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Random linear codes in steganography [PDF]
Biuletyn Wojskowej Akademii Technicznej, 2016 Syndrome coding using linear codes is a technique that allows improvement in the steganographic algorithms parameters. The use of random linear codes gives a great flexibility in choosing the parameters of the linear code.
Kamil Kaczyński
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On the List-Decodability of Random Linear Codes [PDF]
Proceedings of the forty-second ACM symposium on Theory of computing, 2010 For every fixed finite field $\F_q$, $p \in (0,1-1/q)$ and $\epsilon > 0$, we prove that with high probability a random subspace $C$ of $\F_q^n$ of dimension $(1-H_q(p)-\epsilon)n$ has the property that every Hamming ball of radius $pn$ has at most $O(1/\
Guruswami, Venkatesan +2 more
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Improved List-Decodability of Random Linear Binary Codes [PDF]
IEEE Transactions on Information Theory, 2021 There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - ε$ is $(p,O(1/ε))$-list-decodable with high probability. In this work, we show that such codes are $(p, H(p)/ε+ 2)$-list-decodable with high probability, for any $p \
Ray Li, Mary Wootters
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Squares of Random Linear Codes [PDF]
IEEE Transactions on Information Theory, 2015 Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code "typically" fill the whole space?
Cascudo Pueyo, Ignacio +3 more
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Punctured Low-Bias Codes Behave Like Random Linear Codes
2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), 2022 Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not amenable to tractable error-correction algorithms.
Venkatesan Guruswami, Jonathan Mosheiff
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Quantum Error Correction Via Noise Guessing Decoding
IEEE Access, 2023 Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code
Diogo Cruz +2 more
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A Shannon-Theoretic Approach to the Storage–Retrieval Trade-Off in PIR Systems
Information, 2023 We consider the storage–retrieval rate trade-off in private information retrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostly on the canonical two-message two-database case, for which a coding scheme based on random codebook ...
Chao Tian, Hua Sun, Jun Chen
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On linear index coding for random graphs [PDF]
2012 IEEE International Symposium on Information Theory Proceedings, 2012 A sender wishes to broadcast an n character word x in F^n (for a field F) to n receivers R_1,...,R_n. Every receiver has some side information on x consisting of a subset of the characters of x. The side information of the receivers is represented by a graph G on n vertices in which {i,j} is an edge if R_i knows x_j.
Haviv, Ishay, Langberg, Michael
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Soft Interference Cancellation for Random Coding in Massive Gaussian Multiple-Access
Entropy, 2021 In 2017, Polyanskiy showed that the trade-off between power and bandwidth efficiency for massive Gaussian random access is governed by two fundamentally different regimes: low power and high power. For both regimes, tight performance bounds were found by
Ralf R. Müller
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Blind Interleaver Parameters Estimation Using Kolmogorov–Smirnov Test
Sensors, 2021 The use of error-correcting codes (ECCs) is essential for designing reliable digital communication systems. Usually, most systems correct errors under cooperative environments.
Seungwoo Wee +2 more
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