nils-herrmann/clean_scirepeval huggingface dataset:
A robust R-FFAST framework for computing a k-sparse n-length DFT in O(k log n) sample complexity using sparse-graph codes

The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n). If the DFT X⃗ of the signal x⃗ has only k non-zero coefficients (where k <; n), can we do better? In , we presented a novel FFAST (Fast Fourier Aliasing-based Sparse Transform) algorithm that cleverly induces sparse graph codes in the DFT domain, via a Chinese-Remainder-Theorem (CRT)-guided sub-sampling operation of the time-domain samples. The resulting sparse graph code is then exploited to devise a simple and fast iterative onion-peeling style decoder that computes an n length DFT of a signal using only O(k) time-domain samples and O(k log k) computations, in the absence of any noise. In this paper, we extend the FFAST framework of  to the case where the time-domain samples are corrupted by white Gaussian noise. In particular, we show that the extended noise robust algorithm R-FFAST computes an n-length k-sparse DFT X⃗ using O(k log n)1 noise-corrupted time-domain samples, in O(n log n) computations2. While our theoretical results are for signals with a uniformly random support of the non-zero DFT coefficients and additive white Gaussian noise, we provide simulation results which demonstrates that the R-FFAST algorithm performs well even for signals like MR images, that have an approximately sparse Fourier spectrum with a non-uniform support for the dominant DFT coefficients.
Secure Source Coding With a Helper

We consider a secure lossless source coding problem with a rate-limited helper. In particular, Alice observes an independent and identically distributed (i.i.d.) source <formula formulatype="inline"> <tex Notation="TeX">$X^{n}$</tex></formula> and wishes to transmit this source losslessly to Bob over a rate-limited link of capacity not exceeding <formula formulatype="inline"><tex Notation="TeX">$R_{x}$</tex> </formula>. A helper, say Helen, observes an i.i.d. correlated source <formula formulatype="inline"><tex Notation="TeX">$Y^{n}$</tex></formula> and can transmit information to Bob over another link of capacity not exceeding <formula formulatype="inline"><tex Notation="TeX">$R_{y}$</tex></formula>. A passive eavesdropper (say Eve) can observe the coded output of Alice, i.e., the link from Alice to Bob is public. The uncertainty about the source <formula formulatype="inline"><tex Notation="TeX">$X^{n}$</tex> </formula> at Eve (denoted by <formula formulatype="inline"><tex Notation="TeX">$\Delta$</tex></formula>) is measured by the conditional entropy <formula formulatype="inline"><tex Notation="TeX">${{H(X^{n}\vert J_{x})}\over{n}}$</tex> </formula>, where <formula formulatype="inline"> <tex Notation="TeX">$J_{x}$</tex></formula> is the coded output of Alice and <formula formulatype="inline"> <tex Notation="TeX">$n$</tex></formula> is the block length. We completely characterize the rate-equivocation region for this secure source coding model, where we show that Slepian–Wolf binning of <formula formulatype="inline"> <tex Notation="TeX">$X^{n}$</tex></formula> with respect to the coded side information received at Bob is optimal. We next consider a modification of this model in which Alice also has access to the coded output of Helen. We call this model as the two-sided helper model. For the two-sided helper model, we characterize the rate-equivocation region. While the availability of side information at Alice does not reduce the rate of transmission from Alice, it significantly enhances the resulting equivocation at Eve. In particular, the resulting equivocation for the two-sided helper case is shown to be <formula formulatype="inline"><tex Notation="TeX">$\min (H(X),R_{y})$</tex></formula>, i.e., one bit from the two-sided helper provides one bit of uncertainty at Eve. From this result, we infer that Slepian–Wolf binning of <formula formulatype="inline"><tex Notation="TeX">$X$</tex></formula> is suboptimal and one can further decrease the information leakage to the eavesdropper by utilizing the side information at Alice. We, finally, generalize both of these results to the case in which there is additional uncoded side information <formula formulatype="inline"><tex Notation="TeX">$W^{n}$</tex> </formula> available at Bob and characterize the rate-equivocation regions under the assumption that <formula formulatype="inline"><tex Notation="TeX">$Y^{n}\rightarrow X^{n}\rightarrow W^{n}$</tex></formula> forms a Markov chain.
Syndrome-Based Robust Video Transmission Over Networks with Bursty Losses

This paper addresses the problem of low-latency robust video delivery over packet networks characterized by a bursty loss process. We propose a joint source-channel coding based video codec which uses distributed source coding (DSC) principles. This codec can efficiently tune to both the source content as well as to the network loss characteristics while respecting stringent latency constraints. Simulation results show that the proposed system is both objectively (in PSNR) and subjectively (visual quality) superior to predictive video coding systems where the encoded bitstream is protected with forward error correction (FEC) codes.
n-channel symmetric multiple descriptions-part II:An achievable rate-distortion region

In this Part II of a two-part paper, we present a new achievable rate-distortion region for the symmetric n-channel multiple-descriptions coding problem (n>2) where the rate of every description is the same, and the reconstruction distortion depends only on the number of descriptions received. Using a new approach for the random coding constructions, along with a generalization of the technique used in the two-channel El Gamal and Cover region to any n, the rate region presented here achieves points that have not been known in the literature previously. This rate region is derived from a concatenation of source-channel erasure codes developed in Part I of this work by deploying the framework of source coding with side information ("random binning"). The key idea is that by using the framework of source coding with side information, multiple statistically identical realizations representing the coarse version of a source can be simultaneously refined by a single encoding. We point out that there is an important conceptual difference in random coding construction for the multiple-descriptions coding problem between the case of n=2 and n>2. To illustrate the framework, we also present the important case of the Gaussian source in detail.
Optimal systematic distributed storage codes with fast encoding

We consider the problem of constructing explicit erasure codes for distributed storage with the following desirable properties motivated by system constraints: (i) Maximum-Distance-Separable (MDS), (ii)Optimal repair-bandwidth, (iii)Flexibility in repair (as will be described), (iv) Systematic Form, and (v) Fast encoding (enabled by a sparse generator matrix). Existing constructions in the literature satisfy only strict subsets of these desired properties. This paper presents the first explicit code construction which theoretically guarantees all the five desired properties simultaneously. We first present a construction that builds on Product-Matrix (PM) codes by enabling sparsity in its generator matrix. We then present a transformation for general classes of storage and repair optimal codes to enable fast encoding through sparsity. In practice, such sparse codes are roughly 7 times sparser than their standard counterparts, and result in encoding speedup by a factor of about 4 for typical parameters.
Generalized coset codes for distributed binning

In many multiterminal communication problems, constructions of good source codes involve finding distributed partitions (into bins) of a collection of quantizers associated with a group of source encoders. Further, computationally efficient procedures to index these bins are also required. In this work, we consider a constructive approach for distributed binning in an algebraic framework. Several application scenarios fall under the scope of this paper including the CEO problem, distributed source coding, and n-channel symmetric multiple description source coding with n>2. Specifically, in this exposition we consider the case of two codebooks while focusing on the Gaussian CEO problem with mean squared error reconstruction and with two symmetric observations. This problem deals with distributed encoding of correlated noisy observations of a source into descriptions such that the joint decoder having access to them can reconstruct the source with a fidelity criterion. We employ generalized coset codes constructed in a group-theoretic setting for this approach, and analyze the performance in terms of distance properties and decoding algorithms.
Hybrid compressed-uncompressed framework for wireless image transmission

We consider the problem of efficient image transmission over noisy time-varying channels subject to a low transmission energy constraint (and fixed bandwidth/delay constraints). We examine the limits of desirability of a highly compressed representation using a joint source-channel coding (JSCC) framework. Specifically, invoking as a platform a state-of-the-art wavelet image coder, we demonstrate how the resulting highly compressed digital stream, appropriately protected against channel noise, is not always the best solution. We show how a hybrid scheme based on simple partitioning of the wavelet image representation into "compressed" and "uncompressed" components can lead to significantly improved performance (of the order of 3 dB in PSNR for Rayleigh channels) over popular JSCC schemes which are based on compressed, entropy-coded, and appropriately unequal error-protected (UEP) source representations.
Speeding Up Distributed Machine Learning Using Codes

Codes are widely used in many engineering applications to offer <italic>robustness</italic> against <italic>noise</italic>. In large-scale systems, there are several types of noise that can affect the performance of distributed machine learning algorithms—straggler nodes, system failures, or communication bottlenecks—but there has been little interaction cutting across codes, machine learning, and distributed systems. In this paper, we provide theoretical insights on how <italic>coded</italic> solutions can achieve significant gains compared with uncoded ones. We focus on two of the most basic building blocks of distributed learning algorithms: <italic>matrix multiplication</italic> and <italic>data shuffling</italic>. For matrix multiplication, we use codes to alleviate the effect of stragglers and show that if the number of homogeneous workers is <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>, and the runtime of each subtask has an exponential tail, coded computation can speed up distributed matrix multiplication by a factor of <inline-formula> <tex-math notation="LaTeX">$\log n$ </tex-math></inline-formula>. For data shuffling, we use codes to reduce communication bottlenecks, exploiting the excess in storage. We show that when a constant fraction <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> of the data matrix can be cached at each worker, and <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is the number of workers, <italic>coded shuffling</italic> reduces the communication cost by a factor of <inline-formula> <tex-math notation="LaTeX">$\left({\alpha + \frac {1}{n}}\right)\gamma (n)$ </tex-math></inline-formula> compared with uncoded shuffling, where <inline-formula> <tex-math notation="LaTeX">$\gamma (n)$ </tex-math></inline-formula> is the ratio of the cost of unicasting <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> messages to <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> users to multicasting a common message (of the same size) to <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> users. For instance, <inline-formula> <tex-math notation="LaTeX">$\gamma (n) \simeq n$ </tex-math></inline-formula> if multicasting a message to <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> users is as cheap as unicasting a message to one user. We also provide experimental results, corroborating our theoretical gains of the coded algorithms.
Computationally-efficient sparse polynomial interpolation

We consider the problem of interpolating a high-degree sparse polynomial, where the sparsity is in the number of monomial terms with non-zero coefficients. We propose a probabilistic algorithm that requires only O(k) evaluations of a polynomial with complex coefficients, on the unit circle at specified points and has a complexity O(k log k), where k is the sparsity of the polynomial. Thus the evaluation complexity as well as the computational complexity are independent of the maximum degree n in contrast to existing algorithms in the literature. We extend our algorithm to polynomials defined over the finite field using fast algorithms in the literature to compute discrete logs for certain field sizes.
Scaling Peer-to-Peer Video-on-Demand systems using helpers

The throughput of Peer-to-Peer (P2P) Video-on-Demand (VoD) systems is typically capped by the users' aggregate upload bandwidth . The drastic increase in the popularity of VoD and the demand of higher quality content has thus placed substantial burden on the content servers. We investigate a novel P2P VoD architecture that leverages idle internet resources, which we call helpers, to provide a scalable solution to P2P VoD systems. Helpers are volatile in nature, and can be individually unreliable. However, we investigate the statistical aggregation of a large number of helpers to guarantee quality of service. Since helpers do not come with “free” preloaded content, trade-offs between how much a helper should download and how much it can aid the system need to be explored. In this paper, the optimal steady-state design parameters are derived to maximize the helpers' upload bandwidth utilization. Packet level simulations have verified the efficiency of the system. In a typical scenario of 240 users and a required theoretical minimum of 120 helpers with an average upload bandwidth of 256 kbps, a streaming rate of 384 kbps can be sustained with ≪ 2% relative server load. Results also show that the system is robust to helper churn.
Optimal power procurement and demand response with quality-of-usage guarantees

In this paper, we propose a general operating scheme which allows the utility company to jointly perform power procurement and demand response so as to maximize the social welfare. Our model takes into consideration the effect of the renewable energy and the multi-stage feature of the power procurement process. It also enables the utility company to provide quality-of-usage (QoU) guarantee to the power consumers, which ensures that the average power usage level meets the target value for each user. To maximize the social welfare, we develop a low-complexity algorithm called the welfare maximization algorithm (WMA), which performs joint power procurement and dynamic pricing. WMA is constructed based on a two-timescale Lyapunov optimization technique. We prove that WMA achieves a close-to-optimal utility and ensures that the QoU requirement is met with bounded deficit. WMA can be implemented in a distributed manner and is robust with respect to system dynamics uncertainty.
Scaling Laws for Cooperative Node Localization in Non-Line-of-Sight Wireless Networks

We study the problem of cooperative node localization in non-line- of-sight (NLOS) wireless networks and address design questions such as, "How many anchors and what fraction of line-of-sight (LOS) measurements are needed to achieve a specified target accuracy?". We analytically characterize the performance improvement in localization accuracy as a function of the number of nodes in the network and the fraction of LOS measurements. In particular, we show that the Cramer- Rao Lower Bound (CRLB) can be expressed as a product of two factors - a scalar function that depends only on the parameters of the noise distribution and a matrix that depends only on the geometry of node locations. This holds for arbitrary distance and angle measurement modalities under an additive noise model. Further, a simplified expression is obtained for the CRLB, which provides an insightful understanding of the bound and helps deduce the scaling behavior of the estimation error as a function of the number of agents and anchors in the network. The mean squared error in localization is shown to have an inverse linear relationship with the number of anchors or agents. The error is also shown to have an approximately inverse linear relationship with the fraction of LOS readings except at the extremes. The behavior at the extremes suggests that even a small fraction of LOS measurements can provide significant improvements. Conversely, a small fraction of NLOS measurements can significantly degrade the performance.
On Source Encoding with Side-information Under Ambiguous State of Nature

In this paper, we address the case of a single remote sensing unit (encoder), a central processing unit (decoder), and a finite bitrate constraint as an abstraction of a bandwidth-limited channel between the encoder and decoder. The goal is to spend this bit budget in an optimal sense, in terms of classification or estimation performance (minimize the probability of classification error or minimize the probability that the parameter estimation error exceeds a desired tolerance) while ensuring the reconstruction of the raw data with maximum fidelity (in a rate-distortion sense)
Random distributed multiresolution representations with significance querying

We propose random distributed multiresolution representations of sensor network data, so that the most significant encoding coefficients are easily accessible by querying a few sensors, anywhere in the network. Less significant encoding coefficients are available by querying a larger number of sensors, local to the region of interest. Significance can be defined in a multiresolution way, without any prior knowledge of the source data, as global summaries versus local details. Alternatively, significance can be defined in a data-adaptive way, as large differences between neighboring data values. We propose a distributed encoding algorithm that is robust to arbitrary wireless communication connectivity graphs, where links can fail or change with time. This randomized algorithm allows distributed computation that does not require strict global coordination or awareness of network connectivity at individual sensors. Because computations involve sensors in local neighborhoods of the communication graph, they are communication-efficient. Our framework uses local interaction among sensors to enable flexible information retrieval at the global level
Complexity/performance trade-offs for robust distributed video coding

In this work, we analytically study the complexity-performance trade-offs associated with video codecs based on the principle of source coding with side information at the decoder. We address three important aspects. First, we quantify the theoretical performance gains attained with side-information based codecs over prediction-based coders like MPEG under a lossy transmission scenario when there is drift. Secondly, we show that it is possible to closely approach MPEG's compression performance using side-information video coding principles with accurate DFD (displaced frame difference) modeling even without sophisticated channel codes. Thirdly, we analytically show that the value of accurately estimating DFD statistics diminishes as the channel gets noisier.
Hiding the Rumor Source

Anonymous social media platforms, like Secret, Yik Yak, and Whisper, have emerged as important tools for sharing ideas without the fear of judgment. Such anonymous platforms are also important in nations under authoritarian rule, where freedom of expression and the personal safety of message that authors may depend on anonymity. Whether for fear of judgment or retribution, it is sometimes crucial to hide the identities of users who post sensitive messages. In this paper, we consider a global adversary who wishes to identify the author of a message; it observes either a snapshot of the spread of a message at a certain time or sampled timestamp metadata, or both. Recent advances in rumor source detection show that existing messaging protocols are vulnerable against such an adversary. We introduce a novel messaging protocol, which we call adaptive diffusion, and show that under the snapshot adversarial model, adaptive diffusion spreads content fast and achieves perfect obfuscation of the source when the underlying contact network is an infinite regular tree. That is, all users with the message are nearly equally likely to have been the origin of the message. When the contact network is an irregular tree, we characterize the probability of maximum likelihood detection by proving a concentration result over Galton–Watson trees. Experiments on a sampled Facebook network demonstrate that adaptive diffusion effectively hides the location of the source even when the graph is finite, is irregular, and has cycles.
Achievable rates for channels with deletions and insertions

Consider a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit added after it with probability i, or it is transmitted unmodified with probability 1 - d - i. We obtain a lower bound on the capacity of this channel. The transformation of the input sequence by the channel may be viewed in terms of runs as follows: some runs of the input sequence get shorter/longer, some runs get deleted, and some new runs are added. The capacity is difficult to compute mainly due to the last two phenomena: deleted runs, and new inserted runs. We consider a decoder which first decodes the positions of the deleted and inserted runs, and then the transmitted codeword. Analyzing the performance of such a decoder leads to a computable lower bound on the capacity.
Collaborative High-Accuracy Localization in Mobile Multipath Environments

We study the problem of high-accuracy localization of mobile nodes in a multipath-rich environment where submeter accuracy values are required. We employ a peer-to-peer framework where nodes can get pairwise multipath-degraded ranging estimates in local neighborhoods, with the multipath noise correlated across time. The challenge is to enable high-accuracy positioning under severe multipath conditions when the fraction of received signals corrupted by multiple paths is significant. Our contributions are twofold. We provide a practical distributed localization algorithm by invoking an analytical graphical model framework based on particle filtering, and we validate its potential for high-accuracy localization through simulations. In a practical dedicated short-range communication (DSRC) mobile simulation setup, we show that the algorithm can achieve errors of <; 1 m 90% of the time, even when the fraction of line-of-sight (LOS) signals is less than 35%. We also address design questions such as “how many anchors and what fraction of LOS measurements are needed to achieve a specified target accuracy?” by showing that the Cramer-Rao lower bound (CRLB) for localization can be expressed as a product of two factors: a scalar function that depends only on the parameters of the noise distribution and a matrix that depends only on the geometry of node locations and the underlying connectivity graph. A simplified expression is obtained that provides an insightful understanding of the bound and that helps deduce the scaling behavior of the estimation error as a function of the number of agents and anchors in the network.