Related papers: On Zero-Error Capacity of Graphs with One Edge
This paper studies the zero error capacity of the Nearest Neighbor Error (NNE) channels with a multilevel alphabet. In the NNE channels, a transmitted symbol is a $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. It is assumed that only one…
We study the problem of communicating over a discrete memoryless two-way channel using non-adaptive schemes, under a zero probability of error criterion. We derive single-letter inner and outer bounds for the zero-error capacity region,…
The zero-error capacity of a channel (or Shannon capacity of a graph) quantifies how much information can be transmitted with no risk of error. In contrast to the Shannon capacity of a channel, the zero-error capacity has not even been…
Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the…
The zero-error channel capacity is the maximum asymptotic rate that can be reached with error probability exactly zero, instead of a vanishing error probability. The nature of this problem, essentially combinatorial rather than…
We analyze the problem of zero-error communication through timing channels that can be interpreted as discrete-time queues with bounded waiting times. The channel model includes the following assumptions: 1) Time is slotted, 2) at most $ N…
This paper investigates the zero-error capacity of channels with memory. Motivated by the nuanced requirements of semantic communication that incorporate memory, we advance the classical enlightened dictator channel by introducing a new…
Motivated by the problem of zero-error broadcasting, we introduce a new notion of graph capacity, termed $\rho$-capacity, that generalizes the Shannon capacity of a graph. We derive upper and lower bounds on the $\rho$-capacity of arbitrary…
In this work we continue the study of a new class of codes, called \emph{codes over graphs}. Here we consider storage systems where the information is stored on the edges of a complete directed graph with $n$ nodes. The failure model we…
This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are…
We consider the zero-error capacity of deletion channels. Specifically, we consider the setting where we choose a codebook ${\cal C}$ consisting of strings of $n$ bits, and our model of the channel corresponds to an adversary who may delete…
In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on…
The zero-error capacity of quantum channels was defined as the least upper bound of rates at which classical information can be transmitted through a quantum channel with probability of error equal to zero. This paper investigates some…
The capacity of unifilar finite-state channels in the presence of feedback is investigated. We derive a new evaluation method to extract graph-based encoders with their achievable rates, and to compute upper bounds to examine their…
We begin a systematic study of the problem of the zero--error capacity of noisy binary channels with memory and solve some of the non--trivial cases.
Zero-error capacity plays an important role in a whole range of operational tasks, in addition to the fact that it is necessary for practical applications. Due to the importance of zero-error capacity, it is necessary to investigate its…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect…
The zero-error capacity of a discrete classical channel was first defined by Shannon as the least upper bound of rates for which one transmits information with zero probability of error. The problem of finding the zero-error capacity $C_0$,…
Zero-error coding encompasses a variety of source and channel problems where the probability of error must be exactly zero. This condition is stricter than that of the vanishing error regime, where the error probability goes to zero as the…