Design and Implementation of Cost-Effective Probabilistic-Based Noise-Tolerant VLSI Circuits

As the size of CMOS devices is scaled down to nanometers, noise can significantly affect circuit performance. Because noise is random and dynamic in nature, a probabilistic-based approach is better suited to handle these types of errors compared with conventional CMOS designs. In this paper, we propose a cost-effective probabilistic-based noise-tolerant circuit-design methodology. Our cost-effective method is based on master-and-slave Markov random field (MRF) mapping and master-and-slave MRF logic-gate construction. The resulting probabilistic-based MRF circuit trades hardware cost for circuit reliability. To demonstrate a noise-tolerant performance, an 8-bit MRF carry-lookahead adder (MRF_CLA) was implemented using the 0.13-${rm mu}hbox{m}$ CMOS process technology. The chip measurement results show that the proposed master-and-slave MRF_CLA can provide a $7.00times 10^{-5}$ bit-error rate (BER) under 10.6-dB signal-to-noise ratio, while the conventional CMOS_CLA can only provide $8.84times 10^{-3}$ BER. Because of high noise immunity, the master-and-slave MRF_CLA can operate under 0.25 V to tolerate noise interference with only 1.9 ${rm mu}hbox{W/MHz}$ of energy consumption. Moreover, the transistor count can be reduced by 42% as compared with the direct-mapping MRF_CLA design .      

Single-Exclusion Number and the Stopping Redundancy of MDS Codes

For a linear block code ${cal C}$, its stopping redundancy is defined as the smallest number of check nodes in a Tanner graph for ${cal C}$, such that there exist no stopping sets of size smaller than the minimum distance of ${cal C}{bf .},$ Schwartz and Vardy conjectured that the stopping redundancy of a maximum-distance separable (MDS) code should only depend on its length and minimum distance.      

SEChecker: A Sequential Equivalence Checking Framework Based on ${K}$th Invariants

In recent years, considerable research efforts have been devoted to utilizing circuit structural information to improve the efficiency of Boolean satisfiability (SAT) solving, resulting in several efficient circuit-based SAT solvers. In this paper, we present a sequential equivalence checking framework based on a number of circuit-based SAT solving techniques as well as a novel invariant checker. We first introduce the notion of $k$th invariants. In contrast to the traditional invariants that hold for all cycles, $k$ th invariants are guaranteed to hold only after the $k$th cycle from the initial state. We then present a bounded model checker (BMChecker) and an invariant checker (IChecker), both of which are based on circuit SAT techniques. Jointly, BMChecker and IChecker are used to compute the $k$th invariants, and are further integrated in a sequential circuit SAT solver for checking sequential equivalence. Experimental results demonstrate that the new sequential equivalence checking framework can efficiently verify large industrial designs that cannot be verified by existing solutions.      

Integrated Quadrature Couplers and Their Application in Image-Reject Receivers

Several fully-integrated multi-stage lumped-element quadrature hybrids that enhance bandwidth, amplitude and phase accuracies, and robustness are presented, and a fully-integrated double-quadrature heterodyne receiver front-end that uses two-stage Lange/Lange couplers is described. The Lange/Lange cascade exploits the inherent wide bandwidth characteristic of the Lange hybrid and enables a robust design using a relatively low transformer coupling coefficient. The measured image-rejection ratio is $>$ 55 dB over a 200 MHz bandwidth centered around 5.25 $~$GHz without any tuning, trimming, or calibration; the front-end features 23.5 dB gain, $-$79 dBm sensitivity, 5.6 dB SSB NF, $-$7$~$ dBm IIP3, $-$18 dB $S_{11}$ and a 1 mm $times$ 2 mm die area in 0.18$ mu{hbox {m}}$ CMOS.      

High-Temperature High-Power Operation of GaInNAs Laser Diodes in the 1220–1240-nm Wavelength Range

We report on the high-temperature performance of high-power GaInNAs broad area laser diodes with different waveguide designs emitting in the 1220–1240-nm wavelength range. Large optical cavity laser structures enable a maximum continuous-wave output power of $>$8.9 W at ${T}=20 ^{circ}$C with emission at 1220 nm and are characterized by low internal losses of 0.5 cm$^{-1}$ compared to 2.9 cm$^{-1}$ for the conventional waveguide structures. High-power operation up to temperatures of 120 $^{circ}$C is observed with output powers of $>$4 W at ${T}=90 ^{circ}$C. This laser diode showed characteristic temperatures of ${T}_{0} =112$ K and ${T}_{1}=378$ K.      

On the Values of Kloosterman Sums

Given a prime $p$ and a positive integer $n$ , we show that the shifted Kloosterman sums $$sum _{x in BBF _{p^{n}}} psi (x + ax^{p^{n}-2}) = sum _{xin BBF _{p^{n}}^{ast }} psi(x + ax^{-1}) + 1, quad a inBBF _{p^{n}}^{ast }$$ where $psi$ is a nontrivial additive character of a finite field $BBF _{p^{n}}$ of $p^{n}$ elements, do not vanish if $a$ belongs to a small subfield $BBF_{p^{m}} subseteq BBF _{p^{n}}$. This complements recent results of P. Charpin and G. Gong which in turn were motivated by some applications to bent functions.      

On the Cusick–Cheon Conjecture About Balanced Boolean Functions in the Cosets of the Binary Reed–Muller Code

In this paper, an amplification of the Cusick–Cheon conjecture on balanced Boolean functions in the cosets of the binary Reed–Muller code $RM(k,m)$ of order $k$ and length $2^m$, in the cases where $k = 1$ or $k geq (m-1)/2$, is proved.      

A Sub-0.2$^{circ}/$ hr Bias Drift Micromechanical Silicon Gyroscope With Automatic CMOS Mode-Matching

This paper describes a system architecture and CMOS implementation that leverages the inherently high mechanical quality factor (Q) of a MEMS gyroscope to improve performance. The proposed time domain scheme utilizes the often-ignored residual quadrature error in a gyroscope to achieve, and maintain, perfect mode-matching (i.e., $sim$0 Hz split between the high-Q drive and sense mode frequencies), as well as electronically control the sensor bandwidth. A CMOS IC and control algorithm have been interfaced with a 60 $mu{hbox {m}}$ thick silicon mode-matched tuning fork gyroscope $({rm M}^{2}mathchar"707B {rm TFG})$ to implement an angular rate sensing microsystem with a bias drift of 0.16$^{circ}/{hbox{hr}}$. The proposed technique allows microsystem reconfigurability—the sensor can be operated in a conventional low-pass mode for larger bandwidth, or in matched mode for low-noise. The maximum achieved sensor Q is 36,000 and the bandwidth of the microsensor can be varied between 1 to 10 Hz by electronic control of the mechanical frequencies. The maximum scale factor of the gyroscope is 88 ${hbox{mV}}/^{circ}/{hbox{s}}$ . The 3$~$ V IC is fabricated in a standard 0.6 $ mu{hbox {m}}$ CMOS process and consumes 6 mW of power with a die area of 2.25 ${hbox {mm}}^{2}$.      

A Note on Limited-Trial Chase-Like Algorithms Achieving Bounded-Distance Decoding

For the decoding of a binary linear block code of minimal Hamming distance $d$ over additive white Gaussian noise (AWGN) channels, a soft-decision decoder achieves bounded-distance (BD) decoding if its squared error-correction radius is equal to $d$. A Chase-like algorithm outputs the best (most likely) codeword in a list of candidates generated by a conventional algebraic binary decoder in a few trials. It is of interest to design Chase-like algorithms that achieve BD decoding with as least trials as possible. In this paper, we show that Chase-like algorithms can achieve BD decoding with only $O(d^{1/2+varepsilon })$ trials for any given positive number $varepsilon $.      

Robust Precoder Adaptation for MIMO Links With Noisy Limited Feedback

In this paper, we propose two robust limited feedback designs for multiple-input multiple-output (MIMO) adaptation. The first scheme, namely, the combined design jointly optimizes the adaptation, CSIT (channel state information at the transmitter) feedback as well as index assignment strategies. The second scheme, namely, the decoupled design, focuses on the index assignment problem given an error-free limited feedback design. Simulation results show that the proposed framework has significant capacity gain compared to the naive design (designed assuming there is no feedback error). Furthermore, for large number of feedback bits $C_{rm fb}$, we show that under two-nearest constellation feedback channel assumption, the MIMO capacity loss (due to noisy feedback) of the proposed robust design scales like ${cal O}(P_e2^{-{{C_{rm fb}}over{t+1}}})$ for some positive integer $t$. Hence, the penalty due to noisy limited feedback in the proposed robust design approaches zero as $C_{rm fb}$ increases.      

On Fast-Decodable Space–Time Block Codes

We focus on full-rate, fast-decodable space–time block codes (STBCs) for $2times2$ and $4times2$ multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable $2times2$ STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity $4times2$ STBC, and show that it outperforms all previously known codes with certain constellations.      

Properties and Applications of Preimage Distributions of Perfect Nonlinear Functions

The preimage distributions of perfect nonlinear functions from an Abelian group of order $n$ to an Abelian group of order $3$ or $4$, respectively, are studied. Based on the properties of the preimage distributions of perfect nonlinear functions from an Abelian group of order $3^{r}$ to an Abelian group of order $3$, the weight distributions of the ternary linear codes $C_{Pi}$ from the perfect nonlinear functions $Pi (x)$ from $F_{3^{r}}$ to itself are determined. These results suggest that two open problems, proposed by Carlet, Ding, and Yuan in 2005 and 2006, respectively, are answered.      

Lattices for Distributed Source Coding: Jointly Gaussian Sources and Reconstruction of a Linear Function

Consider a pair of correlated Gaussian sources $(X_1,X_2)$. Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear combination of $X_1$ and $X_2$ to within a mean-square distortion of $D$. We obtain an inner bound to the optimal rate–distortion region for this problem. A portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components $X_1$ and $X_2$ first. This results in a better rate region for certain parameter values. Our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory. We then consider the case of linear reconstruction of $K$ sources and provide an inner bound to the optimal rate–distortion region. Some parts of the inner bound are achieved using the following coding structure: lattice vector quantization followed by “correlated” lattice-structured binning.      

Logarithmic Sobolev Inequalities for Information Measures

For $alphageq 1$, the new Vajda-type information measure ${bf J}_{alpha}(X)$ is a quantity generalizing Fisher's information (FI), to which it is reduced for $alpha=2$ . In this paper, a corresponding generalized entropy power ${bf N}_{alpha}(X)$ is introduced, and the inequality ${bf N}_{alpha}(X) {bf J}_{alpha}(X)geq n$ is proved, which is reduced to the well-known inequality of Stam for $alpha=2$. The cases of equality are also determined. Furthermore, the Blachman–Stam inequality for the FI of convolutions is generalized for the Vajda information ${bf J}_{alpha}(X)$ and both families of results in the context of measure of information are discussed. That is, logarithmic Sobolev inequalities (LSIs) are written in terms of new more general entropy-type information measure, and therefore, new information inequalities are arisen. This generalization for special cases yields to the well known information measures and relative bounds.      

Sharp $p$ -Divisibility of Weights in Abelian Codes Over ${BBZ}/p^d{BBZ}$

A theorem of McEliece on the $p$-divisibility of Hamming weights in cyclic codes over ${BBF}_p$ is generalized to Abelian codes over ${{{BBZ}/p^d{BBZ}}}$. This work improves upon results of Helleseth–Kumar–Moreno–Shanbhag, Calderbank–Li–Poonen, Wilson, and Katz. These previous attempts are not sharp in general, i.e., do not report the full extent of the $p$ -divisibility except in special cases, nor do they give accounts of the precise circumstances under which they do provide best possible results. This paper provides sharp results on $p$-divisibilities of Hamming weights and counts of any particular symbol for an arbitrary Abelian code over ${{{BBZ}/p^d{BBZ}}}$. It also presents sharp results on $2$-divisibilities of Lee and Euclidean weights for Abelian codes over ${{{BBZ}/4{BBZ}}}$.      

Cyclic Codes and Sequences From Generalized Coulter–Matthews Function

In this paper, we will study the exponential sum $sum_{xin {BBF}_q}chi(alpha x^{(p^k+1)/2}+beta x)$ that is related to the generalized Coulter–Matthews function $x^{(p^k+1)/2}$ with $k/{rm gcd}(m,k)$ odd. As applications, we obtain the following: the correlation distribution of a $p$-ary $m$-sequence and a decimated $m$-sequence of degree ${p^k+1 over 2}$;      

Arsenic-Segregated Rare-Earth Silicide Junctions: Reduction of Schottky Barrier and Integration in Metallic n-MOSFETs on SOI

As an attempt to considerably reduce the equivalent contact resistivity of Schottky junctions, this letter studies the integration of rare-earth silicides, known to feature the lowest Schottky barriers (SBs) to electrons, coupled with a dopant segregation based on arsenic $(hbox{As}^{+})$ implantation. Both erbium (Er) and ytterbium (Yb) have been considered in the implant-before-silicide (IBS) and implant-to-silicide flavors. It is shown that the two schemes coupled with a limited thermal budget (500 $^{circ}hbox{C}$) produce an SB below the target of 0.1 eV. The implementation of IBS arsenic-segregated $hbox{YbSi}_{1.8}$ junctions in an n-type SB-MOSFET is demonstrated for the first time resulting in a current-drive improvement of more than one decade over the dopant-free counterpart.      

A 5-GHz Wireless LAN Transmitter with Integrated Tunable High-Q RF Filter

A tunable, high-$Q$ RF filter suitable for wireless transmitters has been implemented in a standard digital 0.18-$muhbox{m}$ CMOS technology. Active circuits are used to enhance the $Q$ of two independent LC resonators, which are cascaded to form a wide bandwidth filter that can be tuned in both center frequency and bandwidth. A 5.145-GHz stagger-tuned filter with a 200-MHz bandwidth and 0.8 dB of ripple is demonstrated in an 802.11a sliding-IF transmitter. The transmitter provides spectral mask and EVM-compliant output power of $-$8.26 dBm for a 64-QAM OFDM signal. At lower output power, an EVM of $-$ 32.3 dB is achieved.      

Performance Analysis and Design Criteria of BICM-ID With Signal Space Diversity for Keyhole Nakagami-$m$ Fading Channels

This paper generalizes the application bit-interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) over keyhole Nakagami-$m$ fading channels. The tight union bound on the asymptotic error performance is first analytically derived. The near-optimal rotation matrix with respect to both the asymptotic performance and the convergence behavior is then determined. In particular, it is demonstrated that the suitable rotation matrix is the one that has 1) all entries equal in magnitude, 2) a high diversity order, and 3) a large minimum product of the ratios between squared distances to the power $m$ and log-squared distances to the power $m$ of the rotated constellation scaled by factors of signal-to-noise ratio (SNR) and the parameter $m$ . Various analytical and simulation results show that by employing SSD with a sufficiently large dimension, the error performance can closely approach that over an additive white Gaussian noise (AWGN) channel, even in the worst case of keyhole fading.      

Universal FIR MMSE Filtering

We consider the problem of causal estimation, i.e., filtering, of a real-valued signal corrupted by zero mean, time-independent, real-valued additive noise, under the mean-squared error (MSE) criterion. We build a universal filter whose per-symbol squared error, for every bounded underlying signal, is essentially as small as that of the best finite-duration impulse response (FIR) filter of a given order. We do not assume a stochastic mechanism generating the underlying signal, and assume only that the variance of the noise is known to the filter. The regret of the expected MSE of our scheme is shown to decay as $O(log n/n)$, where $n$ is the length of the signal. Moreover, we present a stronger concentration result which guarantees the performance of our scheme not only in expectation, but also with high probability. Our result implies a conventional stochastic setting result, i.e., when the underlying signal is a stationary process, our filter achieves the performance of the optimal FIR filter. We back our theoretical findings with several experiments showcasing the potential merits of our universal filter in practice. Our analysis combines tools from the problems of universal filtering and competitive on-line regression.