Related papers: Combinatorial neural codes from a mathematical cod…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
To evaluate the nature of the neural code in the cerebral cortex, we have used a combination of theory and experiment to assess how information is represented in a realistic cortical population response. We have shown how a sensory stimulus…
Rate-distortion-perception theory generalizes Shannon's rate-distortion theory by introducing a constraint on the perceptual quality of the output. The perception constraint complements the conventional distortion constraint and aims to…
A combinatorial neural code is a subset of the power set $2^{[n]}$ on $[n]=\{1,\dots, n\}$, in which each $1\leq i\leq n$ represents a neuron and each element (codeword) represents the co-firing event of some neurons. Consider a space…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…
We introduce combinatorial interpretability, a methodology for understanding neural computation by analyzing the combinatorial structures in the sign-based categorization of a network's weights and biases. We demonstrate its power through…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
An error correcting code using a tree-like multilayer perceptron is proposed. An original message $\mbi{s}^0$ is encoded into a codeword $\boldmath{y}_0$ using a tree-like committee machine (committee tree) or a tree-like parity machine…
Lossy image coding is the art of computing that is principally bounded by the image's rate-distortion function. This bound, though never accurately characterized, has been approached practically via deep learning technologies in recent…
This paper applies Information Theoretic analysis to packet-based random multiple access communication systems. A new channel coding approach is proposed for coding within each data packet with built-in support for bursty traffic…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial…
Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
Function-correcting codes are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we extend function-correcting codes from binary symmetric…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…