Related papers: Locally Decodable Codes with Randomized Encoding
In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent…
The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a…
Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, we first build a bridge between locally repairable code and packing. As an application of this bridge, some optimal…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
We construct locally decodable codes (LDCs) to correct insertion-deletion errors in the setting where the sender and receiver share a secret key or where the channel is resource-bounded. Our constructions rely on a so-called…
We construct the first (locally computable, approximately) locally list decodable codes with rate, efficiency, and error tolerance approaching the information theoretic limit, a core regime of interest for the complexity theoretic task of…
As the mobile application landscape expands, wireless networks are tasked with supporting various connection profiles, including real-time communications and delay-sensitive traffic. Among many ensuing engineering challenges is the need to…
We consider the scenario of broadcasting for real-time applications and loss recovery via instantly decodable network coding. Past work focused on minimizing the completion delay, which is not the right objective for real-time applications…
We consider the locally repairable codes (LRC), aiming at sequential recovering multiple erasures. We define the (n,k,r,t)-SLRC (Sequential Locally Repairable Codes) as an [n,k] linear code where any t'(>= t) erasures can be sequentially…
In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements,…
We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
A locally decodable code encodes n-bit strings x in m-bit codewords C(x), in such a way that one can recover any bit x_i from a corrupted codeword by querying only a few bits of that word. We use a quantum argument to prove that LDCs with 2…
Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code…
This paper is concerned with the ordered statistic decoding with local constraints (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly…
A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within…
Randomized encoding is a powerful cryptographic primitive with various applications such as secure multiparty computation, verifiable computation, parallel cryptography, and complexity lower-bounds. Intuitively, randomized encoding…
Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…
The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…