Related papers: Weighted Lifted Codes: Local Correctabilities and …
We consider private information retrieval (PIR) for distributed storage systems (DSSs) with noncolluding nodes where data is stored using a non maximum distance separable (MDS) linear code. It was recently shown that if data is stored using…
We propose three private information retrieval (PIR) protocols for distributed storage systems (DSSs) where data is stored using an arbitrary linear code. The first two protocols, named Protocol 1 and Protocol 2, achieve privacy for the…
Given a database, the private information retrieval (PIR) protocol allows a user to make queries to several servers and retrieve a certain item of the database via the feedbacks, without revealing the privacy of the specific item to any…
Reed-Muller (RM) codes are conjectured to achieve the capacity of any binary-input memoryless symmetric (BMS) channel, and are observed to have a comparable performance to that of random codes in terms of scaling laws. On the negative side,…
We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of…
In this paper, we investigate the application of Reed-Muller (RM) codes for Physical-layer security in a real world wiretap channel scenario. Utilizing software-defined radios (SDRs) in a real indoor environment, we implement a coset coding…
Reed-Muller (RM) codes achieve the capacity of general binary-input memoryless symmetric channels and are conjectured to have a comparable performance to that of random codes in terms of scaling laws. However, such results are established…
The problem of $T$-colluding private information retrieval (PIR) enables the user to retrieve one out of $M$ files from a distributed storage system with $N$ servers without revealing anything about the index of the desired file to any…
Guo, Kopparty and Sudan have initiated the study of error-correcting codes derived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codes are defined as the evaluation of polynomials in a vector space over a field by requiring…
We consider the problem of coded computing, where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We…
We describe a new parameterized family of symmetric error-correcting codes with low-density parity-check matrices (LDPC). Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are…
We consider the problem of weakly-private information retrieval (WPIR) when data is encoded by a maximum distance separable code and stored across multiple servers. In WPIR, a user wishes to retrieve a piece of data from a set of servers…
Motivated by applications in distributed storage, distributed computing, and homomorphic secret sharing, we study communication-efficient schemes for computing linear combinations of coded symbols. Specifically, we design low-bandwidth…
It was recently shown by Fazeli et al. that the storage overhead of a traditional $t$-server private information retrieval (PIR) protocol can be significantly reduced using the concept of a $t$-server PIR code. In this work, we show that a…
Ahlswede and Dueck identification has the potential of exponentially reducing traffic or exponentially increasing rates in applications where a full decoding of the message is not necessary and, instead, a simple verification of the message…
Mart{\'\i}nez-Pe{\~n}as and Kschischang (IEEE Trans.\ Inf.\ Theory, 2019) proposed lifted linearized Reed--Solomon codes as suitable codes for error control in multishot network coding. We show how to construct and decode \ac{LILRS} codes.…
We introduce a new family of codes, termed weighted superimposed codes (WSCs). This family generalizes the class of Euclidean superimposed codes (ESCs), used in multiuser identification systems. WSCs allow for discriminating all bounded,…
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…