Asymptotically good Quantum and locally testable classical LDPC codes

Panteleev, Pavel; Kalachev, Gleb

doi:10.1145/3519935.3520017

Cited by 84 publications

(45 citation statements)

References 46 publications

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“…Depending on a situation, it may be viewed as a lift (i.e., a |G|-fold covering) of the product of two topological spaces, the balanced product of two topological spaces with an action of a group G, or as a fiber bundle. This explains the plethora of different names used in the literature to describe such qLDPC codes [13,[17][18][19][20]. Also note that one can automatically apply this tensor product construction to graphs, hypergraphs, and even to general incidence structures since they all can be viewed as 1-dimensional complexes [13,18].…”

Section: Introductionmentioning

confidence: 94%

“…It is clear that LTCs with constant locality w are LDPC codes. Robustly testable codes appeared in different forms in the first examples of asymptotically good 1 classical LTCs [5,13] and quantum LDPC (qLDPC) codes [13]. In [5] Dinur et al use agreement testable codes [4], which, as they show, are equivalent to the robustly testable codes if the codes have non-vanishing relative distance.…”

Section: Introductionmentioning

confidence: 99%

“…In [5] Dinur et al use agreement testable codes [4], which, as they show, are equivalent to the robustly testable codes if the codes have non-vanishing relative distance. In [13] the authors use the product-expansion property, which, as we will see later, is equivalent (in its strongest form) to the agreement testability of a product of two codes, and hence also to the robust testability. However, in the case of products of more than two codes the situation is much more interesting.…”

Section: Introductionmentioning

confidence: 99%

“…Note that the term product-expansion was originally motivated by the fact that it is a form of coboundary expansion [14,15] in the cochain complex naturally associated with the product of several codes. Such complexes appeared in [13] for the analysis of local neighborhoods in a two-dimensional chain complex of a product of two Tanner codes.…”

Section: Introductionmentioning

confidence: 99%

“…Remark 1. In retrospect one can see that good LTCs and qLDPC codes from [5,13] can be obtained respectively as the second and the first homology of the 2-dimensional tensor product complex 2 A ⊗ G B := A ⊗ R B over a group algebra R = F q G obtained from 1-dimensional chain complexes A and B, representing some linear codes. This general approach was first proposed as a way to obtain qLDPC codes by the authors in [17], and later, in a more general form, by Breuckmann and Eberhardt [18,19].…”

Section: Introductionmentioning

confidence: 99%

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Two-sided Robustly Testable Codes

Kalachev¹,

Panteleev²

2022

Preprint

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We show that the tensor product of two random linear codes is robustly testable with high probability. This implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously robustly testable. Such two-sided robustly testable codes (with a much weaker form of robustness) were the key ingredient in the recent constructions of asymptotically good quantum LDPC codes, which ensured their linear minimum distance. We hope that the existence of such codes with a stronger form of robustness, shown here, can be used to simplify the proofs and provide better distance bounds in these constructions. We also give new very simple examples of non-robustly testable codes. We show that if the paritychecks of two codes are mutually orthogonal, then their product is not robustly testable. In particular, this implies that the product of a code with its dual code is not robustly testable. We also study a property of a collection of linear codes called product-expansion, which can be viewed as a coboundary expansion of the cochain complex naturally associated with the product of these codes. We show that this property is related with the robust testability and the agreement testability of the products of codes.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two-sided Robustly Testable Codes

Kalachev¹,

Panteleev²

2022

Preprint

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A smart surveillance system utilizing modified federated machine learning: Gossip‐verifiable and quantum‐safe approach

Dharani,

Anitha Kumari

2024

Concurrency and Computation

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SummaryEdge computing has the capability to process data closer to its point of origin, leading to the development of critical autonomous infrastructures with frequently communicating peers. The proposed work aims to evaluate the effectiveness of security and privacy mechanisms tailored for distributed systems, particularly focusing on scenarios where the nodes are closed‐circuit television (CCTV) systems. Ensuring public safety, object tracking in surveillance systems is a vital responsibility. The workflow has been specifically crafted and simulated for the purpose of weapon detection within public CCTV systems, utilizing sample edge devices. The system's primary objective is to detect any unauthorized use of weapons in public spaces while concurrently ensuring the integrity of video footage for use in criminal investigations. The outcomes of prior research on distributed machine learning (DML) techniques are compared with modified federated machine learning (FML) techniques, specifically designed for being Gossip verifiable and Quantum Safe. The conventional federated averaging algorithm is modified by incorporating the secret sharing principle, coupled with code‐based McEliece cryptosystem. This adaptation is designed to fortify the system against quantum threats. The Gossip data dissemination protocol, executed via custom blockchain atop the distributed network, serves to authenticate and validate the learning model propagated among the peers in the network. It provides additional layer of integrity to the system. Potential threats to the proposed model are analyzed and the efficiency of the work is assessed using formal proofs. The outcomes of the proposed work demonstrate that the trustworthiness and consistency are meticulously preserved for both the model and data within the DML framework on the Edge computing platform.

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Coboundary expansion for the union of determinantal hypertrees

Mészáros

2024

Random Struct Algorithms

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Asymptotically good Quantum and locally testable classical LDPC codes

Cited by 84 publications

References 46 publications

Two-sided Robustly Testable Codes

Two-sided Robustly Testable Codes

A smart surveillance system utilizing modified federated machine learning: Gossip‐verifiable and quantum‐safe approach

Coboundary expansion for the union of determinantal hypertrees

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