arXiv subjects

Lara Dolecek

Publications and source records attributed to Lara Dolecek.

At least 37 records · Page 2Linked to original sources

arXiv2020

Spatially Coupled Codes with Sub-Block Locality: Joint Finite Length-Asymptotic Design Approach

SC-LDPC codes with sub-block locality can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus providing fast access to the coded information. The same code can also be decoded globally using the entire code block, for increased data reliability. In this paper, we pursue the analysis and design of such codes from both finite-length and asymptotic lenses. This mixed approach has rarely been applied in designing SC codes, but it is beneficial for optimizing code graphs for local and global performance simultaneously. Our proposed framework consists of two steps: 1) designing the local code for both threshold and cycle counts, and 2) designing the coupling of local codes for best cycle count in the global design.

cs.IT↗

arXiv2020

Topology-Aware Cooperative Data Protection in Blockchain-Based Decentralized Storage Networks

From currency to cloud storage systems, the continuous rise of the blockchain technology is moving various information systems towards decentralization. Blockchain-based decentralized storage networks (DSNs) offer significantly higher privacy and lower costs to customers compared with centralized cloud storage associated with specific vendors. Coding is required in order to retrieve data stored on failing components. While coding solutions for centralized storage have been intensely studied, topology-aware coding for heterogeneous 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. As an extension of, which also subsumes, our prior work on coding for centralized cloud storage, our proposed construction preserves desirable properties such as scalability and flexibility in networks with varying topologies.

cs.IT↗

arXiv2020

Non-Uniform Windowed Decoding For Multi-Dimensional Spatially-Coupled LDPC Codes

In this paper, we propose a non-uniform windowed decoder for multi-dimensional spatially-coupled LDPC (MD-SC-LDPC) codes over the binary erasure channel. An MD-SC-LDPC code is constructed by connecting together several SC-LDPC codes into one larger code that provides major benefits over a variety of channel models. In general, SC codes allow for low-latency windowed decoding. While a standard windowed decoder can be naively applied, such an approach does not fully utilize the unique structure of MD-SC-LDPC codes. In this paper, we propose and analyze a novel non-uniform decoder to provide more flexibility between latency and reliability. Our theoretical derivations and empirical results show that our non-uniform decoder greatly improves upon the standard windowed decoder in terms of design flexibility, latency, and complexity.

cs.IT↗

arXiv2020

Efficient Information Reconciliation for Energy-Time Entanglement Quantum Key Distribution

Graph based codes such as low density parity check (LDPC) codes have been shown promising for the information reconciliation phase in quantum key distribution (QKD). However, existing graph coding schemes have not fully utilized the properties of the QKD channel. In this work, we first investigate the channel statistics for discrete variable (DV) QKD based on energy-time entangled photons. We then establish a so-called balanced modulation scheme that is promising for this channel. Based on the modulation, we propose a joint local-global graph coding scheme that is expected to achieve good error-correction performance.

cs.IT↗

arXiv2020

Theoretical Bounds and Constructions of Codes in the Generalized Cayley Metric

Permutation codes have recently garnered substantial research interest due to their potential in various applications including cloud storage systems, genome resequencing and flash memories. In this paper, we study the theoretical bounds and constructions of permutation codes in the generalized Cayley metric. The generalized Cayley metric captures the number of generalized transposition errors in a permutation, and subsumes previously studied error types, including transpositions and translocations, without imposing restrictions on the lengths and positions of the translocated segments. Relying on the breakpoint analysis proposed by Chee and Vu, we first propose a coding scheme that is order-optimal albeit not constructive based on this method. We then develop another construction of permutation codes in the generalized Cayley distance. This scheme is both explicit and systematic. We also prove the existence of order-optimal systematic codes and offer a concrete construction based on this method. For the generalized Cayley metric, we prove that our coding schemes have less redundancy than the existing codes based on interleaving when the codelength is sufficiently large and the number of errors is relatively small.

cs.IT↗

arXiv2019

A Combinatorial Methodology for Optimizing Non-Binary Graph-Based Codes: Theoretical Analysis and Applications in Data Storage

Non-binary (NB) low-density parity-check (LDPC) codes are graph-based codes that are increasingly being considered as a powerful error correction tool for modern dense storage devices. The increasing levels of asymmetry incorporated by the channels underlying modern dense storage systems exacerbates the error floor problem. In a recent research, the weight consistency matrix (WCM) framework was introduced as an effective NB-LDPC code optimization methodology that is suitable for modern Flash memory and magnetic recording (MR) systems. In this paper, we provide the in-depth theoretical analysis needed to understand and properly apply the WCM framework. We focus on general absorbing sets of type two (GASTs). In particular, we introduce a novel tree representation of a GAST called the unlabeled GAST tree, using which we prove that the WCM framework is optimal. Then, we enumerate the WCMs. We demonstrate the significance of the savings achieved by the WCM framework in the number of matrices processed to remove a GAST. Moreover, we provide a linear-algebraic analysis of the null spaces of WCMs associated with a GAST. We derive the minimum number of edge weight changes needed to remove a GAST via its WCMs, along with how to choose these changes. Additionally, we propose a new set of problematic objects, namely the oscillating sets of type two (OSTs), which contribute to the error floor of NB-LDPC codes with even column weights on asymmetric channels, and we show how to customize the WCM framework to remove OSTs. We also extend the domain of the WCM framework applications by demonstrating its benefits in optimizing column weight 5 codes, codes used over Flash channels with soft information, and spatially-coupled codes. The performance gains achieved via the WCM framework range between 1 and nearly 2.5 orders of magnitude in the error floor region over interesting channels.

cs.IT↗

arXiv2019

Multi-Dimensional Spatially-Coupled Code Design: Enhancing the Cycle Properties

A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants in the parity-check matrix of a block code into several components and piecing copies of these components in a diagonal structure. By connecting several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better cycle properties than their one-dimensional counterparts. In our framework, the multi-dimensional coupling is performed via an informed relocation of problematic circulants. This work is general in the terms of the number of constituent SC codes that are connected together, the number of neighboring SC codes that each constituent SC code is connected to, and the length of the cycles whose populations we aim to reduce. Finally, we present a decoding algorithm that utilizes the structures of the MD-SC code to achieve lower decoding latency. Compared to the conventional SC codes, our MD-SC codes have a notably lower population of small cycles, and a dramatic BER improvement. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

cs.IT↗

arXiv2019

Coding for Deletion Channels with Multiple Traces

Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple binary and non-binary codes based on Varshamov-Tenengolts (VT) codes. The proposed codes split the codeword in blocks and employ a VT code in each block. The availability of multiple traces helps the decoder to identify deletion-free copies of a block, and to avoid mis-synchronization while decoding. The encoding complexity of the proposed scheme is linear in the codeword length; the decoding complexity is linear in the codeword length, and quadratic in the number of deletions and the number of traces. The proposed scheme offers an explicit low-complexity technique for correcting deletions using multiple traces.

cs.IT↗

arXiv2019

A Finite-Length Construction of Irregular Spatially-Coupled Codes

Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes offer performance advantage over their regular counterparts. In this paper, we present a novel combinatorial framework for designing finite-length irregular SC LDPC codes. Our irregular SC codes have the desirable properties of regular SC codes thanks to their structure while offering significant performance benefits that come with the node degree irregularity. Coding constructions proposed in this work contribute to the existing portfolio of finite-length graph code designs.

cs.IT↗

arXiv2019

Hierarchical Coding to Enable Scalability and Flexibility in Heterogeneous Cloud Storage

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. Codes with hierarchical locality have been intensively studied due to their effectiveness in reducing the average reading time in cloud storage. In this paper, we present the first codes with hierarchical locality that achieve scalability and flexibility in heterogeneous cloud storage using small field size. We propose a double-level construction utilizing so-called Cauchy Reed-Solomon codes. We then develop a triple-level construction based on this double-level code; this construction can be easily generalized into any hierarchical structure with a greater number of layers since it naturally achieves scalability in the cloud storage systems.

cs.IT↗

arXiv2019

A Channel-Aware Combinatorial Approach to Design High Performance Spatially-Coupled Codes for Magnetic Recording Systems

Because of their capacity-approaching performance and their complexity/latency advantages, spatially-coupled (SC) codes are among the most attractive error-correcting codes for use in modern dense data storage systems. SC codes are constructed by partitioning an underlying block code and coupling the partitioned components. Here, we focus on circulant-based SC codes. Recently, the optimal overlap (OO), circulant power optimizer (CPO) approach was introduced to construct high performance SC codes for additive white Gaussian noise (AWGN) and Flash channels. The OO stage operates on the protograph of the SC code to derive the optimal partitioning that minimizes the number of graphical objects that undermine the performance of SC codes under iterative decoding. Then, the CPO optimizes the circulant powers to further reduce this number. Since the nature of detrimental objects in the graph of a code critically depends on the characteristics of the channel of interest, extending the OO-CPO approach to construct SC codes for channels with intrinsic memory is not a straightforward task. In this paper, we tackle one relevant extension; we construct high performance SC codes for practical 1-D magnetic recording channels, i.e., partial-response (PR) channels. Via combinatorial techniques, we carefully build and solve the optimization problem of the OO partitioning, focusing on the objects of interest in the case of PR channels. Then, we customize the CPO to further reduce the number of these objects in the graph of the code. SC codes designed using the proposed OO-CPO approach for PR channels outperform prior state-of-the-art SC codes by up to around 3 orders of magnitude in frame error rate (FER) and 1.1 dB in signal-to-noise ratio (SNR). More intriguingly, our SC codes outperform structured block codes of the same length and rate by up to around 1.8 orders of magnitude in FER and 0.4 dB in SNR.

cs.IT↗

arXiv2018

Exploiting Errors for Efficiency: A Survey from Circuits to Algorithms

When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, programming languages, and system software can trade deviations from correct behavior for lower resource usage. We present, for the first time, a synthesis of research results on computing systems that only make as many errors as their users can tolerate, from across the disciplines of computer aided design of circuits, digital system design, computer architecture, programming languages, operating systems, and information theory. Rather than over-provisioning resources at each layer to avoid errors, it can be more efficient to exploit the masking of errors occurring at one layer which can prevent them from propagating to a higher layer. We survey tradeoffs for individual layers of computing systems from the circuit level to the operating system level and illustrate the potential benefits of end-to-end approaches using two illustrative examples. To tie together the survey, we present a consistent formalization of terminology, across the layers, which does not significantly deviate from the terminology traditionally used by research communities in their layer of focus.

cs.AR↗

arXiv2018

Multi-Dimensional Spatially-Coupled Code Design Through Informed Relocation of Circulants

A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better girth properties than their 1D-SC counterparts. In our framework, informed multi-dimensional coupling is performed via an optimal relocation and an (optional) power adjustment of problematic circulants in the constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are demonstrated to have up to 85% reduction in the population of the smallest cycle, and up to 3.8 orders of magnitude BER improvement in the early error floor region. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

cs.IT↗

arXiv2018

Coding for Channels with SNR Variation: Spatial Coupling and Efficient Interleaving

In magnetic-recording systems, consecutive sections experience different signal to noise ratios (SNRs). To perform error correction over these systems, one approach is to use an individual block code for each section. However, the performance over a section affected by a lower SNR is weaker compared to the performance over a section affected by a higher SNR. Spatially-coupled (SC) codes are a family of graph-based codes with capacity approaching performance and low latency decoding. An SC code is constructed by partitioning an underlying block code to several component matrices, and coupling copies of the component matrices together. The contribution of this paper is threefold. First, we present a new partitioning technique to efficiently construct SC codes with column weights 4 and 6. Second, we present an SC code construction for channels with SNR variation. Our SC code construction provides local error correction for each section by means of the underlying codes that cover one section each, and simultaneously, an added level of error correction by means of coupling among the underlying codes. Third, we introduce a low-complexity interleaving scheme specific to SC codes that further improves their performance over channels with SNR variation. Our simulation results show that our SC codes outperform individual block codes by more than 1 and 2 orders of magnitudes in the error floor region compared to the block codes with and without regular interleaving, respectively. This improvement is more pronounced by increasing the memory and column weight.

cs.IT↗

arXiv2018

Correcting Grain-Errors in Magnetic Media

This paper studies new bounds and constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error. In many cases of interest, our results improve upon the currently best known bounds and constructions. Some of the approaches adopted in the context of grain-errors may have application to other channel models.

cs.IT↗

arXiv2018

High Performance Non-Binary Spatially-Coupled Codes for Flash Memories

Modern dense Flash memory devices operate at very low error rates, which require powerful error correcting coding (ECC) techniques. An emerging class of graph-based ECC techniques that has broad applications is the class of spatially-coupled (SC) codes, where a block code is partitioned into components that are then rewired multiple times to construct an SC code. Here, our focus is on SC codes with the underlying circulant-based structure. In this paper, we present a three-stage approach for the design of high performance non-binary SC (NB-SC) codes optimized for practical Flash channels; we aim at minimizing the number of detrimental general absorbing sets of type two (GASTs) in the graph of the designed NB-SC code. In the first stage, we deploy a novel partitioning mechanism, called the optimal overlap partitioning, which acts on the protograph of the SC code to produce optimal partitioning corresponding to the smallest number of detrimental objects. In the second stage, we apply a new circulant power optimizer to further reduce the number of detrimental GASTs. In the third stage, we use the weight consistency matrix framework to manipulate edge weights to eliminate as many as possible of the GASTs that remain in the NB-SC code after the first two stages (that operate on the unlabeled graph of the code). Simulation results reveal that NB-SC codes designed using our approach outperform state-of-the-art NB-SC codes when used over Flash channels.

cs.IT↗

arXiv2018

Finite-Length Construction of High Performance Spatially-Coupled Codes via Optimized Partitioning and Lifting

Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention thanks to their capacity approaching performance and low decoding latency. An SC code is constructed by partitioning an underlying block code into a number of components and coupling their copies together. In this paper, we first introduce a general approach for the enumeration of detrimental combinatorial objects in the graph of finite-length SC codes. Our approach is general in the sense that it effectively works for SC codes with various column weights and memories. Next, we present a two-stage framework for the construction of high-performance binary SC codes optimized for additive white Gaussian noise channel; we aim at minimizing the number of detrimental combinatorial objects in the error floor regime. In the first stage, we deploy a novel partitioning scheme, called the optimal overlap partitioning, to produce optimal partitioning corresponding to the smallest number of detrimental objects. In the second stage, we apply a new circulant power optimizer to further reduce the number of detrimental objects in the lifted graph. An SC code constructed by our new framework has nearly 5 orders of magnitudes error floor performance improvement compared to the uncoupled setting.

cs.IT↗

arXiv2017

Don't Fear the Bit Flips: Optimized Coding Strategies for Binary Classification

After being trained, classifiers must often operate on data that has been corrupted by noise. In this paper, we consider the impact of such noise on the features of binary classifiers. Inspired by tools for classifier robustness, we introduce the same classification probability (SCP) to measure the resulting distortion on the classifier outputs. We introduce a low-complexity estimate of the SCP based on quantization and polynomial multiplication. We also study channel coding techniques based on replication error-correcting codes. In contrast to the traditional channel coding approach, where error-correction is meant to preserve the data and is agnostic to the application, our schemes specifically aim to maximize the SCP (equivalently minimizing the distortion of the classifier output) for the same redundancy overhead.

stat.ML↗