相关论文: Good traceability codes do exist

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Perfect nonlinear monomials were employed to…

In this paper, we study rate-distortion theory for general sources with an emphasis on the existence of optimal reconstruction distributions on noncompact alphabets. Classical attainability results typically rely on compactness of the…

The likelihood encoder with a random codebook is demonstrated as an effective tool for source coding. Coupled with a soft covering lemma (associated with channel resolvability), likelihood encoders yield simple achievability proofs for…

Tensors are a fundamental operation in distributed computing, \emph{e.g.,} machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall…

We introduce a scheme for distributing and storing software with cryptographic functionality in the whitebox attacker model. Our scheme satisfies two relevant properties: incompressibility and traceability. The main idea is to store a large…

This work studies the problem of constructing capacity-achieving codes from an algorithmic perspective. Specifically, we prove that there exists a Turing machine which, given a discrete memoryless channel $p_{Y|X}$, a target rate $R$ less…

Many physical systems considered promising qubit candidates are not, in fact, two-level systems. Such systems can leak out of the preferred computational states, leading to errors on any qubits that interact with leaked qubits. Without…

Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is their response to a periodic drive at a fraction of its frequency. Current successful experiments are…

The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. The identifying codes can be applied, for example, to sensor networks. In this paper, we consider as sensors the set Z^2 where one sensor can…

In [Hastings et al 2014] it is stated that the code distance of a logical qubit stored using dislocations is 2L + O(1), where L is the separation between the dislocation twists. This code distance assumed only physical X and Z errors are…

Interactive coding allows two parties to conduct a distributed computation despite noise corrupting a certain fraction of their communication. Dani et al.\@ (Inf.\@ and Comp., 2018) suggested a novel setting in which the amount of noise is…

In this paper, memories built from components subject to transient faults are considered. A fault-tolerant memory architecture based on low-density parity-check codes is proposed and the existence of reliable memories for the adversarial…

We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed $k \ge 2$, we construct a family of codes over alphabet of size $k$ with positive rate, which allow efficient recovery from a worst-case deletion…

In recent years, printable graphical codes have attracted a lot of attention enabling a link between the physical and digital worlds, which is of great interest for the IoT and brand protection applications. The security of printable codes…

We study the combined counting statistics of two capacitively coupled transport channels. In particular, we examine the conditions necessary for utilizing one channel as detector sensitive to the occupation of the other. A good detector…

The deletion channel takes as input a bit string $\mathbf{x} \in \{0,1\}^n$, and deletes each bit independently with probability $q$, yielding a shorter string. The trace reconstruction problem is to recover an unknown string $\mathbf{x}$…

A locally recoverable code (LRC code) is a code over a finite alphabet such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. Bounds on the rate and distance of such codes have…

We show that for a fixed $q$, the number of $q$-ary $t$-error correcting codes of length $n$ is at most $2^{(1 + o(1)) H_q(n,t)}$ for all $t \leq (1 - q^{-1})n - C_q\sqrt{n \log n}$ (for sufficiently large constant $C_q$), where $H_q(n, t)…

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…

We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime…