arXiv subjects

Lara Dolecek

Publications and source records attributed to Lara Dolecek.

42 records · Page 3Linked to original sources

arXiv2017

Exact Reconstruction from Insertions in Synchronization Codes

This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes. These sequences have been corrupted by a fixed number of symbol insertions (larger than the minimum edit distance of the code), yielding a number of distinct traces to be used for reconstruction. We wish to know the minimum number of traces needed for exact reconstruction. This is a general version of a problem tackled by Levenshtein for uncoded sequences. We introduce an exact formula for the maximum number of common supersequences shared by sequences at a certain edit distance, yielding an upper bound on the number of distinct traces necessary to guarantee exact reconstruction. Without specific knowledge of the codewords, this upper bound is tight. We apply our results to the famous single deletion/insertion-correcting Varshamov-Tenengolts (VT) codes and show that a significant number of VT codeword pairs achieve the worst-case number of outputs needed for exact reconstruction. We also consider extensions to other channels, such as adversarial deletion and insertion/deletion channels and probabilistic channels.

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arXiv2015

A Perspective on Future Research Directions in Information Theory

Information theory is rapidly approaching its 70th birthday. What are promising future directions for research in information theory? Where will information theory be having the most impact in 10-20 years? What new and emerging areas are ripe for the most impact, of the sort that information theory has had on the telecommunications industry over the last 60 years? How should the IEEE Information Theory Society promote high-risk new research directions and broaden the reach of information theory, while continuing to be true to its ideals and insisting on the intellectual rigor that makes its breakthroughs so powerful? These are some of the questions that an ad hoc committee (composed of the present authors) explored over the past two years. We have discussed and debated these questions, and solicited detailed inputs from experts in fields including genomics, biology, economics, and neuroscience. This report is the result of these discussions.

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arXiv2013

Spatially Coupled Sparse Codes on Graphs - Theory and Practice

Since the discovery of turbo codes 20 years ago and the subsequent re-discovery of low-density parity-check codes a few years later, the field of channel coding has experienced a number of major advances. Up until that time, code designers were usually happy with performance that came within a few decibels of the Shannon Limit, primarily due to implementation complexity constraints, whereas the new coding techniques now allow performance within a small fraction of a decibel of capacity with modest encoding and decoding complexity. Due to these significant improvements, coding standards in applications as varied as wireless mobile transmission, satellite TV, and deep space communication are being updated to incorporate the new techniques. In this paper, we review a particularly exciting new class of low-density parity-check codes, called spatially-coupled codes, which promise excellent performance over a broad range of channel conditions and decoded error rate requirements.

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arXiv2013

A Deterministic Polynomial-Time Protocol for Synchronizing from Deletions

In this paper, we consider a synchronization problem between nodes $A$ and $B$ that are connected through a two--way communication channel. {Node $A$} contains a binary file $X$ of length $n$ and {node $B$} contains a binary file $Y$ that is generated by randomly deleting bits from $X$, by a small deletion rate $β$. The location of deleted bits is not known to either node $A$ or node $B$. We offer a deterministic synchronization scheme between nodes $A$ and $B$ that needs a total of $O(nβ\log \frac{1}β)$ transmitted bits and reconstructs $X$ at node $B$ with probability of error that is exponentially low in the size of $X$. Orderwise, the rate of our scheme matches the optimal rate for this channel.

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arXiv2012

The Cycle Consistency Matrix Approach to Absorbing Sets in Separable Circulant-Based LDPC Codes

For LDPC codes operating over additive white Gaussian noise channels and decoded using message-passing decoders with limited precision, absorbing sets have been shown to be a key factor in error floor behavior. Focusing on this scenario, this paper introduces the cycle consistency matrix (CCM) as a powerful analytical tool for characterizing and avoiding absorbing sets in separable circulant-based (SCB) LDPC codes. SCB codes include a wide variety of regular LDPC codes such as array-based LDPC codes as well as many common quasi-cyclic codes. As a consequence of its cycle structure, each potential absorbing set in an SCB LDPC code has a CCM, and an absorbing set can be present in an SCB LDPC code only if the associated CCM has a nontrivial null space. CCM-based analysis can determine the multiplicity of an absorbing set in an SCB code and CCM-based constructions avoid certain small absorbing sets completely. While these techniques can be applied to an SCB code of any rate, lower-rate SCB codes can usually avoid small absorbing sets because of their higher variable node degree. This paper focuses attention on the high-rate scenario in which the CCM constructions provide the most benefit. Simulation results demonstrate that under limited-precision decoding the new codes have steeper error-floor slopes and can provide one order of magnitude of improvement in the low FER region.

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arXiv2011

Absorbing Set Spectrum Approach for Practical Code Design

This paper focuses on controlling the absorbing set spectrum for a class of regular LDPC codes known as separable, circulant-based (SCB) codes. For a specified circulant matrix, SCB codes all share a common mother matrix, examples of which are array-based LDPC codes and many common quasi-cyclic codes. SCB codes retain the standard properties of quasi-cyclic LDPC codes such as girth, code structure, and compatibility with efficient decoder implementations. In this paper, we define a cycle consistency matrix (CCM) for each absorbing set of interest in an SCB LDPC code. For an absorbing set to be present in an SCB LDPC code, the associated CCM must not be full columnrank. Our approach selects rows and columns from the SCB mother matrix to systematically eliminate dominant absorbing sets by forcing the associated CCMs to be full column-rank. We use the CCM approach to select rows from the SCB mother matrix to design SCB codes of column weight 5 that avoid all low-weight absorbing sets (4, 8), (5, 9), and (6, 8). Simulation results demonstrate that the newly designed code has a steeper error-floor slope and provides at least one order of magnitude of improvement in the low error rate region as compared to an elementary array-based code.

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