17 papers · ranked by Valyu relevance
S. Romano, A. Salles, M. Amalric, S. Dehaene + 2 more
Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of…
Mahdi Cheraghchi, Venkatesan Guruswami
Non-malleable codes, introduced by Dziembowski, Pietrzak and Wichs (ICS 2010), encode messages s in a manner so that tampering the codeword causes the decoder to either output s or a message that is independent of s. While this is an impossible goal to achieve against unrestricted tampering functions, rather…
Henk D. L. Hollmann, Patrick Solé
We construct a family of linear optimal functional-repair regenerating storage codes with parameters $({m,(n,k),(r,α,β)}={(2r-α+1)α/2,(r+1,r),(r,α,1)})$ for any integers $r,α$ with $1\leqα\leqr$, over any field when $α\in{1,r-1,r}$, and over any finite field $F_{q}$ with $q\geqr-1$ otherwise. These storage codes are…
Maximilian Gehri, Lukas Stelzl, Heinz Koeppl
Biochemical systems process signals through stochastic reaction dynamics that are inherently continuous in time and often exhibit memory, feedback, and nonequilibrium driving. At the same time, they are frequently modeled by effective reactions, e.g., multi-step processes such as transcription are treated as single…
Neri Merhav, Luca Faes
We propose a universal ensemble for the random selection of rate-distortion codes which is asymptotically optimal in a sample-wise sense. According to this ensemble, each reproduction vector, $x^$, is selected independently at random under the probability distribution that is proportional to $2-LZ(x^)$, where $LZ(x^)$…
Madhura Pathegama, Alexander Barg, Igal Sason
The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a lattice in the Euclidean space. We aim to characterize the cases when the output…
Xiao Ma
In this paper, by treating Reed-Muller (RM) codes as a special class of low-density parity-check (LDPC) codes and assuming that sub-blocks of the parity-check matrix are randomly interleaved to each other as Gallager's codes, we present a short proof that RM codes are entropy-achieving as source coding for Bernoulli…
Minjia Shi, Liqin Qian, Patrick Solé
In this paper, new few weights linear codes over the local ring R = Fp+uFp+vFp+uvFp, with u 2 = v 2 = 0, uv = vu, are constructed by using the trace function defined over an extension ring of degree m. These trace codes have the algebraic structure of abelian codes. Their weight distributions are evaluated explicitly…
Michail Gkagkos, Charalambos D. Charalambous, Eduard Jorswieck
The main focus of this paper is the derivation of the structural properties of the test channels of Wyner’s operational information rate distortion function (RDF), $R¯(Δ_{X})$, for arbitrary abstract sources and, subsequently, the derivation of additional properties for a tuple of multivariate correlated, jointly…
Neri Merhav, Raúl Alcaraz
We extend Ziv and Lempel’s model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless finite-state encoder that compresses the reconstruction codeword with no…
Nikita Polyanskii, Yihan Zhang
This paper is a collection of results on combinatorial properties of codes for the Zchannel. A Z-channel with error fraction τ takes as input a length-n binary codeword and injects in an adversarial manner nτ asymmetric errors, i.e., errors that only zero out bits but do not flip 0's to 1's. It is known that the…
Yasutada Oohama
We consider the rate distortion problem with side information at the decoder posed and investigated by Wyner and Ziv. Using side information and encoded original data, the decoder must reconstruct the original data with an arbitrary prescribed distortion level. The rate distortion region indicating the trade-off…
Masahito Hayashi, Masaki Owari, Go Kato, Ning Cai
We discuss the effect of sequential error injection on information leakage under a network code. We formulate a network code for the single transmission setting and the multiple transmission setting. Under this formulation, we show that the eavesdropper cannot increase the power of eavesdropping by sequential error…
Suman Ghosh, Lakshmi Prasad Natarajan
We consider network coding for a noiseless broadcast channel where each receiver demands a subset of messages available at the transmitter and is equipped with noisy side information in the form an erroneous version of the message symbols it demands. We view the message symbols as elements from a finite field and…
V. Arvind Rameshwar, Navin Kashyap
—This paper considers the memoryless inputconstrained binary erasure channel (BEC). The channel input constraint is the (, ∞)-runlength limited (RLL) constraint, which mandates that any pair of successive 1s in the input sequence be separated by at least 0s. We consider a scenario where there is causal, noiseless…
Rodrick Wallace
The living state is cognitive at every scale and level of organization. Since it is possible to associate a broad class of cognitive processes with ‘dual’ information sources, many pathologies can be addressed using statistical models based on the Shannon Coding, the Shannon-McMillan Source Coding, the Rate Distortion…
Rodrick Wallace
We generalize the recently-uncovered Data Rate Theorem in the context of cognitive systems having a ‘dual’ information source, including those of the living state that is particularly characterized by cognition at every scale and level of organization. The unification of information theory and control theory via the…