In a locally recoverable or repairable code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distrib...
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ISBN:
(纸本)9781479908219;9781479908226
In a locally recoverable or repairable code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed storage where a most frequent error-event is a single storage node failure (erasure). A common objective is to repair the node by downloading data from as few other storage node as possible. In this paper, we bound the minimum distance of a code in terms of of its length, size and locality. Unlike previous bounds, our bound follows from a significantly simple analysis and depends on the size of the alphabet being used.
This paper is concerned with optimal transform coding in conjunction with dithered quantization. While the optimal deterministic quantizer's error is uncorrelated with the reconstructed value, the dithered quantiz...
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ISBN:
(纸本)9780769535920
This paper is concerned with optimal transform coding in conjunction with dithered quantization. While the optimal deterministic quantizer's error is uncorrelated with the reconstructed value, the dithered quantizer yields quantization errors that are correlated with the reconstruction but are white and independent of the source. These properties offer potential benefits, but also have implications on the optimization of the rest of the coder. We derive the optimal transform for consequent dithered quantization. For fixed rate coding, we show that the transform derived for dithered quantization is universally optimal (for all sources), unlike the conventional quantization case where optimality of the Karhunen-Loeve transform is guaranteed for Gaussian sources. Moreover, we establish variable rate coding optimality for Gaussian sources.
We construct a new family of permutationally invariant codes that correct t Pauli errors for any t >= 1. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors...
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ISBN:
(纸本)9798350382853;9798350382846
We construct a new family of permutationally invariant codes that correct t Pauli errors for any t >= 1. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. This is an extended abstract of the preprint [1].
A new 4B5B block inversion coding is proposed for dc-balanced transmission in high-speed optical parallel links. An 8-bit byte is partitioned into two 4-bit data and converted to two 5-bit blocks by an inversion encod...
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We focus on a distributed coded computation scheme for matrix multiplication. In this system, the product matrix is encoded and decoded through the overall system to correct errors in computation. We propose a group-t...
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ISBN:
(纸本)9784885523410
We focus on a distributed coded computation scheme for matrix multiplication. In this system, the product matrix is encoded and decoded through the overall system to correct errors in computation. We propose a group-type distributed coded computation scheme, for one example, a scheme based on a Gabidulin code, and evaluate the computation time complexity and the error-correcting capability of the overall system. The full version of this paper is in [1].
We tackle the problem of Byzantine errors in distributed gradient descent within the Byzantine-resilient gradient coding framework. Our proposed solution can recover the exact full gradient in the presence of s malici...
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ISBN:
(纸本)9798350382853;9798350382846
We tackle the problem of Byzantine errors in distributed gradient descent within the Byzantine-resilient gradient coding framework. Our proposed solution can recover the exact full gradient in the presence of s malicious workers with a data replication factor of only s+1. It generalizes previous solutions to any data assignment scheme that has a regular replication over all data samples. The scheme detects malicious workers through additional interactive communication and a small number of local computations at the main node, leveraging group-wise comparisons between workers with a provably optimal grouping strategy. The scheme requires at most s interactive rounds that incur a total communication cost logarithmic in the number of data samples.
We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary l...
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ISBN:
(纸本)9798350348941;9798350348934
We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime. We define optimality as the direct minimization of analytical expressions of error probabilities using an alternating optimization (AO) algorithm. Additionally, we provide lower and upper bounds on error probabilities, leading to the derivation of error exponents applicable to large code-length regime. Numerical results are presented to demonstrate that, with the proposed algorithm, binary linear codes with an optimal covering radius perform near-optimally for the independence test in DHT.
In this paper, we investigate relationships between the following formalizations of information-theoretic security for key agreement protocols which may have agreement-errors: formalizations extended (or relaxed) from...
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ISBN:
(纸本)9781479904464
In this paper, we investigate relationships between the following formalizations of information-theoretic security for key agreement protocols which may have agreement-errors: formalizations extended (or relaxed) from Shannon's perfect secrecy by using mutual information and statistical distance;and the ones of composable security by Maurer et al. and Canetti. Then, we explicitly show that those are essentially equivalent. We also derive lower bounds on the adversary's (or distinguisher's) advantage and the size of a correlated randomness resource required under all of the above formalizations at once through our relationships. In addition, we observe impossibility results which easily follow from the lower bounds.
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage. This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, ...
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ISBN:
(纸本)9798350382853;9798350382846
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage. This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire strands, and symbol deletion errors. Non-asymptotic upper bounds on the size of codes with t occurrences of these error types are derived. Explicit constructions are presented which can achieve the bounds.
On error exponents in the simple quantum hypothesis testing problem, a noncommutative analogue of the Hoeffding bound [1] is presented. If the hypotheses, namely two density operators, are mutually commutative, the bo...
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ISBN:
(纸本)0780377281
On error exponents in the simple quantum hypothesis testing problem, a noncommutative analogue of the Hoeffding bound [1] is presented. If the hypotheses, namely two density operators, are mutually commutative, the bound is identical with the classical counter part and thus is optimal. As a by-product, a simple proof of the direct part of the quantum Stein's lemma [2] [3] is also given.
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