Related papers: On the Symmetries of the Deletion Channel
The deletion channel is the simplest point-to-point communication channel that models lack of synchronization. Despite significant effort, little is known about its capacity, and even less about optimal coding schemes. In this paper we…
We consider a new formulation of a class of synchronization error channels and derive analytical bounds and numerical estimates for the capacity of these channels. For the binary channel with only deletions, we obtain an expression for the…
The deletion channel is the simplest point-to-point communication channel that models lack of synchronization. Input bits are deleted independently with probability d, and when they are not deleted, they are not affected by the channel.…
The one-bit deletion and duplication channel is investigated. An input to this channel consists of a block of bits which experiences either a deletion, or a duplication, or remains unchanged. For this channel a capacity expression is…
From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…
We investigate the fundamental limits of reliable communication over multi-view channels, in which the channel output is comprised of a large number of independent noisy views of a transmitted symbol. We consider first the setting of…
This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is…
In this paper, we study the symmetry of polar codes on symmetric binary-input discrete memoryless channels (B-DMC). The symmetry property of polar codes is originally pointed out in Arikan's work for general B-DMC channels. With the…
The channel output entropy of a transmitted word is the entropy of the possible channel outputs and similarly, the input entropy of a received word is the entropy of all possible transmitted words. The goal of this work is to study these…
The decomposition of channel information into synergies of different order is an open, active problem in the theory of complex systems. Most approaches to the problem are based on information theory, and propose decompositions of mutual…
A fundamental question in information theory is to quantify the loss of information under a noisy channel. Partial orders and contraction coefficients are typical tools to that end, however, they are often also challenging to evaluate. For…
Computing channel capacity is in general intractable because it is given by the limit of a sequence of optimization problems whose dimensionality grows to infinity. As a result, constant-sized characterizations of feedback or non-feedback…
Memoryless channels with deletion errors as defined by a stochastic channel matrix allowing for bit drop outs are considered in which transmitted bits are either independently deleted with probability $d$ or unchanged with probability…
We consider binary input deletion/substitution channels, which model certain types of synchronization errors encountered in practice. Specifically, we focus on the regime of small deletion and substitution probabilities, and by extending an…
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work…
Symmetry plays a crucial role in understanding the properties of mathematical structures and optimization problems. Recent work has explored this phenomenon in the context of neural networks, where the loss function is invariant under…
Physical systems evolve from one state to another along paths of least energy barrier. Without a priori knowledge of the energy landscape, multidimensional search methods aim to find such minimum energy pathways between the initial and…
Synchronization channels, such as the well-known deletion channel, are surprisingly harder to analyze than memoryless channels, and they are a source of many fundamental problems in information theory and theoretical computer science. One…
One of the basic tenets in information theory, the data processing inequality states that output divergence does not exceed the input divergence for any channel. For channels without input constraints, various estimates on the amount of…
We propose a general formulation of the renormalisation group as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally…