paper a mixed-split scheme is proposed in the context of 2-D DPCM based LSF quantization scheme employing split vector product VQ mechanism. Experimental evaluation shows that the new scheme is successfully being able to show better distortion performance than existing safety-net scheme for noisy channel even at considerably lower search complexity, by efficiently exploiting LSF trajectory behavior across the consecutive speech frames.

On the two-dimensional thermoelectric power in quantum wells of non-parabolic materials under magnetic quantization

We present a simplified theoretical formulation of the thermoelectric power (TP) under magnetic quantization in quantum wells (QWs) of nonlinear optical materials on the basis of a newly formulated magneto-dispersion law. We consider the anisotropies in the effective electron masses and the spin-orbit constants within the framework of k.p formalism by incorporating the influence of the crystal field splitting. The corresponding results for III-V materials form a special case of our generalized analysis under certain limiting conditions. The TP in QWs of Bismuth, II-VI, IV-VI and stressed materials has been studied by formulating appropriate electron magneto-dispersion laws. We also address the fact that the TP exhibits composite oscillations with a varying quantizing magnetic field in QWs of n-Cd3As2, n-CdGeAs2, n-InSb, p-CdS, stressed InSb, PbTe and Bismuth. This reflects the combined signatures of magnetic and spatial quantizations of the carriers in such structures. The TP also decreases with increasing electron statistics and under the condition of non-degeneracy, all the results as derived in this paper get transformed into the well-known classical equation of TP and thus confirming the compatibility test. We have also suggested an experimental method of determining the elastic constants in such systems with arbitrary carrier energy spectra from the known value of the TP. (C) 2010 Elsevier Ltd. All rights reserved.

Receiver-Only Optimized Vector Quantization for Noisy Channels

This paper considers the design and analysis of a filter at the receiver of a source coding system to mitigate the excess Mean-Squared Error (MSE) distortion caused due to channel errors. It is assumed that the source encoder is channel-agnostic, i.e., that a Vector Quantization (VQ) based compression designed for a noiseless channel is employed. The index output by the source encoder is sent over a noisy memoryless discrete symmetric channel, and the possibly incorrect received index is decoded by the corresponding VQ decoder. The output of the VQ decoder is processed by a receive filter to obtain an estimate of the source instantiation. In the sequel, the optimum linear receive filter structure to minimize the overall MSE is derived, and shown to have a minimum-mean squared error receiver type structure. Further, expressions are derived for the resulting high-rate MSE performance. The performance is compared with the MSE obtained using conventional VQ as well as the channel optimized VQ. The accuracy of the expressions is demonstrated through Monte Carlo simulations.

Receiver-only optimized Vector Quantization for fading channels

This paper considers the design and analysis of a filter at the receiver of a source coding system to mitigate the excess distortion caused due to channel errors. The index output by the source encoder is sent over a fading discrete binary symmetric channel and the possibly incorrect received index is mapped to the corresponding codeword by a Vector Quantization (VQ) decoder at the receiver. The output of the VQ decoder is then processed by a receive filter to obtain an estimate of the source instantiation. The distortion performance is analyzed for weighted mean square error (WMSE) and the optimum receive filter that minimizes the expected distortion is derived for two different cases of fading. It is shown that the performance of the system with the receive filter is strictly better than that of a conventional VQ and the difference becomes more significant as the number of bits transmitted increases. Theoretical expressions for an upper and lower bound on the WMSE performance of the system with the receive filter and a Rayleigh flat fading channel are derived. The design of a receive filter in the presence of channel mismatch is also studied and it is shown that a minimax solution is the one obtained by designing the receive filter for the worst possible channel. Simulation results are presented to validate the theoretical expressions and illustrate the benefits of receive filtering.

Hardware implementation of 4x4 DCT/Quantization block using multiplication and error-free algorithm

The 4ÃÂ4 discrete cosine transform is one of the most important building blocks for the emerging video coding standard, viz. H.264. The conventional implementation does some approximation to the transform matrix elements to facilitate integer arithmetic, for which hardware is suitably prepared. Though the transform coding does not involve any multiplications, quantization process requires sixteen 16-bit multiplications. The algorithm used here eliminates the process of approximation in transform coding and multiplication in the quantization process, by usage of algebraic integer coding. We propose an area-efficient implementation of the transform and quantization blocks based on the algebraic integer coding. The designs were synthesized with 90 nm TSMC CMOS technology and were also implemented on a Xilinx FPGA. The gate counts and throughput achievable in this case are 7000 and 125 Msamples/sec.

Reduced Rate Ultra Low Delay Audio Coder using Multistage Vector Quantization

Communication applications are usually delay restricted, especially for the instance of musicians playing over the Internet. This requires a one-way delay of maximum 25 msec and also a high audio quality is desired at feasible bit rates. The ultra low delay (ULD) audio coding structure is well suited to this application and we investigate further the application of multistage vector quantization (MSVQ) to reach a bit rate range below 64 Kb/s, in a scalable manner. Results at 32 Kb/s and 64 Kb/s show that the trained codebook MSVQ performs best, better than KLT normalization followed by a simulated Gaussian MSVQ or simulated Gaussian MSVQ alone. The results also show that there is only a weak dependence on the training data, and that we indeed converge to the perceptual quality of our previous ULD coder at 64 Kb/s.

High-rate analysis of channel-optimized vector quantization

High-rate analysis of channel-optimized vector quantizationThis paper considers the high-rate performance of channel optimized source coding for noisy discrete symmetric channels with random index assignment. Specifically, with mean squared error (MSE) as the performance metric, an upper bound on the asymptotic (i.e., high-rate) distortion is derived by assuming a general structure on the codebook. This structure enables extension of the analysis of the channel optimized source quantizer to one with a singular point density: for channels with small errors, the point density that minimizes the upper bound is continuous, while as the error rate increases, the point density becomes singular. The extent of the singularity is also characterized. The accuracy of the expressions obtained are verified through Monte Carlo simulations.

High-Rate Vector Quantization for Noisy Channels With Applications to Wideband Speech Spectrum Compression

This paper considers the high-rate performance of source coding for noisy discrete symmetric channels with random index assignment (IA). Accurate analytical models are developed to characterize the expected distortion performance of vector quantization (VQ) for a large class of distortion measures. It is shown that when the point density is continuous, the distortion can be approximated as the sum of the source quantization distortion and the channel-error induced distortion. Expressions are also derived for the continuous point density that minimizes the expected distortion. Next, for the case of mean squared error distortion, a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component. The extent of the singularity is also characterized. These results provide analytical models for the expected distortion performance of both conventional VQ as well as for channel-optimized VQ. As a practical example, compression of the linear predictive coding parameters in the wideband speech spectrum is considered, with the log spectral distortion as performance metric. The theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion.

Threshold voltage modeling under size quantization for ultra-thin silicon double-gate metal-oxide-semiconductor field-effect transistor

We report on the threshold voltage modeling of ultra-thin (1 nm-5 nm) silicon body double-gate (DG) MOSFETs using self-consistent Poisson-Schrodinger solver (SCHRED). We define the threshold voltage (V th) of symmetric DG MOSFETs as the gate voltage at which the center potential (Φ c) saturates to Φ c (s a t), and analyze the effects of oxide thickness (t ox) and substrate doping (N A) variations on V th. The validity of this definition is demonstrated by comparing the results with the charge transition (from weak to strong inversion) based model using SCHRED simulations. In addition, it is also shown that the proposed V t h definition, electrically corresponds to a condition where the inversion layer capacitance (C i n v) is equal to the oxide capacitance (C o x) across a wide-range of substrate doping densities. A capacitance based analytical model based on the criteria C i n v C o x is proposed to compute Φ c (s a t), while accounting for band-gap widening. This is validated through comparisons with the Poisson-Schrodinger solution. Further, we show that at the threshold voltage condition, the electron distribution (n(x)) along the depth (x) of the silicon film makes a transition from a strong single peak at the center of the silicon film to the onset of a symmetric double-peak away from the center of the silicon film. © 2012 American Institute of Physics.

Analysis of size quantization and temperature effects on the threshold voltage of thin silicon film double-gate metal-oxide-semiconductor field-effect transistor (MOSFET)

In this paper, we analyze the combined effects of size quantization and device temperature variations (T = 50K to 400 K) on the intrinsic carrier concentration (n(i)), electron concentration (n) and thereby on the threshold voltage (V-th) for thin silicon film (t(si) = 1 nm to 10 nm) based fully-depleted Double-Gate Silicon-on-Insulator MOSFETs. The threshold voltage (V-th) is defined as the gate voltage (V-g) at which the potential at the center of the channel (Phi(c)) begins to saturate (Phi(c) = Phi(c(sat))). It is shown that in the strong quantum confinement regime (t(si) <= 3nm), the effects of size quantization far over-ride the effects of temperature variations on the total change in band-gap (Delta E-g(eff)), intrinsic carrier concentration (n(i)), electron concentration (n), Phi(c(sat)) and the threshold voltage (V-th). On the other hand, for t(si) >= 4 nm, it is shown that size quantization effects recede with increasing t(si), while the effects of temperature variations become increasingly significant. Through detailed analysis, a physical model for the threshold voltage is presented both for the undoped and doped cases valid over a wide-range of device temperatures, silicon film thicknesses and substrate doping densities. Both in the undoped and doped cases, it is shown that the threshold voltage strongly depends on the channel charge density and that it is independent of incomplete ionization effects, at lower device temperatures. The results are compared with the published work available in literature, and it is shown that the present approach incorporates quantization and temperature effects over the entire temperature range. We also present an analytical model for V-th as a function of device temperature (T). (C) 2013 AIP Publishing LLC.

Channel quantization for physical layer network-coded two-way relaying

The design of modulation schemes for the physical layer network-coded two way relaying scenario is considered with the protocol which employs two phases: Multiple access (MA) Phase and Broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. In other words, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map giving the best performance in a particular region. We obtain such a quantization analytically for the case when M-PSK (for M any power of 2) is the signal set used during the MA phase. We show that the complex plane can be classified into two regions: a region in which any network coding map which satisfies the so called exclusive law gives the same best performance and a region in which the choice of the network coding map affects the performance, which is further quantized based on the choice of the network coding map which optimizes the performance. The quantization thus obtained analytically, leads to the same as the one obtained using computer search for 4-PSK signal set by Koike-Akino et al., for the specific value of M = 4.

A note on D1-D5 entropy and geometric quantization

We quantize the space of 2-charge fuzzballs in IIB supergravity on K3. The resulting entropy precisely matches the D1-D5 black hole entropy, including a specific numerical coefficient. A partial match (ie., a smaller coefficient) was found by Rychkov a decade ago using the Lunin-Mathur subclass of solutions - we use a simple observation to generalize his approach to the full moduli space of K3 fuzzballs, filling a small gap in the literature.