Related papers: Improved Lower Bounds for Secure Codes and Related…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite…
The relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…
Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
The paper introduces new bounds on the asymptotic density of parity-check matrices and the achievable rates under ML decoding of binary linear block codes transmitted over memoryless binary-input output-symmetric channels. The lower bounds…
The aim of this paper is to prove coding theorems for the wiretap channel coding problem and secret key agreement problem based on the the notion of a hash property for an ensemble of functions. These theorems imply that codes using sparse…
Digital data transfer can be protected by means of suitable error correcting codes. Among the families of state-of-the-art codes, LDPC (Low Density Parity-Check) codes have received a great deal of attention recently, because of their…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
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…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Yet, the codes being deployed in practice are fairly short. In this work, we address what we…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention thanks to their capacity approaching performance and low decoding latency. An SC code is constructed by partitioning an underlying…
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
We propose a two-stage concatenated coding scheme for reliable and secure communication over intersymbol interference wiretap channels. We first establish the secrecy capacity. Then, motivated by the theoretical codes that achieve the…
Frameproof codes are a class of secure codes that were originally introduced in the pioneering work of Boneh and Shaw in the context of digital fingerprinting. They can be used to enhance the security and credibility of digital content. Let…