Independence and Alpern multitowers

Campbell, James T.; McCutcheon, Randall; Windsor, Alistair

doi:10.1080/14689367.2018.1504891

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…For the first component of the proof, we shall require an improved version of Alpern's Lemma [2], recently proved in [10].…”

Section: B Sliding Block Codesmentioning

confidence: 99%

Quantized-Constraint Concatenation and the Covering Radius of Constrained Systems

Elimelech¹,

Meyerovitch²,

Schwartz³

2023

Preprint

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We introduce a novel framework for implementing error-correction in constrained systems. The main idea of our scheme, called Quantized-Constraint Concatenation (QCC), is to employ a process of embedding the codewords of an error-correcting code in a constrained system as a (noisy, irreversible) quantization process. This is in contrast to traditional methods, such as concatenation and reverse concatenation, where the encoding into the constrained system is reversible. The possible number of channel errors QCC is capable of correcting is linear in the block length n, improving upon the O( √ n) possible with the stateof-the-art known schemes. For a given constrained system, the performance of QCC depends on a new fundamental parameter of the constrained system -its covering radius.Motivated by QCC, we study the covering radius of constrained systems in both combinatorial and probabilistic settings. We reveal an intriguing characterization of the covering radius of a constrained system using ergodic theory. We use this equivalent characterization in order to establish efficiently computable upper bounds on the covering radius.

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“…For the first component of the proof, we shall require an improved version of Alpern's Lemma [2], recently proved in [10].…”

Section: B Sliding Block Codesmentioning

confidence: 99%

Quantized-Constraint Concatenation and the Covering Radius of Constrained Systems

Elimelech¹,

Meyerovitch²,

Schwartz³

2023

Preprint

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“…Proof. By [5][Corollary 1], there exists a ξ-independent {2l, 2l + 1} castle with bases B = B 2l and F = B 2l+1 . Note that as T is invertible then,…”

Section: The Strong Alpern Tower Lemma and Realizations Of Triangular...mentioning

confidence: 99%

Local limit theorem in deterministic systems

Kosloff¹,

Volný²

2019

Preprint

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“…whose rescaled sums converge to a SαS(σ) random variable. In this step it is important that we can mimic the (Y (n)) n∈Z process using the Alpern lemma independent of a partition of [3,4] in a similar fashion to the methods of [6]. The proof of the CLT for the target process is carried out in Section 3.…”

Section: Introductionmentioning

confidence: 99%