arXiv subjects

Muriel Médard

Publications and source records attributed to Muriel Médard.

At least 73 records · Page 4Linked to original sources

arXiv2022

Rainbow Differential Privacy

We extend a previous framework for designing differentially private (DP) mechanisms via randomized graph colorings that was restricted to binary functions, corresponding to colorings in a graph, to multi-valued functions. As before, datasets are nodes in the graph and any two neighboring datasets are connected by an edge. In our setting, we assume that each dataset has a preferential ordering for the possible outputs of the mechanism, each of which we refer to as a rainbow. Different rainbows partition the graph of datasets into different regions. We show that if the DP mechanism is pre-specified at the boundary of such regions and behaves identically for all same-rainbow boundary datasets, at most one optimal such mechanism can exist and the problem can be solved by means of a morphism to a line graph. We then show closed form expressions for the line graph in the case of ternary functions. Treatment of ternary queries in this paper displays enough richness to be extended to higher-dimensional query spaces with preferential query ordering, but the optimality proof does not seem to follow directly from the ternary proof.

cs.CR↗

arXiv2022

Partial Encryption after Encoding for Security and Reliability in Data Systems

We consider the problem of secure and reliable communication over a noisy multipath network. Previous work considering a noiseless version of our problem proposed a hybrid universal network coding cryptosystem (HUNCC). By combining an information-theoretically secure encoder together with partial encryption, HUNCC is able to obtain security guarantees, even in the presence of an all-observing eavesdropper. In this paper, we propose a version of HUNCC for noisy channels (N-HUNCC). This modification requires four main novelties. First, we present a network coding construction which is jointly, individually secure and error-correcting. Second, we introduce a new security definition which is a computational analogue of individual security, which we call individual indistinguishability under chosen ciphertext attack (individual IND-CCA1), and show that NHUNCC satisfies it. Third, we present a noise based decoder for N-HUNCC, which permits the decoding of the encoded-thenencrypted data. Finally, we discuss how to select parameters for N-HUNCC and its error-correcting capabilities.

cs.IT↗

arXiv2022

Broadcast Approach Meets Network Coding for Data Streaming

For data streaming applications, existing solutions are not yet able to close the gap between high data rates and low delay. This work considers the problem of data streaming under mixed delay constraints over a single communication channel with delayed feedback. We propose a novel layered adaptive causal random linear network coding (LAC-RLNC) approach with forward error correction. LAC-RLNC is a variable-to-variable coding scheme, i.e., variable recovered information data at the receiver over variable short block length and rate is proposed. Specifically, for data streaming with base and enhancement layers of content, we characterize a high dimensional throughput-delay trade-off managed by the adaptive causal layering coding scheme. The base layer is designed to satisfy the strict delay constraints, as it contains the data needed to allow the streaming service. Then, the sender can manage the throughput-delay trade-off of the second layer by adjusting the retransmission rate a priori and posterior as the enhancement layer, that contains the remaining data to augment the streaming service's quality, is with the relax delay constraints. We numerically show that the layered network coding approach can dramatically increase performance. We demonstrate that LAC-RLNC compared with the non-layered approach gains a factor of three in mean and maximum delay for the base layer, close to the lower bound, and factor two for the enhancement layer.

cs.IT↗

arXiv2022

Syfer: Neural Obfuscation for Private Data Release

Balancing privacy and predictive utility remains a central challenge for machine learning in healthcare. In this paper, we develop Syfer, a neural obfuscation method to protect against re-identification attacks. Syfer composes trained layers with random neural networks to encode the original data (e.g. X-rays) while maintaining the ability to predict diagnoses from the encoded data. The randomness in the encoder acts as the private key for the data owner. We quantify privacy as the number of attacker guesses required to re-identify a single image (guesswork). We propose a contrastive learning algorithm to estimate guesswork. We show empirically that differentially private methods, such as DP-Image, obtain privacy at a significant loss of utility. In contrast, Syfer achieves strong privacy while preserving utility. For example, X-ray classifiers built with DP-image, Syfer, and original data achieve average AUCs of 0.53, 0.78, and 0.86, respectively.

cs.LG↗

arXiv2021

Guessing random additive noise decoding with symbol reliability information (SRGRAND)

The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and Van Tilborg's 1978 theorem on the NP-hardness of decoding linear codes. These results shifted focus away from creating code-independent decoders, but recent low-latency communication applications necessitate relatively short codes, providing motivation to reconsider the development of universal decoders. We introduce a scheme for employing binarized symbol soft information within Guessing Random Additive Noise Decoding, a universal hard detection decoder. We incorporate codebook-independent quantization of soft information to indicate demodulated symbols to be reliable or unreliable. We introduce two decoding algorithms: one identifies a conditional Maximum Likelihood (ML) decoding; the other either reports a conditional ML decoding or an error. For random codebooks, we present error exponents and asymptotic complexity, and show benefits over hard detection. As empirical illustrations, we compare performance with majority logic decoding of Reed-Muller codes, with Berlekamp-Massey decoding of Bose-Chaudhuri-Hocquenghem codes, with CA-SCL decoding of CA-Polar codes, and establish the performance of Random Linear Codes, which require a universal decoder and offer a broader palette of code sizes and rates than traditional codes.

cs.IT↗

arXiv2021

Post-Quantum Security for Ultra-Reliable Low-Latency Heterogeneous Networks

We consider the problem of post-quantum secure and ultra-reliable communication through a heterogeneous network consisting of multiple connections. Three performance metrics are considered: security, throughput, and in-order delivery delay. In this setting, previous work has looked, individually, at the trade-offs between in-order delivery delay and throughput, and between security and throughput. This is the first work considering the trade-off between all three for heterogeneous communication networks, while taking the computational complexity into account. We present LL-HUNCC, a low latency hybrid universal network coding cryptosystem. LL-HUNCC is an efficient coding scheme which allows for secure communications over a noisy untrusted heterogeneous network by encrypting only a small part of the information being sent. This scheme provides post-quantum security with high throughput and low in-order delivery delay guarantees. We evaluate LL-HUNCC via simulations on a setting inspired by a practical scenario for heterogeneous communications involving a satellite communication link and a 5G communication network. Under this scenario, we compare LL-HUNCC to the state-of-the-art where all communication paths are encrypted via a post-quantum public-key cryptosystem.

cs.IT↗

arXiv2021

Repeat-Free Codes

In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are calculated. Then, an efficient algorithm, which uses two bits of redundancy, is presented to encode length-$n$ sequences for $k=2+2\log (n)$. This algorithm is then improved to support any value of $k$ of the form $k=a\log (n)$, for $1<a$, while its redundancy is $o(n)$. We also calculate the capacity of repeat-free sequences when combined with local constraints which are given by a constrained system, and the capacity of multi-dimensional repeat-free codes.

cs.IT↗

arXiv2021

CRC Codes as Error Correction Codes

CRC codes have long since been adopted in a vast range of applications. The established notion that they are suitable primarily for error detection can be set aside through use of the recently proposed Guessing Random Additive Noise Decoding (GRAND). Hard-detection (GRAND-SOS) and soft-detection (ORBGRAND) variants can decode any short, high-rate block code, making them suitable for error correction of CRC-coded data. When decoded with GRAND, short CRC codes have error correction capability that is at least as good as popular codes such as BCH codes, but with no restriction on either code length or rate. The state-of-the-art CA-Polar codes are concatenated CRC and Polar codes. For error correction, we find that the CRC is a better short code than either Polar or CA-Polar codes. Moreover, the standard CA-SCL decoder only uses the CRC for error detection and therefore suffers severe performance degradation in short, high rate settings when compared with the performance GRAND provides, which uses all of the CA-Polar bits for error correction. Using GRAND, existing systems can be upgraded from error detection to low-latency error correction without re-engineering the encoder, and additional applications of CRCs can be found in IoT, Ultra-Reliable Low Latency Communication (URLLC), and beyond. The universality of GRAND, its ready parallelized implementation in hardware, and the good performance of CRC as codes make their combination a viable solution for low-latency applications.

cs.IT↗

arXiv2021

Robust Improvement of the Age of Information by Adaptive Packet Coding

We consider a wireless communication network with an adaptive scheme to select the number of packets to be admitted and encoded for each transmission, and characterize the information timeliness. For a network of erasure channels and discrete time, we provide closed form expressions for the Average and Peak Age of Information (AoI) as functions of admission control and adaptive coding parameters, the feedback delay, and the maximum feasible end-to-end rate that depends on channel conditions and network topology. These new results guide the system design for robust improvements of the AoI when transmitting time sensitive information in the presence of topology and channel changes. We illustrate the benefits of using adaptive packet coding to improve information timeliness by characterizing the network performance with respect to the AoI along with its relationship to throughput (rate of successfully decoded packets at the destination) and per-packet delay. We show that significant AoI performance gains can be obtained in comparison to the uncoded case, and that these gains are robust to network variations as channel conditions and network topology change.

cs.IT↗

arXiv2021

Stream Distributed Coded Computing

The emerging large-scale and data-hungry algorithms require the computations to be delegated from a central server to several worker nodes. One major challenge in the distributed computations is to tackle delays and failures caused by the stragglers. To address this challenge, introducing efficient amount of redundant computations via distributed coded computation has received significant attention. Recent approaches in this area have mainly focused on introducing minimum computational redundancies to tolerate certain number of stragglers. To the best of our knowledge, the current literature lacks a unified end-to-end design in a heterogeneous setting where the workers can vary in their computation and communication capabilities. The contribution of this paper is to devise a novel framework for joint scheduling-coding, in a setting where the workers and the arrival of stream computational jobs are based on stochastic models. In our initial joint scheme, we propose a systematic framework that illustrates how to select a set of workers and how to split the computational load among the selected workers based on their differences in order to minimize the average in-order job execution delay. Through simulations, we demonstrate that the performance of our framework is dramatically better than the performance of naive method that splits the computational load uniformly among the workers, and it is close to the ideal performance.

cs.IT↗

arXiv2021

Low Influence, Utility, and Independence in Differential Privacy: A Curious Case of $3 \choose 2$

We study the relationship between randomized low influence functions and differentially private mechanisms. Our main aim is to formally determine whether differentially private mechanisms are low influence and whether low influence randomized functions can be differentially private. We show that differential privacy does not necessarily imply low influence in a formal sense. However, low influence implies approximate differential privacy. These results hold for both independent and non-independent randomized mechanisms, where an important instance of the former is the widely-used additive noise techniques in the differential privacy literature. Our study also reveals the interesting dynamics between utility, low influence, and independence of a differentially private mechanism. As the name of this paper suggests, we show that any two such features are simultaneously possible. However, in order to have a differentially private mechanism that has both utility and low influence, even under a very mild utility condition, one has to employ non-independent mechanisms.

cs.IT↗

arXiv2021

Spatial Concentration of Caching in Wireless Heterogeneous Networks

We propose a decentralized caching policy for wireless heterogeneous networks that makes content placement decisions based on pairwise interactions between cache nodes. We call our proposed scheme γ-exclusion cache placement (GEC), where a parameter γ controls an exclusion radius that discourages nearby caches from storing redundant content. GEC takes into account item popularity and the nodes' caching priorities and leverages negative dependence to relax the classic 0-1 knapsack problem to yield spatially balanced sampling across caches. We show that GEC guarantees a better concentration (reduced variance) of the required cache storage size than the state of the art, and that the cache size constraints can be satisfied with high probability. Given a cache hit probability target, we compare the 95\% confidence intervals of the required cache sizes for three caching schemes: (i) independent placement, (ii) hard exclusion caching (HEC), and (iii) the proposed GEC approach. For uniform spatial traffic, we demonstrate that GEC provides approximately a 3x and 2x reduction in required cache size over (i) and (ii), respectively. For non-uniform spatial traffic based on realistic peak-hour variations in urban scenarios, the gains are even greater.

cs.IT↗

arXiv2020

Serial Quantization for Sparse Time Sequences

Sparse signals are encountered in a broad range of applications. In order to process these signals using digital hardware, they must be first sampled and quantized using an analog-to-digital convertor (ADC), which typically operates in a serial scalar manner. In this work, we propose a method for serial quantization of sparse time sequences (SQuaTS) inspired by group testing theory, which is designed to reliably and accurately quantize sparse signals acquired in a sequential manner using serial scalar ADCs. Unlike previously proposed approaches which combine quantization and compressed sensing (CS), our SQuaTS scheme updates its representation on each incoming analog sample and does not require the complete signal to be observed and stored in analog prior to quantization. We characterize the asymptotic tradeoff between accuracy and quantization rate of SQuaTS as well as its computational burden. We also propose a variation of SQuaTS, which trades rate for computational efficiency. Next, we show how SQuaTS can be naturally extended to distributed quantization scenarios, where a set of jointly sparse time sequences are acquired individually and processed jointly. Our numerical results demonstrate that SQuaTS is capable of achieving substantially improved representation accuracy over previous CS-based schemes without requiring the complete set of analog signal samples to be observed prior to its quantization, making it an attractive approach for acquiring sparse time sequences.

cs.IT↗

arXiv2020

Keep the bursts and ditch the interleavers

To facilitate applications in IoT, 5G, and beyond, there is an engineering need to enable high-rate, low-latency communications. Errors in physical channels typically arrive in clumps, but most decoders are designed assuming that channels are memoryless. As a result, communication networks rely on interleaving over tens of thousands of bits so that channel conditions match decoder assumptions. Even for short high rate codes, awaiting sufficient data to interleave at the sender and de-interleave at the receiver is a significant source of unwanted latency. Using existing decoders with non-interleaved channels causes a degradation in block error rate performance owing to mismatch between the decoder's channel model and true channel behaviour. Through further development of the recently proposed Guessing Random Additive Noise Decoding (GRAND) algorithm, which we call GRAND-MO for GRAND Markov Order, here we establish that by abandoning interleaving and embracing bursty noise, low-latency, short-code, high-rate communication is possible with block error rates that outperform their interleaved counterparts by a substantial margin. Moreover, while most decoders are twinned to a specific code-book structure, GRAND-MO can decode any code. Using this property, we establish that certain well-known structured codes are ill-suited for use in bursty channels, but Random Linear Codes (RLCs) are robust to correlated noise. This work suggests that the use of RLCs with GRAND-MO is a good candidate for applications requiring high throughput with low latency.

cs.IT↗

arXiv2020

Adaptive Causal Network Coding with Feedback for Multipath Multi-hop Communications

We propose a novel multipath multi-hop adaptive and causal random linear network coding (AC-RLNC) algorithm with forward error correction. This algorithm generalizes our joint optimization coding solution for point-to-point communication with delayed feedback. AC-RLNC is adaptive to the estimated channel condition, and is causal, as the coding adjusts the retransmission rates using a priori and posteriori algorithms. In the multipath network, to achieve the desired throughput and delay, we propose to incorporate an adaptive packet allocation algorithm for retransmission, across the available resources of the paths. This approach is based on a discrete water filling algorithm, i.e., bit-filling, but, with two desired objectives, maximize throughput and minimize the delay. In the multipath multi-hop setting, we propose a new decentralized balancing optimization algorithm. This balancing algorithm minimizes the throughput degradation, caused by the variations in the channel quality of the paths at each hop. Furthermore, to increase the efficiency, in terms of the desired objectives, we propose a new selective recoding method at the intermediate nodes. We derive bounds on the throughput and the mean and maximum in order delivery delay of AC-RLNC, both in the multipath and multipath multi-hop case. In the multipath case, we prove that in the non-asymptotic regime, the suggested code may achieve more than 90% of the channel capacity with zero error probability. In the multipath multi-hop case, the balancing procedure is proven to be optimal with regards to the achieved rate. Through simulations, we demonstrate that the performance of our adaptive and causal approach, compared to selective repeat (SR)-ARQ protocol, is capable of gains up to a factor two in throughput and a factor of more than three in delay.

cs.IT↗

arXiv2020

Noise Recycling

We introduce Noise Recycling, a method that enhances decoding performance of channels subject to correlated noise without joint decoding. The method can be used with any combination of codes, code-rates and decoding techniques. In the approach, a continuous realization of noise is estimated from a lead channel by subtracting its decoded output from its received signal. This estimate is then used to improve the accuracy of decoding of an orthogonal channel that is experiencing correlated noise. In this design, channels aid each other only through the provision of noise estimates post-decoding. In a Gauss-Markov model of correlated noise, we constructive establish that noise recycling employing a simple successive order enables higher rates than not recycling noise. Simulations illustrate noise recycling can be employed with any code and decoder, and that noise recycling shows Block Error Rate (BLER) benefits when applying the same predetermined order as used to enhance the rate region. Finally, for short codes we establish that an additional BLER improvement is possible through noise recycling with racing, where the lead channel is not pre-determined, but is chosen on the fly based on which decoder completes first.

cs.IT↗

arXiv2020

Bringing Network Coding into SDN: A Case-study for Highly Meshed Heterogeneous Communications

Modern communications have moved away from point-to-point models to increasingly heterogeneous network models. In this article, we propose a novel controller-based protocol to deploy adaptive causal network coding in heterogeneous and highly-meshed communication networks. Specifically, we consider using Software-Defined-Network (SDN) as the main controller. We first present an architecture for the highly-meshed heterogeneous multi-source multi-destination networks that represents the practical communication networks encountered in the fifth generation of wireless networks (5G) and beyond. Next, we present a promising solution to deploy network coding over the new architecture. In fact, we investigate how to generalize adaptive and causal random linear network coding (AC-RLNC), proposed for multipath multi-hop (MP-MH) communication channels, to a protocol for the new multi-source multi-destination network architecture using controller. To this end, we present a modularized implementation of AC-RLNC solution where the modules work together in a distributed fashion and perform the AC-RLNC technology. We also present a new controller-based setting through which the network coding modules can communicate and can attain their required information. Finally, we briefly discuss how the proposed architecture and network coding solution provide a good opportunity for future technologies, e.g., distributed coded computation and storage, mmWave communication environments, and innovative and efficient security features.

cs.NI↗

arXiv2020

Function Load Balancing over Networks

Using networks as a means of computing can reduce the communication flow or the total number of bits transmitted over the networks. In this paper, we propose to distribute the computation load in stationary networks, and formulate a flow-based delay minimization problem that jointly captures the aspects of communications and computation. We exploit the distributed compression scheme of Slepian-Wolf that is applicable under any protocol information where nodes can do compression independently using different codebooks. We introduce the notion of entropic surjectivity as a measure to determine how sparse the function is and to understand the limits of functional compression for computation. We leverage Little's Law for stationary systems to provide a connection between surjectivity and the computation processing factor that reflects the proportion of flow that requires communications. This connection gives us an understanding of how much a node (in isolation) should compute to communicate the desired function within the network without putting any assumptions on the topology. Our results suggest that to effectively compute different function classes that have different entropic surjectivities, the networks can be re-structured with the transition probabilities being tailored for functions, i.e., task-based link reservations, which can enable mixing versus separately processing of a diverse function classes. They also imply that most of the available resources are reserved for computing low complexity functions versus fewer resources for processing of high complexity ones. We numerically evaluate our technique for search, MapReduce, and classification functions, and infer how sensitive the processing factor for each computation task to the entropic surjectivity is.

cs.IT↗