Currently there has been increasing demand for real-time training on resource-limited IoT devices such as smart sensors, which realizes standalone online adaptation for streaming data without data transfers to remote servers. OS-ELM (Online Sequential Extreme Learning Machine) has been one of promising neural-network-based online algorithms for on-chip learning because it can perform online training at low computational cost and is easy to implement as a digital circuit. Existing OS-ELM digital circuits employ fixed-point data format and the bit-widths are often manually tuned, however, this may cause overflow or underflow which can lead to unexpected behavior of the circuit. For on-chip learning systems, an overflow/underflow-free design has a great impact since online training is continuously performed and the intervals of intermediate variables will dynamically change as time goes by. In this paper, we propose an overflow/underflow-free bit-width optimization method for fixed-point digital circuits of OS-ELM. Experimental results show that our method realizes overflow/underflow-free OS-ELM digital circuits with 1.0x - 1.5x more area cost compared to the baseline simulation method where overflow or underflow can happen.

In this paper, the hardware architecture of a CORDIC-based Arithmetic Processor utilizing both angle recoding (ARD) CORDIC algorithm and scaling-free (SCFE) CORDIC algorithm is proposed and implemented in 180 nm CMOS technology. The arithmetic processor is capable of calculating the sine, cosine, sine hyperbolic, cosine hyperbolic, and multiplication function. The experimental results prove that the design is able to work at 100 MHz frequency and requires 12.96 mW power consumption. In comparison with some previous work, the design can be seen as a good choice for high-throughput low-energy applications.

This paper proposes a new quantization framework on activation function of deep neural networks (DNN). We implement fixed-point DNN by quantizing the activations into powers-of-two integers. The costly multiplication operations in using DNN can be replaced with low-cost bit-shifts to massively save computations. Thus, applying DNN-based speech recognition on embedded systems becomes much easier. Experiments show that the proposed method leads to no performance degradation.

A global tone mapping operation (TMO) for high dynamic range (HDR) images with fixed-point arithmetic is proposed and evaluated in this paper. A TMO generates a low dynamic range (LDR) image from an HDR image by compressing its dynamic range. Since an HDR image is generally expressed in a floating-point data format, a TMO also deals with floating-point data even though a resultant LDR image is integer data. The proposed method treats a floating-point number as two 8-bit integer numbers which correspond to an exponent part and a mantissa part, and applies tone mapping to these integer numbers separately. Moreover, the method conducts all calculations in the tone mapping with only fixed-point arithmetic. As a result, the method reduces a memory cost and a computational cost. The evaluation shows that the proposed method reduces 81.25% of memory usage. The experimental results show that the processing speed of the proposed method with fixed-point arithmetic is 23.1 times faster than the conventional method with floating-point arithmetic. Furthermore, they also show the PSNR of LDR images obtained by the proposed method are comparable to those of the conventional method, though reducing computational and memory cost.

In this paper, we proposed that an area- and speed-effective fixed-point pipelined divider be used for reducing the bit-width of a division unit to fit a mobile rendering processor. To decide the bit-width of a division unit, error analysis has been carried out in various ways. As a result, when the original bit-width was 31-bit, the proposed method reduced the bit-width to 24-bit and reduced the area by 42% with a maximum error of 0.00001%.

We propose a feasible V-BLAST detector based on modified Householder QRD (M-H-QRD) over spatially correlated fading channel, which can almost match the performance of the V-BLAST algorithm with much lower complexity and better numerical stability. Compared to the sorted QRD (S-QRD) detector, the proposed detector requires a smaller minimum word-length to reach the same value of error floor for fixed-point (FP) numerical precision despite no significant performance difference for floating-point machine precision. All these advantages make it attractive when implemented using FP arithmetic.

Permutation ambiguity of the classical Independent Component Analysis (ICA) may cause problems in feature extraction for pattern classification. Especially when only a small subset of components is derived from data, these components may not be most distinctive for classification, because ICA is an unsupervised method. We include a selective prior for de-mixing coefficients into the classical ICA to alleviate the problem. Since the prior is constructed upon the classification information from the training data, we refer to the proposed ICA model with a selective prior as a supervised ICA (sICA). We formulated the learning rule for sICA by taking a Maximum a Posteriori (MAP) scheme and further derived a fixed point algorithm for learning the de-mixing matrix. We investigate the performance of sICA in facial expression recognition from the aspects of both correct rate of recognition and robustness even with few independent components.

In this paper, a novel independent component analysis (ICA) approach is proposed, which is robust against the interference of impulse noise. To implement ICA in a noisy environment is a difficult problem, in which traditional ICA may lead to poor results. We propose a method that consists of noise detection and image signal recovery. The proposed approach includes two procedures. In the first procedure, we introduce a self-organizing map (SOM) network to determine if the observed image pixels are corrupted by noise. We will mark each pixel to distinguish normal and corrupted ones. In the second procedure, we use one of two traditional ICA algorithms (fixed-point algorithm and Gaussian moments-based fixed-point algorithm) to separate the images. The fixed-point algorithm is proposed for general ICA model in which there is no noise interference. The Gaussian moments-based fixed-point algorithm is robust to noise interference. Therefore, according to the mark of image pixel, we choose the fixed-point or the Gaussian moments-based fixed-point algorithm to update the separation matrix. The proposed approach has the capacity not only to recover the mixed images, but also to reduce noise from observed images. The simulation results and analysis show that the proposed approach is suitable for practical unsupervised separation problem.

In this paper, we present an efficient downlink power control scheme, for wireless networks, based on two key ideas: (i) global-local fixed-point-approximation technique (GLOFPAT) and (ii) bottleneck removal criterion (BRC). The proposed scheme copes with all scenarios including infeasible case where no power allocation can provide all multiple accessing users with target quality of service (QoS). For feasible case, the GLOFPAT efficiently computes a desired power allocation which corresponds to the allocation achieved by conventional algorithms. For infeasible case, the GLOFPAT offers valuable information to detect bottleneck users, to be removed based on the BRC, which deteriorate overall QoS. The GLOFPAT is a mathematically-sound distributed algorithm approximating desired power allocation as a unique fixed-point of an isotone mapping. The unique fixed-point of the global mapping is iteratively computed by fixed-point-approximations of multiple distributed local mappings, which can be computed in parallel by base stations respectively. For proper detection of bottleneck users, complete analysis of the GLOFPAT is presented with aid of the Tarski's fixed-point theorem. Extensive simulations demonstrate that the proposed scheme converges faster than the conventional algorithm and successfully increases the number of happy users receiving target QoS.

This paper treats the least-squares linear filtering and smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables. Using an innovation approach we obtain the filtering algorithm and a general expression for the smoother which leads to fixed-point, fixed-interval and fixed-lag smoothing recursive algorithms. The proposed algorithms do not require the knowledge of the state-space model generating the signal, but only the covariance information of the signal and the observation noise, as well as the probability that the signal exists in the observed values.

This article presents a three-step method for designing linear phase FIR filters with signed-powers-of-two (SPT) coefficients. In Step one, a prototype optimal FIR filter is designed by the Remez exchange algorithm. In Step two, a scaling factor is selected by employing simple ad-hoc rules. In Step three, each coefficient of the prototype filter is scaled by the scaling factor and is quantized coarsely as the canonic-signed-digit (CSD) representation. Then, a mixed-integer-linear-programming (MILP) algorithm is applied to three least significant digits (LSDs) of the filter's coefficients to reduce the number of SPT terms. Design examples demonstrate that the proposed algorithm is able to produce linear phase fixed-point FIR filters using fewer SPT terms than the existing methods under the same normalized peak ripple magnitude (NPRM) specification.

This paper proposes new recursive fixed-point smoother and filter using covariance information in linear discrete-time stochastic systems. In this paper, to be able to treat the estimation of the stochastic signal, a performance criterion, extended from the criterion in the H estimation problem, is newly proposed. The criterion is transformed equivalently into a min-max principle in game theory, and an observation equation in a Krein space is obtained as a result. The estimation accuracy of the proposed estimators are compared with the recursive least-squares (RLS) Wiener estimators, the Kalman filter and the fixed-point smoother based on the state-space model.

Finding DC operating-points of nonlinear circuits is an important and difficult task. The Newton-Raphson method employed in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. The fixed-point homotopy method is one of the excellent methods. However, from the viewpoint of implementation, it is important to study it further so that the method can be easily and widely used by many circuit designers. This paper presents a practical method to implement the fixed-point homotopy method. A special circuit called the solution-tracing circuit for the fixed-point homotopy method is proposed. By using this circuit, the solution curves of homotopy equations can be traced by performing the SPICE transient analysis. Therefore, no modification to the existing programs is necessary. Moreover, it is proved that the proposed method is globally convergent. Numerical examples show that the proposed technique is effective and can be easily implemented. By the proposed technique, many SPICE users can easily implement the fixed-point homotopy method.

This paper proposes new recursive fixed-point smoother and filter using covariance information in linear continuous-time stochastic systems. To be able to treat the stochastic signal estimation problem, a performance criterion, extended from the criterion in the H filtering problem by introducing the stochastic expectation, is newly introduced in this paper. The criterion is transformed equivalently into a min-max principle in game theory, and an observation equation in the Krein spaces is obtained as a result. For γ2<, the estimation accuracies of the fixed-point smoother and the filter are superior to the recursive least-squares (RLS) Wiener estimators previously designed in the transient estimation state. Here, γ represents a parameter in the proposed criterion. This paper also presents the fixed-point smoother and the filter using the state-space parameters from the devised estimators using the covariance information.

In this paper, we shall construct mathematical theory based on the concept of set-valued mappings, suitable for available operation of network systems extraordinarily complicated and diversified on large scales. Fundamental conditions for availability of system behaviors of such network systems are clarified in a form of fixed point theorem for system of set-valued mappings.

This paper proposes a private communication system with chaos using fixed-point digital computation. When fixed-point computation is adopted, chaotic properties of the modulated signal should be checked carefully as well as calculation error problems (especially, overflow problems). In this paper, we propose a novel chaos modem system for private communications including a chaotic neuron type nonlinearity, an unstable digital filter and an overflow function. We demonstrate that the modulated signal reveals hyperchaotic property within 10,000 data point fixed-point computation, and evaluate the security of this system in view of the sensitivity of coefficients for demodulation.

This paper describes a new design method for multiply-adders able to process a large quantity of multimedia data. I propose a (signed digits)(unsigned digits) fixed-point multiply-add/subtract unit. The unit eliminates the problems caused by the critical one-bit arithmetic precision drop-off peculiar to the conventional (signed digits)(signed digits) fixed-point multiply scheme. By simultaneously counting in the carry-save form, based on 7-3 counters simultaneously inputting the accumulation terms and the add/sub operation terms of multiplication results, carries are propagated faster than in the conventional method.

This paper proposes a new design method of nonlinear filtering and fixed-point smoothing algorithms in discrete-time stochastic systems. The observed value consists of nonlinearly modulated signal and additive white Gaussian observation noise. The filtering and fixed-point smoothing algorithms are designed based on the same idea as the extended Kalman filter derived based on the recursive least-squares Kalman filter in linear discrete-time stochastic systems. The proposed filter and fixed-point smoother necessitate the information of the autocovariance function of the signal, the variance of the observation noise, the nonlinear observation function and its differentiated one with respect to the signal. The estimation accuracy of the proposed extended filter is compared with the extended maximum a posteriori (MAP) filter theoretically. Also, the current estimators are compared in estimation accuracy with the extended MAP estimators, the extended Kalman estimators and the Kalman neuro computing method numerically.