Related papers: Coding methods for string reconstruction from erro…
We consider the problem of encoding a string of length $n$ from an integer alphabet of size $\sigma$ so that access and substring equality queries (that is, determining the equality of any two substrings) can be answered efficiently. Any…
A common complaint about adaptive prefix coding is that it is much slower than static prefix coding. Karpinski and Nekrich recently took an important step towards resolving this: they gave an adaptive Shannon coding algorithm that encodes…
Given a permutation pi, the application of prefix reversal f^(i) to pi reverses the order of the first i elements of pi. The problem of Sorting By Prefix Reversals (also known as pancake flipping), made famous by Gates and Papadimitriou…
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable…
A code is called solid if, roughly speaking, any correctly-transmitted codeword in an arbitrarily corrupted string of codewords can still be decoded correctly and unambiguously. So-called variable-length solid codes, in which codewords may…
Knowledge of the input format of binary executables is important for finding bugs and vulnerabilities, such as generating data for fuzzing or manual reverse engineering. This paper presents an algorithm to recover the structure and semantic…
According to Kolmogorov complexity, every finite binary string is compressible to a shortest code -- its information content -- from which it is effectively recoverable. We investigate the extent to which this holds for infinite binary…
Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…
We derive the coding capacity for duplication-correcting codes capable of correcting any number of duplications. We do so both for reverse-complement duplications, as well as palindromic (reverse) duplications. We show that except for…
In the standard trace reconstruction problem, the goal is to \emph{exactly} reconstruct an unknown source string $\mathsf{x} \in \{0,1\}^n$ from independent "traces", which are copies of $\mathsf{x}$ that have been corrupted by a…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. \"Osterg{\aa}rd and O. Pottonen, The perfect binary one-error-correcting codes of length 15: Part I - Classification,…
We construct error correcting nonlinear binary codes using a construction of Bose and Chowla in additive number theory. Our method extends a construction of Graham and Sloane for constant weight codes. The new codes improve 1028 of the 7168…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the…
Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…
This paper gives some theory and efficient design of binary block systematic codes capable of controlling the deletions of the symbol ``$0$'' (referred to as $0$-deletions) and/or the insertions of the symbol ``$0$'' (referred to as…
Fractional repetition (FR) codes are a family of repair-efficient storage codes that provide exact and uncoded node repair at the minimum bandwidth regenerating point. The advantageous repair properties are achieved by a tailor-made…
We present two new algorithms for the reconstruction of turbo codes from a noisy intercepted bitstream. With these algorithms, we were able to reconstruct various turbo codes with realistic parameter sizes. To the best of our knowledge,…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…