Unary Encoding Research Articles

Optimal Trading Mechanism Based on Differential Privacy Protection and Stackelberg Game in Big Data Market

Big data has become a fundamental resource and a commodity in economic activities, thus, it is necessary to build a market model capable of supporting efficient data trading. However, two major challenges remain. Firstly, researches have considered constructing data trading mechanisms, while few of them are based on the method of measuring data value in multiple dimensions. Secondly, a data market involved an intermediary trading platform (i.e., a third party) which is honest but curious, results may be obtained due the the leakage of private information. In this paper, we design TM-OUE, a data trading mechanism based on Optimized Unary Encoding that enables reasonable trading mechanism and protects the privacy of data trading. First of all, we combine qualitative and quantitative methods to measure the value of data in multiple dimensions and formulate data trading model between the data provider and data users. Then, we utilize an Optimized Unary Encoding (OUE) protocol to protect the privacy of the data trading mechanism. Based on the above steps, we develop a two-stage single leader multi-follower Stackelberg game to jointly maximize profits of the data provider and data users. Experimental results demonstrate that TM-OUE can offer appropriate price for data and maximize benefits both for data providers and data users, which guarantees fair data trades while protecting privacy.

Efficient quantum simulation of electron-phonon systems by variational basis state encoder

Digital quantum simulation of electron-phonon systems requires truncating infinite phonon levels into $N$ basis states and then encoding them with qubit computational basis. Unary encoding and binary encoding are the two most representative encoding schemes, which demand $O(N)$ and $O(logN)$ qubits as well as $O(N)$ and $O(NlogN)$ quantum gates, respectively. In this paper, we propose a variational basis state encoding algorithm that reduces the scaling of the number of qubits and quantum gates to both $O(1)$ for systems obeying the area law of entanglement entropy. The cost for the scaling reduction is a constant amount of additional measurement. The accuracy and efficiency of the approach are verified by both numerical simulation and realistic quantum hardware experiments. In particular, we find using one or two qubits for each phonon mode is sufficient to produce quantitatively correct results across weak and strong coupling regimes. Our approach paves the way for practical quantum simulation of electron-phonon systems on both near-term hardware and error-corrected quantum computers.

Binary operations on neuromorphic hardware with application to linear algebraic operations and stochastic equations

Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses—so-called neuromorphic systems—is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement operations. We use the mechanisms to construct a neuromorphic, binary matrix multiplication algorithm that may be used as a primitive for linear differential equation integration, deep networks, and other standard calculations. We also construct a random walk circuit and apply it in Brownian motion simulations. We study how both algorithms scale in circuit size and iteration time.

On the Risks of Collecting Multidimensional Data Under Local Differential Privacy

The private collection of multiple statistics from a population is a fundamental statistical problem. One possible approach to realize this is to rely on the local model of differential privacy (LDP). Numerous LDP protocols have been developed for the task of frequency estimation of single and multiple attributes. These studies mainly focused on improving the utility of the algorithms to ensure the server performs the estimations accurately. In this paper, we investigate privacy threats (re-identification and attribute inference attacks) against LDP protocols for multidimensional data following two state-of-the-art solutions for frequency estimation of multiple attributes. To broaden the scope of our study, we have also experimentally assessed five widely used LDP protocols, namely, generalized randomized response, optimal local hashing, subset selection, RAPPOR and optimal unary encoding. Finally, we also proposed a countermeasure that improves both utility and robustness against the identified threats. Our contributions can help practitioners aiming to collect users' statistics privately to decide which LDP mechanism best fits their needs.

Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates

This paper investigates the problem of collecting multidimensional data throughout time (i.e., longitudinal studies) for the fundamental task of frequency estimation under Local Differential Privacy (LDP) guarantees. Contrary to frequency estimation of a single attribute, the multidimensional aspect demands particular attention to the privacy budget. Besides, when collecting user statistics longitudinally, privacy progressively degrades. Indeed, the “multiple” settings in combination (i.e., many attributes and several collections throughout time) impose several challenges, for which this paper proposes the first solution for frequency estimates under LDP. To tackle these issues, we extend the analysis of three state-of-the-art LDP protocols (Generalized Randomized Response – GRR, Optimized Unary Encoding – OUE, and Symmetric Unary Encoding – SUE) for both longitudinal and multidimensional data collections. While the known literature uses OUE and SUE for two rounds of sanitization (a.k.a. memoization), i.e., L-OUE and L-SUE, respectively, we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility (i.e., L-OSUE). Also, for attributes with small domain sizes, we propose Longitudinal GRR (L-GRR), which provides higher utility than the other protocols based on unary encoding. Last, we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates (ALLOMFREE), which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol, i.e., either L-GRR or L-OSUE. As shown in the results, ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.

Local Information Privacy and Its Application to Privacy-Preserving Data Aggregation

In this article, we propose local information privacy (LIP), and design LIP based mechanisms for statistical aggregation while protecting users’ privacy without relying on a trusted third party. The concept of context-awareness is incorporated in LIP, which can be viewed as exploiting of data prior (both in privatizing and post-processing) to enhance data utility. We present an optimization framework to minimize the mean square error of data aggregation while protecting the privacy of each user’s input data or a correlated latent variable by satisfying LIP constraints. Then, we study optimal mechanisms under different scenarios considering the prior uncertainty and correlation with a latent variable. Three types of mechanisms are studied in this article, including randomized response (RR), unary encoding (UE), and local hashing (LH), and we derive closed-form solutions for the optimal perturbation parameters that are prior-dependent. We compare LIP-based mechanisms with those based on LDP, and theoretically show that the former achieve enhanced utility. We then study two applications: (weighted) summation and histogram estimation, and show how proposed mechanisms can be applied to each application. Finally, we validate our analysis by simulations using both synthetic and real-world data. Results show the impact on data utility by different prior distributions, correlations, and input domain sizes. Results also show that our LIP-based mechanisms provide better utility-privacy tradeoffs than LDP-based ones.

TPE-GAN: Thumbnail Preserving Encryption Based on GAN With Key

To balance the privacy and usability of images in the cloud, Tajik <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> recently designed a thumbnail preserving encryption (TPE) based on sum-preserving encryption, however, multiple iterations make it inefficient. We use CycleGan to simulate randomized unary encoding (RUE) and achieve a more efficient TPE. Thumbnail consistency loss is proposed to guarantee the visual quality of the encrypted image, and the quality of decrypted image is improved via ssim-loss. Besides, a decryption network with a key is retrained such that it can decrypt cipher images in multiple domains, and a binary string is adopted as the key instead of the decryption network parameters to facilitate sharing of images. Simulations verify the effectiveness of the proposed algorithm.

On the implementation of a global optimization method for mixed-variable problems

We describe the optimization algorithm implemented in the open-source derivative-free solver RBFOpt. The algorithm is based on the radial basis function method of Gutmann and the metric stochastic response surface method of Regis and Shoemaker. We propose several modifications aimed at generalizing and improving these two algorithms: (i) the use of an extended space to represent categorical variables in unary encoding; (ii) a refinement phase to locally improve a candidate solution; (iii) interpolation models without the unisolvence condition, to both help deal with categorical variables, and initiate the optimization before a uniquely determined model is possible; (iv) a master-worker framework to allow asynchronous objective function evaluations in parallel. Numerical experiments show the effectiveness of these ideas.

PLDP: Personalized Local Differential Privacy for Multidimensional Data Aggregation

The collection of multidimensional crowdsourced data has caused a public concern because of the privacy issues. To address it, local differential privacy (LDP) is proposed to protect the crowdsourced data without much loss of usage, which is popularly used in practice. However, the existing LDP protocols ignore users’ personal privacy requirements in spite of offering good utility for multidimensional crowdsourced data. In this paper, we consider the personality of data owners in protection and utilization of their multidimensional data by introducing the notion of personalized LDP (PLDP). Specifically, we design personalized multiple optimized unary encoding (PMOUE) to perturb data owners’ data, which satisfies ϵ total -PLDP. Then, the aggregation algorithm for frequency estimation on multidimensional data under PLDP is developed, which is described in two situations. Experiments are conducted on four real datasets, and the results show that the proposed aggregation algorithm yields high utility. Moreover, case studies with four real datasets demonstrate the efficiency and superiority of the proposed scheme.

Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

The differences in performance among binary-integer encodings in an Ising machine, which can solve combinatorial optimization problems, are investigated. Many combinatorial optimization problems can be mapped to find the lowest-energy (ground) state of an Ising model or its equivalent model, the Quadratic Unconstrained Binary Optimization (QUBO). Since the Ising model and QUBO consist of binary variables, they often express integers as binary when using Ising machines. A typical example is the combinatorial optimization problem under inequality constraints. Here, the quadratic knapsack problem is adopted as a prototypical problem with an inequality constraint. It is solved using typical binary-integer encodings: one-hot encoding, binary encoding, and unary encoding. Unary encoding shows the best performance for large-sized problems.

Hybrid Binary-Unary Hardware Accelerator

Stream-based computing such as stochastic computing has been used in recent years to create designs with significantly smaller area by harnessing unary encoding of data. However, the area saving comes at an exponential price in latency, making the area × delay cost unattractive. In this article, we present a novel method which uses a hybrid binary / unary representation to perform computations. We first divide the input range into a few sub-regions, perform unary computations on each sub-region individually, and finally pack the outputs of all sub-regions back to compact binary. Moreover, we propose a synthesis methodology and a regression model to predict an optimal or close-to-optimal design in the design space. To the best of our knowledge, we are the first to show a scalable method based on parallel bit-stream data representation that can beat conventional binary in terms of a real cost, i.e., area × delay and energy consumption in almost all functions that we tried at resolutions of 8-, 10-, and 12-bits. Our method outperforms the binary, stochastic, and fully unary methods on a number of functions, especially low-cost binary CORDIC-based functions, and on a common edge detection algorithm on FPGA and in ASIC implementation. In terms of area × delay cost, our {on FPGA, in ASIC} cost is on average only { $4.72\%$ 4 . 72 % , $24.36\%$ 24 . 36 % } and { $20.16\%$ 20 . 16 % , $60.12\%$ 60 . 12 % } of the parallel binary pipeline implementation at 8- and 10-bit resolution, respectively. These numbers are 2–3 orders of magnitude better than the results of traditional stochastic methods. Our method is not competitive with the parallel CORDIC-based pipeline binary method for high-resolution (12-bit), highly oscillating functions such as $\sin (15 x)$ sin ( 15 x ) . However, for complex functions like $gamma$ g a m m a function, the proposed method can beat any other methods in terms of area × delay, throughput, latency, and energy per sample costs. To implement the Roberts cross edge detection algorithm, the proposed method takes 5.7 and 39.45 percent of the area × delay cost of FPGA and ASIC implementation of the binary method, respectively. In terms of energy efficiency for FPGA implementation, our method uses only 8.4, 12.7, and 27.7 percent of the energy per sample usage of serial binary implementations at 8-, 10-, and 12-bit resolutions, respectively. These numbers change to 23.9, 38.54, and 99.3 percent compared to parallel binary implementations.

Complexity of planning for connected agents

We study a variant of the multi-agent path finding (MAPF) problem in which the group of agents are required to stay connected with a supervising base station throughout the execution. In addition, we consider the problem of covering an area with the same connectivity constraint. We show that both problems are PSPACE-complete on directed and undirected topological graphs while checking the existence of a bounded plan is NP-complete when the bound is given in unary (and PSPACE-hard when the encoding is in binary). Moreover, we identify a realistic class of topological graphs on which the decision problem falls in NLOGSPACE although the bounded versions remain NP-complete for unary encoding.

Two-Way Automata Characterizations of L/poly Versus NL

Let L/p o l y and N L be the standard complexity classes, of languages recognizable in logarithmic space by Turing machines which are deterministic with polynomially-long advice and nondeterministic without advice, respectively. We recast the question whether L / poly ? NL $\mathsf {L}/\mathsf {poly}~{\supseteq }~{\mathsf {NL}}$ in terms of deterministic and nondeterministic two-way finite automata (2dfas and 2nfas). We prove it equivalent to the question whether every s-state unary 2nfa has an equivalent poly(s)-state 2dfa, or whether a poly(h)-state 2dfa can check accessibility in h-vertex graphs (even under unary encoding) or check two-way liveness in h-tall, h-column graphs. This complements two recent improvements of an old theorem of Berman and Lingas. On the way, we introduce new types of reductions between regular languages (even unary ones), use them to prove the completeness of specific languages for two-way nondeterministic polynomial size, and propose a purely combinatorial conjecturethat implies L / poly ?? NL $\mathsf {L}/\mathsf {poly}~{\nsupseteq }~\mathsf {NL}$ .

Design of a lossless image compression system for video capsule endoscopy and its performance in in-vivo trials.

In this paper, a new low complexity and lossless image compression system for capsule endoscopy (CE) is presented. The compressor consists of a low-cost YEF color space converter and variable-length predictive with a combination of Golomb-Rice and unary encoding. All these components have been heavily optimized for low-power and low-cost and lossless in nature. As a result, the entire compression system does not incur any loss of image information. Unlike transform based algorithms, the compressor can be interfaced with commercial image sensors which send pixel data in raster-scan fashion that eliminates the need of having large buffer memory. The compression algorithm is capable to work with white light imaging (WLI) and narrow band imaging (NBI) with average compression ratio of 78% and 84% respectively. Finally, a complete capsule endoscopy system is developed on a single, low-power, 65-nm field programmable gate arrays (FPGA) chip. The prototype is developed using circular PCBs having a diameter of 16 mm. Several in-vivo and ex-vivo trials using pig's intestine have been conducted using the prototype to validate the performance of the proposed lossless compression algorithm. The results show that, compared with all other existing works, the proposed algorithm offers a solution to wireless capsule endoscopy with lossless and yet acceptable level of compression.

Bin packing with fixed number of bins revisited

As Bin Packing is NP-hard already for k=2 bins, it is unlikely to be solvable in polynomial time even if the number of bins is a fixed constant. However, if the sizes of the items are polynomially bounded integers, then the problem can be solved in time nO(k) for an input of length n by dynamic programming. We show, by proving the W[1]-hardness of Unary Bin Packing (where the sizes are given in unary encoding), that this running time cannot be improved to f(k)⋅nO(1) for any function f(k) (under standard complexity assumptions). On the other hand, we provide an algorithm for Bin Packing that obtains in time 2O(klog2k)+O(n) a solution with additive error at most 1, i.e., either finds a packing into k+1 bins or decides that k bins do not suffice.

Lossless and Low-Power Image Compressor for Wireless Capsule Endoscopy

We present a lossless and low-complexity image compression algorithm for endoscopic images. The algorithm consists of a static prediction scheme and a combination of golomb-rice and unary encoding. It does not require any buffer memory and is suitable to work with any commercial low-power image sensors that output image pixels in raster-scan fashion. The proposed lossless algorithm has compression ratio of approximately 73% for endoscopic images. Compared to the existing lossless compression standard such as JPEG-LS, the proposed scheme has better compression ratio, lower computational complexity, and lesser memory requirement. The algorithm is implemented in a 0.18 μm CMOS technology and consumes 0.16 mm × 0.16 mm silicon area and 18 μW of power when working at 2 frames per second.

Batching in a two-stage flowshop with dedicated machines in the second stage

The problem of batching and scheduling n identical jobs of F, F ≥ 2, part types in a shop made up of F+1 machines is studied. The processing of each job comprises two stages. The first stage is undertaken on the machine common to all jobs and the second stage is undertaken on the machine specific to a particular part type. Setup times are necessary at the first stage to switch processing from a job of one part type to a job of another part type. Jobs of the same part type processed contiguously at the first stage form a batch. The objective is to find a batch schedule minimizing makespan. We show that this problem is equivalent to a special case of a single machine family scheduling problem to minimize maximum lateness and therefore it can be solved in O(n F ) time by a known algorithm. Furthermore, for the case where F = 2, we present an iterative exact algorithm with O(k 0log L) running time, where k 0 is the maximum number of batches in a schedule created in any iteration of the algorithm and L is the problem input length in unary encoding. The algorithm finds a schedule with the minimum number of batches k* in any optimal solution. Computational experiments were conducted to investigate the relationship between k* and k 0. For all tested examples, k 0 = max {k*1,k*2}, where k*1 (k*2) was the minimum number of batches in any optimal schedule starting with a batch of one part type (the other part type).

Kerneltron: support vector "machine" in silicon

Detection of complex objects in streaming video poses two fundamental challenges: training from sparse data with proper generalization across variations in the object class and the environment; and the computational power required of the trained classifier running real-time. The Kerneltron supports the generalization performance of a support vector machine (SVM) and offers the bandwidth and efficiency of a massively parallel architecture. The mixed-signal very large-scale integration (VLSI) processor is dedicated to the most intensive of SVM operations: evaluating a kernel over large numbers of vectors in high dimensions. At the core of the Kerneltron is an internally analog, fine-grain computational array performing externally digital inner-products between an incoming vector and each of the stored support vectors. The three-transistor unit cell in the array combines single-bit dynamic storage, binary multiplication, and zero-latency analog accumulation. Precise digital outputs are obtained through oversampled quantization of the analog array outputs combined with bit-serial unary encoding of the digital inputs. The 256 input, 128 vector Kerneltron measures 3 mm/spl times/3mm in 0.5 /spl mu/m CMOS, delivers 6.5 GMACS throughput at 5.9 mW power, and attains 8-bit output resolution.

Input compression and efficient VLSI architectures for rank order and stack filters

Rank-order-based filters include rank-order filters, stack filters, and weighted order statistic filters. The output of a rank-order-based filter is always one of the sample points in its input window; which one is chosen depends only upon the ranks and positions of the samples within the window. This paper introduces new architectures for rank-order-based filters. They all achieve fast, efficient operation by exploiting an algorithm called input compression. Under this algorithm, the sample points in the input window are first mapped to their relative ranks — the sample points in a window of size N + 1 would thus be mapped to the integers 0− N. The rank-order-based filter to be implemented is then applied directly to this compressed input, and the rank chosen is then mapped back to the sample of that rank in the original data to obtain the final output. This approach has been used to implement rank-order filters, in which case the same rank is always chosen from the compressed data. In this paper, which rank is chosen also depends on the positions of the ranks in the compressed data. Implementations employing input compression have several advantages. They are computationally efficient like running order sorters, yet can be pipelined to a fine degree like sorting networks. In stack filter implementations, the threshold decomposition circuitry can be eliminated when input compression is combined with unary encoding of the ranks. Weighted order statistic filter implementations based on input compression can support programmable, noninteger weights.

Deterministic two-way one-head pushdown automata are very powerful

We show that if a language over a two-letter alphabet belongs to P , then its unary encoding belongs to 2DPDA(1).