相关论文: Bounds for flag codes
We address the maximum attainable rate of fingerprinting codes under the marking assumption, studying lower and upper bounds on the value of the rate for various sizes of the attacker coalition. Lower bounds are obtained by considering…
Random linear network coding is a feasible encoding tool for network coding, specially for the non-coherent network, and its performance is important in theory and application. In this letter, we study the performance of random linear…
The bandwidth of a graph is the labeling of vertices with minimum maximum edge difference. For many graph families this is NP-complete. A classic result computes the bandwidth for the hypercube. We generalize this result to give sharp lower…
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent…
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
Locally recoverable codes deal with the task of reconstructing a lost symbol by relying on a portion of the remaining coordinates smaller than an information set. We consider the case of codes over finite chain rings, generalizing known…
Deterministic identification offers an efficient solution for scenarios where decoding entire messages is unnecessary. It is commonly used in alarm systems and control systems. A key advantage of this approach is that the capacity for…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the…
Selection comparator networks have been studied for many years. Recently, they have been successfully applied to encode cardinality constraints for SAT-solvers. To decrease the size of generated formula there is a need for constructions of…
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…
We develop an abstract way of defining linear-optics networks designed to perform quantum information tasks such as quantum gates. We will be mainly concerned with the nonlinear sign shift gate, but it will become obvious that all other…
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$, where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a…
We consider a single-source, multiple-relay, single-destination lossy network employing Random Linear Network coding at all transmitting nodes. We address the problem of calculating the probability of successful decoding at the destination…
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…
Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from…
The subspace channel was introduced by Koetter and Kschischang as an adequate model for the communication channel from the source node to a sink node of a multicast network that performs random linear network coding. So far, attention has…
We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state…