Small Number Of Bits Research Articles

Outage reduction in cooperative networks with limited feedback

In this paper, we propose a limited feedback scheme to improve outage performance for a wireless cooperative decode-and-forward network. Specifically, based on the instantaneous conditions of the source-destination and relay-destination channels, the destination will allocate the transmission time of the source and relay and feed back the allocation result to the source. Both limited and full (or infinite) rate feedback are considered. Under the practical assumption that only imperfect channel estimation is available at the receiver, we analyze the outage performance by deriving upper bounds on the outage probabilities. It will be demonstrated that, even with only one-bit feedback, the proposed feedback scheme can outperform the no feedback case. Furthermore, the outage performance can approach the optimality by exploiting limited (only a small number of bits) uniformly quantized feedback from the destination.

Tight bounds for clock synchronization

We present a novel clock synchronization algorithm and prove tight upper and lower bounds on the worst-case clock skew that may occur between any two participants in any given distributed system. More importantly, the worst-case clock skew between neighboring nodes is (asymptotically) at most a factor of two larger than the best possible bound. While previous results solely focused on the dependency of the skew bounds on the network diameter, we prove that our techniques are optimal also with respect to the maximum clock drift, the uncertainty in message delays, and the imposed bounds on the clock rates. The presented results all hold in a general model where both the clock drifts and the message delays may vary arbitrarily within pre-specified bounds. Furthermore, our algorithm exhibits a number of other highly desirable properties. First, the algorithm ensures that the clock values remain in an affine linear envelope of real time. A better worst-case bound on the accuracy with respect to real time cannot be achieved in the absence of an external timer. Second, the algorithm minimizes the number and size of messages that need to be exchanged in a given time period. Moreover, only a small number of bits must be stored locally for each neighbor. Finally, our algorithm can easily be adapted for a variety of other prominent synchronization models.

Evolved transforms improve image compression

Many image processing applications, including JPEG20001 and fingerprint compression,2 use wavelets. By redistributing an image’s energy into a set of lower-resolution trend subimages, discrete wavelet transforms (DWTs) can significantly reduce the number of bits required for representation. Quantization (approximating a signal with a smaller number of bits) and thresholding (setting all but the largest transform values to zero) may achieve additional compression. However, these techniques introduce irreversible information loss, since the mean squared error (MSE) of reconstructed images increases proportionately with both techniques. One approach that may circumvent this problem is evolutionary computation (EC), which uses fitness-based selection and genetics-inspired operators to evolve solutions to a combinatorial optimization task. Yet very few researchers have applied this technique to the wavelet domain. Grasemann and Mikkulainen3 combined a genetic algorithm (GA) with a lifting scheme, a methodology for synthesizing new perfect reconstruction wavelets from an existing wavelet filter. This method improved performance for specific classes of images.3 Unlike their technique, however, our GA imposes none of the mathematical properties required of wavelets, such as conservation of energy. Since 2004, our team has used EC to evolve transforms that outperform wavelets for many compression and reconstruction tasks involving quantization and thresholding. Each run creates an initial population by randomly mutating the wavelet and scaling numbers of a selected wavelet’s forward and inverse transforms. Candidate solutions compress and subsequently reconstruct images from a training population. Each candidate’s fitness reflects two parameters: the compressed image size, and the reconstructed one’s MSE. The best individual is copied into a new generation, which is otherwise populated by combining fitness-driven selection with specialized mutation and crossover Figure 1. A typical satellite image.

An Efficient Unknown Blocking Scheme for Low Control Data Volume and High Observability

This paper presents an efficient method to block unknowns for temporal compactors. The proposed blocking logic can reduce data volume required to control the blocking logic and increase the number of scan cells that are observed by temporal compactors. Control patterns, which specify values required at the control signals of the blocking logic, are compressed by linear feedback shift register reseeding. In this paper, the blocking logic gates for some scan chains that do not capture unknowns are bypassed. Since all scan cells in these scan chains can be observed without specifying the corresponding bits in control patterns, more scan cells are observed while a smaller number of bits are required to be specified. The seed size is further reduced by reducing the numbers of specified bits in the densely specified control patterns. The proposed method can always achieve the same fault coverage that can be achieved by directly observing scan chains without any output compaction. Experiments with large industrial designs clearly demonstrate that the proposed method is scalable to large circuits. Hardware overhead for the proposed unknown blocking scheme is very low.

Graph searching with advice

Fraigniaud et al. [L. Blin, P. Fraigniaud, N. Nisse, S. Vial, Distributing chasing of network intruders, in: 13th Colloquium on Structural Information and Communication Complexity, SIROCCO, in: LNCS, vol. 4056, Springer-Verlag, 2006, pp. 70–84] introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper deals with the number of bits of advice required to perform efficiently the graph searching problem in a distributed setting. In this variant of the problem, all searchers are initially placed at a particular node of the network. The aim of the team of searchers is to clear a contaminated graph in a monotone connected way, i.e., the cleared part of the graph is permanently connected, and never decreases while the search strategy is executed. Moreover, the clearing of the graph must be performed using the optimal number of searchers, i.e. the minimum number of searchers sufficient to clear the graph in a monotone connected way in a centralized setting. We show that the minimum number of bits of advice permitting the monotone connected and optimal clearing of a network in a distributed setting is Θ ( n log n ) , where n is the number of nodes of the network. More precisely, we first provide a labelling of the vertices of any graph G , using a total of O ( n log n ) bits, and a protocol using this labelling that enables the optimal number of searchers to clear G in a monotone connected distributed way. Then, we show that this number of bits of advice is optimal: any distributed protocol requires Ω ( n log n ) bits of advice to clear a network in a monotone connected way, using an optimal number of searchers.

Speeding Up Chemical Database Searches Using a Proximity Filter Based on the Logical Exclusive OR

In many large chemoinformatics database systems, molecules are represented by long binary fingerprint vectors whose components record the presence or absence in the molecular graphs of particular functional groups or combinatorial features, such as labeled paths or labeled trees. To speed up database searches, we propose to store with each fingerprint a small header vector containing primarily the result of applying the logical exclusive OR (XOR) operator to the fingerprint vector after modulo wrapping to a smaller number of bits, such as 128 bits. From the XOR headers of two molecules, tight bounds on the intersection and union of their fingerprint vectors can be rapidly obtained, yielding tight bounds on derived similarity measures, such as the Tanimoto measure. During a database search, every time these bounds are unfavorable, the corresponding molecule can be rapidly discarded with no need for further inspection. We derive probabilistic models that allow us to estimate precisely the behavior of the XOR headers and the level of pruning under different conditions in terms of similarity threshold and fingerprint density. These theoretical results are corroborated by experimental results on a large set of molecules. For a Tanimoto threshold of 0.5 (respectively 0.9), this approach requires searching less than 50% (respectively 10%) of the database, leading to typical search speedups of 2 to 3 times over the previous state-of-the-art.

Adaptive subcarrier allocation and bit loading for voice/data transmission in multiuser OFDM systems

AbstractA new algorithm of adaptive subcarrier allocation and bit loading (A‐SABL) is proposed for simultaneous voice and data transmission in multiuser OFDM systems. The algorithm takes advantage of the frequency diversity and the voice/data transmission requirements to dynamically assign the number of subcarriers and bits/per symbol on each subcarrier for each user in a single cell. Due to the strict delay requirement of voice service, the subcarriers with low channel gains are assigned for voice transmission with a small number of bits per symbol to guarantee its required bit‐error‐rate (BER) and transmission rate. Based on the remaining subcarriers with high channel gains and the transmission power, the throughput of data transmission is then maximized by loading as many bits as possible on each subcarrier to achieve the required transmission bit rate and BER. Theoretical analysis and simulation on the proposed algorithm show that a better performance is obtained than previously reported schemes. Copyright © 2008 John Wiley & Sons, Ltd.

Scheduling Power-Constrained Tests through the SoC Functional Bus

This paper proposes a test methodology for core-based testing of System-on-Chips by utilizing the functional bus as a test access mechanism. The functional bus is used as a transportation channel for the test stimuli and responses from a tester to the cores under test (CUT). To enable test concurrency, local test buffers are added to all CUTs. In order to limit the buffer area overhead while minimizing the test application time, we propose a packet-based scheduling algorithm called PAcket Set Scheduling (PASS), which finds the complete packet delivery schedule under a given power constraint. The utilization of test packets, consisting of a small number of bits of test data, for test data delivery allow an efficient sharing of bus bandwidth with the help of an effective buffer-based test architecture. The experimental results show that the methodology is highly effective, especially for smaller bus widths, compared to previous approaches that do not use the functional bus.

Quantum Property Testing

A language L has a property tester if there exists a probabilistic algorithm that given an input x queries only a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L. We define a similar notion of quantum property testing and show that there exist languages with good quantum property testers but no good classical testers. We also show there exist languages which require a large number of queries even for quantumly testing.

Partial resolution for redundant operation table

In this work, we discuss several drawbacks of the conventional wide-width redundant operation table such as the waste of area cost and power consumption. We found that the waste of area cost and power consumption is caused by storing meaningless bits of the narrow-width operand values. Based on this analysis, we propose a way to avoid these storing of meaningless information of the narrow-width operands. The proposed method, partial resolution method, divides the conventional wide-width redundant operation table into two tables as the wide-width table for the half entries and the narrow-width table for the other half entries. The wide-width and the narrow-width redundant operation tables store different dynamic instructions whose operand values are wide and narrow, respectively. Since the narrow-width redundant operation table stores smaller number of bits, it requires lower area cost and also power consumption compared with the wide-width redundant operation table. The partial resolution method decreases the area cost by about 7% and 20% for the integer and the floating-point tables, respectively, and reduces the dynamic power consumption by about 34% and 30% for the integer and the floating-point tables, respectively, compared with the conventional wide-width redundant operation table with 2K entries. Meanwhile, the performance simulation with a high-end microarchitecture model and SPEC2000 benchmarks shows that the partial resolution method affects the performance very little, and even increases slightly in terms of IPC (Instruction per Cycle) value.

Optimal Transmission and Limited Feedback Design for OFDM/MIMO Systems in Frequency Selective Block Fading Channels

In this paper, we propose a systematic design framework to deal with the problem of limited CSIT feedback for MIMO-OFDM systems with correlated subcarriers. Based on the framework, we obtain the optimal transmission and CSI feedback strategies given the limited CSI feedback constraint. We propose a MIMO-OFDM design with combined adaptive power control and beam-forming framework for optimizing MIMO-OFDM link capacity with limited feedback in frequency selective fading channels. We derive a computationally efficient algorithm which exploits subcarrier correlation to search for the design of the optimal transmission and feedback strategy. We found that with a small number of bits for CSIT feedback, there is already significant capacity gain in the MIMO-OFDM systems

Packet clock recovery using a bismuth oxide fiber-based optical power limiter

We demonstrate an optical clock recovery circuit that extracts the line rate component on a per packet basis from short data packets at 40Gb/s. The circuit comprises a Fabry-Perot filter followed by a novel power limiting configuration, which in turn consists of a 5m highly nonlinear bismuth oxide fiber in cascade with an optical bandpass filter. Both experimental and simulation-based results are in close agreement and reveal that the proposed circuit acquires the timing information within only a small number of bits, yielding a packet clock for every respective data packet. Moreover, we investigate theoretically the scaling laws for the parameters of the circuit for operation beyond 40 Gb/s and present simulation results showing successful packet clock extraction for 160 Gb/s data packets. Finally, the circuit's potential for operation at 320 Gb/s is discussed, indicating that ultrafast packet clock recovery should be in principle feasible by exploiting the passive structure of the device and the fsec-scale nonlinear response of the optical fiber.

Decentralized Estimation in an Inhomogeneous Sensing Environment

We consider decentralized estimation of a noise-corrupted deterministic parameter by a bandwidth-constrained sensor network with a fusion center. The sensor noises are assumed to be additive, zero mean, spatially uncorrelated, but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment. The classical best linear unbiased estimator (BLUE) linearly combines the real-valued sensor observations to minimize the mean square error (MSE). Unfortunately, such a scheme cannot be implemented in a practical bandwidth-constrained sensor network due to its requirement to transmit real-valued messages. In this paper, we construct a decentralized estimation scheme (DES) where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal-to-noise ratio (SNR). The resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter. The proposed DES is universal in the sense that each sensor compression scheme requires only the knowledge of local SNR, rather than the noise probability distribution functions (pdf), while the final fusion step is also independent of the local noise pdfs. We show that the MSE of the proposed DES is within a constant factor of 25/8 of that achieved by the classical centralized BLUE estimator.

OFDM Power Loading Using Limited Feedback

Orthogonal frequency division multiplexing (OFDM) is a practical broadband signaling technique for use in multipath fading channels. Over the past ten years, research has shown that power loading, where the power allocations on the OFDM frequency tones are jointly optimized, can improve error rate or capacity performance. The implementation of power loading, however, is dependent on the presence of complete forward link channel knowledge at the transmitter. In systems using frequency division duplexing (FDD), this assumption is unrealistic. In this paper, we propose power loading for OFDM symbols using a limited number of feedback bits sent from the receiver to the transmitter. The power loading vector is designed at the receiver, which is assumed to have perfect knowledge of the forward link channel, and conveyed back to the transmitter over a limited rate feedback channel. To allow for the vector to be represented by a small number of bits, the power loading vector is restricted to lie in a finite set, or codebook, of power loading vectors. This codebook is designed offline and known a priori to both the transmitter and receiver. We present two power allocation selection algorithms that optimize the probability of symbol error and capacity, respectively. Simulation results show that the proposed limited feedback techniques provide performance close to full channel knowledge power loading.

Constructing Locally Computable Extractors and Cryptosystems in the Bounded-Storage Model

We consider the problem of constructing randomness extractors that are locally computable; that is, read only a small number of bits from their input. As recently shown by Lu locally computable extractors directly yield secure private-key cryptosystems in Maurer’s bounded-storage model. We suggest a general “sample-then-extract” approach to constructing locally computable extractors: use essentially any randomness-efficient sampler to select bits from the input and then apply any extractor to the selected bits. Plugging in known sampler and extractor constructions, we obtain locally computable extractors, and hence cryptosystems in the bounded-storage model, whose parameters improve upon previous constructions. We also provide lower bounds showing that the parameters we achieve are nearly optimal. The correctness of the sample-then-extract approach follows from a fundamental lemma of Nisan and Zuckerman, which states that sampling bits from a weak random source roughly preserves the min-entropy rate. We also present a refinement of this lemma, showing that the min-entropy rate is preserved up to an arbitrarily small additive loss, whereas the original lemma loses a logarithmic factor.

All-optical packet address and payload separation

An all-optical address and data separation scheme is presented for short 10-Gb/s packets. The technique uses a novel packet clock recovery circuit that consists of a Fabry-Perot filter and a ultrafast nonlinear interferometer (UNI) gate to generate a local packet clock. A second cascaded UNI gate is used to separate the header and the payload, performing a simple AND operation between the packet and its self-derived clock. The proposed technique requires a small number of bits as guard band and this number is independent of the line rate.

Optimization and implementation of the integer wavelet transform for image coding

This paper deals with the design and implementation of an image transform coding algorithm based on the integer wavelet transform (IWT). First of all, criteria are proposed for the selection of optimal factorizations of the wavelet filter polyphase matrix to be employed within the lifting scheme. The obtained results lead to the IWT implementations with very satisfactory lossless and lossy compression performance. Then, the effects of finite precision representation of the lifting coefficients on the compression performance are analyzed, showing that, in most cases, a very small number of bits can be employed for the mantissa keeping the performance degradation very limited. Stemming from these results, a VLSI architecture is proposed for the IWT implementation, capable of achieving very high frame rates with moderate gate complexity.

Scalar versus vector quantization: worst case analysis

We study the potential merits of vector quantization and show that there can be an arbitrary discrepancy between the worst case rates required for scalar and vector quantization. Specifically, we describe a random variable and a distortion measure where quantization of a single instance to within a given distortion requires an arbitrarily large number of bits in the worst case, but quantization of multiple independent instances to within the same distortion requires an arbitrarily small number of bits per instance in the worst case. We relate this discrepancy to expander graphs, representation- and cover-numbers of set systems, and a problem studied by Slepian, Wolf, and Wyner (1973).

Are Bitvectors Optimal?

We study the it static membership problem: Given a set S of at most n keys drawn from a universe U of size m, store it so that queries of the form "Is u in S?" can be answered by making few accesses to the memory. We study schemes for this problem that use space close to the information theoretic lower bound of $\Omega(n\log(\frac{m}{n}))$ bits and yet answer queries by reading a small number of bits of the memory. We show that, for $\epsilon > 0$, there is a scheme that stores $O(\frac{n}{\epsilon^2}\log m)$ bits and answers membership queries using a randomized algorithm that reads just one bit of memory and errs with probability at most $\epsilon$. We consider schemes that make no error for queries in S but are allowed to err with probability at most $\epsilon$ for queries not in S. We show that there exist such schemes that store $O((\frac{n}{\epsilon})^2 \log m)$ bits and answer queries using just one bitprobe. If multiple probes are allowed, then the number of bits stored can be reduced to $O(n^{1+\delta}\log m)$ for any $\delta > 0$. The schemes mentioned above are based on probabilistic constructions of set systems with small intersections. We show lower bounds that come close to our upper bounds (for a large range of n and $\epsilon$): Schemes that answer queries with just one bitprobe and error probability $\epsilon$ must use $\Omega(\frac{n}{\epsilon\log(1/\epsilon)} \log m)$ bits of storage; if the error is restricted to queries not in S, then the scheme must use $\Omega(\frac{n^2}{\epsilon^2 \log (n/\epsilon)}\log m)$ bits of storage. We also consider deterministic schemes for the static membership problem and show tradeoffs between space and the number of probes.

How many shuffles to randomize a deck of cards?

A celebrated theorem of Aldous, Bayer and Diaconis asserts that it takes ∼3/2 log 2 n riffle shuffles to randomize a deck of n cards, asymptotically as n → ∞, and that the randomization occurs abruptly according to a 9cut–off phenomenon9. These results depend upon measuring randomness by a quantity known as the total variation distance. If randomness is measured by uncertainty or entropy in the sense of information theory, the behaviour is different. It takes only ∼log 2 n shuffles to reduce the information to a proportion arbitrarily close to zero, and ∼3/2 log 2 n to reduce it to an arbitrarily small number of bits. At 3/2> log 2 n shuffles, ca .0.0601 bits remain, independently of n .