Related papers: Coding for Locality in Reconstructing Permutations
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
Modern distributed computation infrastructures are often plagued by unavailabilities such as failing or slow servers. These unavailabilities adversely affect the tail latency of computation in distributed infrastructures. The simple…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most $r$) other symbols. We present a family of LRC codes that attain the maximum possible value of the…
Coded caching is a technique that generalizes conventional caching and promises significant reductions in traffic over caching networks. However, the basic coded caching scheme requires that each file hosted in the server be partitioned…
Using derandomization, we provide an upper bound on the compression size of solutions to the graph coloring problem. In general, if solutions to a combinatorial problem exist with high probability and the probability is simple, then there…
We extend the notion of locality from the Hamming metric to the rank and subspace metrics. Our main contribution is to construct a class of array codes with locality constraints in the rank metric. Our motivation for constructing such codes…
In this paper we consider the classical maximum set packing problem where set cardinality is upper bounded by $k$. We show how to design a variant of a polynomial-time local search algorithm with performance guarantee $(k+2)/3$. This local…
We introduce \emph{Term Coding}, a novel framework for analysing extremal problems in discrete mathematics by encoding them as finite systems of \emph{term equations} (and, optionally, \emph{non-equality constraints}). In its basic form,…
Locally repairable codes enables fast repair of node failure in a distributed storage system. The code symbols in a codeword are stored in different storage nodes, such that a disk failure can be recovered by accessing a small fraction of…
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…
Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
The continuously increasing amount of digital data generated by today's society asks for better storage solutions. This survey looks at a new generation of coding techniques designed specifically for the needs of distributed networked…
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
We present new upper bounds on the parameters of batch codes with restricted query size. These bounds are an improvement on the Singleton bound. The techniques for derivations of these bounds are based on the ideas in the literature for…
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…
In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time. In settings such as that of a large data center, an important consideration is the efficient repair of a failed node.…