SearcharxivSearch

arXiv subjects

Lara Dolecek

Publications and source records attributed to Lara Dolecek.

At least 19 recordsLinked to original sources

Improved Interactive Protocol for Synchronizing From Deletions

Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the other and related through a constant rate of deletions, using an improved communication protocol. Building upon prior work, we integrate advanced multi-deletion correction codes into an existing baseline protocol, which previously relied on single-deletion correction. Our proposed protocol reduces communication cost by leveraging more general partitioning techniques as well as multi-deletion error correction. We derive a generalized upper bound on the expected number of transmitted bits, applicable to a broad class of deletion correction codes. Experimental results demonstrate that our approach outperforms the baseline in communication cost. These findings establish the efficacy of the improved protocol in achieving low-redundancy synchronization in scenarios where deletion errors occur.

cs.IT

Block-MDS QC-LDPC Codes for Information Reconciliation in Key Distribution

Quantum key distribution (QKD) is a popular protocol that provides information theoretically secure keys to multiple parties. Two important post-processing steps of QKD are 1) the information reconciliation (IR) step, where parties reconcile mismatches in generated keys through classical communication, and 2) the privacy amplification (PA) step, where parties distill their common key into a new secure key that the adversary has little to no information about. In general, these two steps have been abstracted as two distinct problems. In this work, we consider a new technique of performing the IR and PA steps jointly through sampling that relaxes the requirement on the IR step, allowing for more success in key creation. We provide a novel LDPC code construction known as Block-MDS QC-LDPC codes that can utilize the relaxed requirement by creating LDPC codes with pre-defined sub-matrices of full-rank. We demonstrate through simulations that our technique of sampling can provide notable gains in successfully creating secret keys.

cs.IT

Fully Private Grouped Matrix Multiplication with Colluding Workers

In this paper, we present a novel variation of the coded matrix multiplication problem which we refer to as fully private grouped matrix multiplication (FPGMM). In FPGMM, a master wants to compute a group of matrix products between two matrix libraries that can be accessed by all workers while ensuring that any number of prescribed colluding workers learn nothing about which matrix products the master desires, nor the number of matrix products. We present an achievable scheme using a variant of Cross-Subspace Alignment (CSA) codes that offers flexibility in communication and computation cost. Additionally, we demonstrate how our scheme can outperform naive applications of schemes used in a related privacy focused coded matrix multiplication problem.

cs.IT

Non-Binary LDPC Code Design for Energy-Time Entanglement Quantum Key Distribution

In energy-time entanglement Quantum Key Distribution (QKD), two users extract a shared secret key from the arrival times (discretized as symbols) of entangled photon pairs. In prior work, Zhou et al. proposed a multi-level coding (MLC) scheme that splits the observed symbols into bit layers and utilizes binary Low-Density Parity-Check (LDPC) codes for reconciliation of the symbols. While binary LDPC codes offer low latency for key generation, splitting the symbols into bits results in a loss of key generation rate due to error propagation. Additionally, existing LDPC codes do not fully utilize the properties of the QKD channel to optimize the key rates. In this paper, we mitigate the above issues by first generalizing the MLC scheme to a non-binary(NB) MLC scheme that has layers with non-binary symbols and utilizes NB-LDPC codes. We show the NB-MLC scheme offers flexibility in system design. Additionally, we show that the NB-MLC scheme with a small symbol size per layer offers the best trade-off between latency and key rate. We then propose a framework to jointly optimize the rate and degree profile of the NB-LDPC codes that is tailored towards the QKD channel resulting in higher key rates than prior work.

cs.IT

QKD Based on Time-Entangled Photons and its Key-Rate Promise

For secure practical systems, quantum key distribution (QKD) must provide high key rates over long distances. Time-entanglement-based QKD promises to increase the secret key rate and distribution distances compared to other QKD implementations. This article describes the major steps in QKD protocols, focusing on the nascent QKD technology based on high-dimensional time-bin entangled photons. We overview state-of-the-art from the information and coding theory perspective. In particular, we discuss the key rate loss due to single-photon detector imperfections. We hope the open questions posed and discussed in this paper will inspire information and coding theorists to contribute to and impact fledgling quantum applications and influence future quantum communication systems.

cs.IT

Polar Coded Merkle Tree: Mitigating Data Availability Attacks in Blockchain Systems Using Informed Polar Code Design

Data availability (DA) attack is a well-known problem in certain blockchains where users accept an invalid block with unavailable portions. Previous works have used LDPC and 2-D Reed Solomon (2DRS) codes with Merkle trees to mitigate DA attacks. These codes perform well across various metrics such as DA detection probability and communication cost. However, these codes are difficult to apply to blockchains with large blocks due to large decoding complexity and coding fraud proof size (2D-RS codes), and intractable code guarantees for large code lengths (LDPC codes). In this paper, we focus on large block size applications and address the above challenges by proposing the novel Polar Coded Merkle Tree (PCMT): a Merkle tree encoded using the encoding graph of polar codes. We provide a specialized polar code design algorithm called Sampling Efficient Freezing and an algorithm to prune the polar encoding graph. We demonstrate that the PCMT built using the above techniques results in a better DA detection probability and communication cost compared to LDPC codes, has a lower coding fraud proof size compared to LDPC and 2D-RS codes, provides tractable code guarantees at large code lengths (similar to 2D-RS codes), and has comparable decoding complexity to 2D-RS and LDPC codes.

cs.IT

A Unified Spatially Coupled Code Design: Threshold, Cycles, and Locality

Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in this paper we present a unified framework for jointly optimizing the codes' thresholds and cycle counts to address both regimes. The framework is based on efficient traversal and pruning of the code search space, building on the fact that the performance of a protograph-based SC-LDPC code depends on some characteristics of the code's partitioning matrix, which by itself is much smaller than the code's full parity-check matrix. We then propose an algorithm that traverses all nonequivalent partitioning matrices, and outputs a list of codes, each offering an attractive point on the trade-off between asymptotic and finite-length performance. We further extend the framework to designing SC-LDPC codes with sub-block locality, which is a recently introduced feature offering fast access to sub-blocks within the code block. Our simulations show that our framework results in SC-LDPC codes that outperform the state-of-the-art constructions, and that it offers the flexibility to choose low-SNR, high-SNR, or in-between SNR region as the primary design target.

cs.IT

Overcoming Data Availability Attacks in Blockchain Systems: Short Code-Length LDPC Code Design for Coded Merkle Tree

Light nodes are clients in blockchain systems that only store a small portion of the blockchain ledger. In certain blockchains, light nodes are vulnerable to a data availability (DA) attack where a malicious node makes the light nodes accept an invalid block by hiding the invalid portion of the block from the nodes in the system. Recently, a technique based on LDPC codes called Coded Merkle Tree was proposed by Yu et al. that enables light nodes to detect a DA attack by randomly requesting/sampling portions of the block from the malicious node. However, light nodes fail to detect a DA attack with high probability if a malicious node hides a small stopping set of the LDPC code. In this paper, we demonstrate that a suitable co-design of specialized LDPC codes and the light node sampling strategy leads to a high probability of detection of DA attacks. We consider different adversary models based on their computational capabilities of finding stopping sets. For the different adversary models, we provide new specialized LDPC code constructions and coupled light node sampling strategies and demonstrate that they lead to a higher probability of detection of DA attacks compared to approaches proposed in earlier literature.

cs.IT

Polar Coded Merkle Tree: Improved Detection of Data Availability Attacks in Blockchain Systems

Light nodes in blockchain systems are known to be vulnerable to data availability (DA) attacks where they accept an invalid block with unavailable portions. Previous works have used LDPC and 2-D Reed Solomon (2D-RS) codes with Merkle Trees to mitigate DA attacks. While these codes have demonstrated improved performance across a variety of metrics such as DA detection probability, they are difficult to apply to blockchains with large blocks due to generally intractable code guarantees for large codelengths (LDPC), large decoding complexity (2D-RS), or large coding fraud proof sizes (2D-RS). We address these issues by proposing the novel Polar Coded Merkle Tree (PCMT) which is a Merkle Tree built from the encoding graphs of polar codes and a specialized polar code construction called Sampling-Efficient Freezing (SEF). We demonstrate that the PCMT with SEF polar codes performs well in detecting DA attacks for large block sizes.

cs.IT

Variable Coded Batch Matrix Multiplication

A majority of coded matrix-matrix computation literature has broadly focused in two directions: matrix partitioning for computing a single computation task and batch processing of multiple distinct computation tasks. While these works provide codes with good straggler resilience and fast decoding for their problem spaces, these codes would not be able to take advantage of the natural redundancy of re-using matrices across batch jobs. In this paper, we introduce the Variable Coded Distributed Batch Matrix Multiplication (VCDBMM) problem which tasks a distributed system to perform batch matrix multiplication where matrices are not necessarily distinct among batch jobs. Inspired in part by Cross-Subspace Alignment codes, we develop Flexible Cross-Subspace Alignments (FCSA) codes that are flexible enough to utilize this redundancy. We provide a full characterization of FCSA codes which allow for a wide variety of system complexities including good straggler resilience and fast decoding. We theoretically demonstrate that, under certain practical conditions, FCSA codes are within a factor of 2 of the optimal solution when it comes to straggler resilience. Furthermore, our simulations demonstrate that our codes can achieve even better optimality gaps in practice, even going as low as 1.7.

cs.IT

Breaking the Computational Bottleneck: Design of Near-Optimal High-Memory Spatially-Coupled Codes

Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an underlying block code, followed by rearranging and concatenating the partitioned components in a convolutional manner. The number of partitioned components determines the memory of SC codes. In this paper, we investigate the relation between the performance of SC codes and the density distribution of partitioning matrices. While adopting higher memories results in improved SC code performance, obtaining finite-length, high-performance SC codes with high memory is known to be computationally challenging. We break this computational bottleneck by developing a novel probabilistic framework that obtains (locally) optimal density distributions via gradient descent. Starting from random partitioning matrices abiding by the obtained distribution, we perform low-complexity optimization algorithms that minimize the number of detrimental objects to construct high-memory, high-performance quasi-cyclic SC codes. We apply our framework to various objects of interests, from the simplest short cycles, to more sophisticated objects such as concatenated cycles aiming at finer-grained optimization. Simulation results show that codes obtained through our proposed method notably outperform state-of-the-art SC codes with the same constraint length and optimized SC codes with uniform partitioning. The performance gain is shown to be universal over a variety of channels, from canonical channels such as additive white Gaussian noise and binary symmetric channels, to practical channels underlying flash memory and magnetic recording systems.

cs.IT

Communication-Efficient LDPC Code Design for Data Availability Oracle in Side Blockchains

A popular method of improving the throughput of blockchain systems is by running smaller side blockchains that push the hashes of their blocks onto a trusted blockchain. Side blockchains are vulnerable to stalling attacks where a side blockchain node pushes the hash of a block to the trusted blockchain but makes the block unavailable to other side blockchain nodes. Recently, Sheng et al. proposed a data availability oracle based on LDPC codes and a data dispersal protocol as a solution to the above problem. While showing improvements, the codes and dispersal protocol were designed disjointly which may not be optimal in terms of the communication cost associated with the oracle. In this paper, we provide a tailored dispersal protocol and specialized LDPC code construction based on the Progressive Edge Growth (PEG) algorithm, called the dispersal-efficient PEG (DE-PEG) algorithm, aimed to reduce the communication cost associated with the new dispersal protocol. Our new code construction reduces the communication cost and, additionally, is less restrictive in terms of system design.

cs.IT

Channel Models and Coding Solutions for 1S1R Crossbar Resistive Memory with High Line Resistance

Crossbar resistive memory with the 1 Selector 1 Resistor (1S1R) structure is attractive for nonvolatile, high-density, and low-latency storage-class memory applications. As technology scales down to the single-nm regime, the increasing resistivity of wordline/bitline becomes a limiting factor to device reliability. This paper presents write/read communication channels while considering the line resistance and device variabilities by statistically relating the degraded write/read margins and the channel parameters. Binary asymmetric channel (BAC) models are proposed for the write/read operations. Simulations based on these models suggest that the bit-error rate of devices are highly non-uniform across the memory array. These models provide quantitative tools for evaluating the trade-offs between memory reliability and design parameters, such as array size, technology nodes, and aspect ratio, and also for designing coding-theoretic solutions that would be most effective for crossbar memory. Method for optimizing the read threshold is proposed to reduce the raw bit-error rate (RBER). We propose two schemes for efficient channel coding based on Bose-Chaudhuri-Hocquenghem (BCH) codes. An interleaved coding scheme is proposed to mitigate the non-uniformity of reliability and a location dependent coding framework is proposed to leverage this non-uniformity. Both of our proposed coding schemes effectively reduce the undetected bit-error rate (UBER).

eess.SY

Hierarchical Hybrid Error Correction for Time-Sensitive Devices at the Edge

Computational storage, known as a solution to significantly reduce the latency by moving data-processing down to the data storage, has received wide attention because of its potential to accelerate data-driven devices at the edge. To meet the insatiable appetite for complicated functionalities tailored for intelligent devices such as autonomous vehicles, properties including heterogeneity, scalability, and flexibility are becoming increasingly important. Based on our prior work on hierarchical erasure coding that enables scalability and flexibility in cloud storage, we develop an efficient decoding algorithm that corrects a mixture of errors and erasures simultaneously. We first extract the basic component code, the so-called extended Cauchy (EC) codes, of the proposed coding solution. We prove that the class of EC codes is strictly larger than that of relevant codes with known explicit decoding algorithms. Motivated by this finding, we then develop an efficient decoding method for the general class of EC codes, based on which we propose the local and global decoding algorithms for the hierarchical codes. Our proposed hybrid error correction not only enables the usage of hierarchical codes in computational storage at the edge, but also applies to any Cauchy-like codes and allows potentially wider applications of the EC codes.

cs.IT

GRADE-AO: Towards Near-Optimal Spatially-Coupled Codes With High Memories

Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their excellent performance. SC codes are constructed by partitioning an underlying block code, followed by rearranging and concatenating the partitioned components in a "convolutional" manner. The number of partitioned components determines the "memory" of SC codes. While adopting higher memories results in improved SC code performance, obtaining optimal SC codes with high memory is known to be hard. In this paper, we investigate the relation between the performance of SC codes and the density distribution of partitioning matrices. We propose a probabilistic framework that obtains (locally) optimal density distributions via gradient descent. Starting from random partitioning matrices abiding by the obtained distribution, we perform low complexity optimization algorithms over the cycle properties to construct high memory, high performance quasi-cyclic SC codes. Simulation results show that codes obtained through our proposed method notably outperform state-of-the-art SC codes with the same constraint length and codes with uniform partitioning.

cs.IT

Concentrated Stopping Set Design for Coded Merkle Tree: Improving Security Against Data Availability Attacks in Blockchain Systems

In certain blockchain systems, light nodes are clients that download only a small portion of the block. Light nodes are vulnerable to data availability (DA) attacks where a malicious node hides an invalid portion of the block from the light nodes. Recently, a technique based on erasure codes called Coded Merkle Tree (CMT) was proposed by Yu et al. that enables light nodes to detect a DA attack with high probability. The CMT is constructed using LDPC codes for fast decoding but can fail to detect a DA attack if a malicious node hides a small stopping set of the code. To combat this, Yu et al. used well-studied techniques to design random LDPC codes with high minimum stopping set size. Although effective, these codes are not necessarily optimal for this application. In this paper, we demonstrate a more specialized LDPC code design to improve the security against DA attacks. We achieve this goal by providing a deterministic LDPC code construction that focuses on concentrating stopping sets to a small group of variable nodes rather than only eliminating stopping sets. We design these codes by modifying the Progressive Edge Growth algorithm into a technique called the entropy-constrained PEG (EC-PEG) algorithm. This new method demonstrates a higher probability of detecting DA attacks and allows for good codes at short lengths.

cs.IT

Write and Read Channel Models for 1S1R Crossbar Resistive Memory with High Line Resistance

Crossbar resistive memory with 1 Selector 1 Resistor (1S1R) structure is attractive for low-cost and high-density nonvolatile memory applications. As technology scales down to the single-nm regime, the increasing resistivity of wordline/bitline becomes a limiting factor to device reliability. This paper presents write/read communication channels while considering the line resistance and device variabilities by statistically relating the degraded write/read margins and the channel parameters. Binary asymmetric channel (BAC) models are proposed for the write/read operations. Simulations based on these models suggest that the bit-error rate of devices are highly non-uniform across the memory array. These models provide quantitative tools for evaluating the trade-offs between memory reliability and design parameters, such as array size, technology nodes, and aspect ratio, and also for designing coding-theoretic solutions that would be most effective for crossbar memory.

eess.SY

Hierarchical Coding for Cloud Storage: Topology-Adaptivity, Scalability, and Flexibility

In order to accommodate the ever-growing data from various, possibly independent, sources and the dynamic nature of data usage rates in practical applications, modern cloud data storage systems are required to be scalable, flexible, and heterogeneous. The recent rise of the blockchain technology is also moving various information systems towards decentralization to achieve high privacy at low costs. While codes with hierarchical locality have been intensively studied in the context of centralized cloud storage due to their effectiveness in reducing the average reading time, those for decentralized storage networks (DSNs) have not yet been discussed. In this paper, we propose a joint coding scheme where each node receives extra protection through the cooperation with nodes in its neighborhood in a heterogeneous DSN with any given topology. This work extends and subsumes our prior work on coding for centralized cloud storage. In particular, our proposed construction not only preserves desirable properties such as scalability and flexibility, which are critical in dynamic networks, but also adapts to arbitrary topologies, a property that is essential in DSNs but has been overlooked in existing works.

cs.IT