Related papers: Coding for Locality in Reconstructing Permutations
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Ever-increasing amounts of data are created and processed in internet-scale companies such as Google, Facebook, and Amazon. The efficient storage of such copious amounts of data has thus become a fundamental and acute problem in modern…
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of…
Counting permutations of $[n]$ by the number of records, i.e. left-to-right maxima, is a classic problem in combinatorial enumeration. In the first volume of ``The Art of Computer Programming", Donald Knuth demonstrated its relevance for…
Motivated by applications of distributed storage systems to key-value stores, the multi-version coding problem was formulated to efficiently store frequently updated data in asynchronous decentralized storage systems. Inspired by…
We consider the problem of revealing/sharing data in an efficient and secure way via a compact representation. The representation should ensure reliable reconstruction of the desired features/attributes while still preserve privacy of the…
We initiate a study of locally decodable codes with randomized encoding. Standard locally decodable codes are error correcting codes with a deterministic encoding function and a randomized decoding function, such that any desired message…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
Combinatorial evolution - the creation of new things through the combination of existing things - can be a powerful way to evolve rather than design technical objects such as electronic circuits. Intriguingly, this seems to be an ongoing…
In most notions of locality in error correcting codes -- notably locally recoverable codes (LRCs) and locally decodable codes (LDCs) -- a decoder seeks to learn a single symbol of a message while looking at only a few symbols of the…
By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of…
This paper presents a theoretical study of a new type of LDPC codes motivated by practical storage applications. LDPCL codes (suffix L represents locality) are LDPC codes that can be decoded either as usual over the full code block, or…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in…
This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded…
Repair locality is a desirable property for erasure codes in distributed storage systems. Recently, different structures of local repair groups have been proposed in the definitions of repair locality. In this paper, the concept of…
This work considers the problem of transmitting multiple compressible sources over a network at minimum cost. The aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be…