Related papers: A Zero-Knowledge Proof for the Syndrome Decoding P…
Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our…
In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from…
Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and…
In this paper, we present a simple bare-bones solution of a Zero-Knowledge authentication protocol which uses non-commutative algebra and a variation of the generalized symmetric decomposition problem (GSDP) as a one-way function. The…
In this paper show that the list and bounded-distance decoding problems of certain bounds for the Reed-Solomon code are at least as hard as the discrete logarithm problem over finite fields.
A blind decryption scheme enables a user to query decryptions from a decryption server without revealing information about the plaintext message. Such schemes are useful, for example, for the implementation of privacy preserving encrypted…
Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…
Reed-Muller codes are some of the oldest and most widely studied error-correcting codes, of interest for both their algebraic structure as well as their many algorithmic properties. A recent beautiful result of Saptharishi, Shpilka and Volk…
The asymptotic rate vs. distance problem is a long-standing fundamental problem in coding theory. The best upper bound to date was given in 1977 and has received since then numerous proofs and interpretations. Here we provide a new,…
Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental problem in coding theory and practice is to efficiently decode the received word…
Quantum computing has the potential to solve problems that are intractable for classical systems, yet the high error rates in contemporary quantum devices often exceed tolerable limits for useful algorithm execution. Quantum Error…
In this paper we propose a new approach to code-based signatures that makes use in particular of rank metric codes. When the classical approach consists in finding the unique preimage of a syndrome through a decoding algorithm, we propose…
In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes,…
We investigate the combination between causal/zero-delay source coding and information-theoretic secrecy. Two source coding models with secrecy constraints are considered. We start by considering zero-delay perfectly secret lossless…
The secrecy performance of a source-channel model is studied in the context of lossy source compression over a noisy broadcast channel. The source is causally revealed to the eavesdropper during decoding. The fidelity of the transmission to…
This paper investigates the soft covering lemma under both the relative entropy and the total variation distance as the measures of deviation. The exact order of the expected deviation of the random i.i.d. code for the soft covering problem…
Hook errors are a major challenge in implementing logical operations with the surface code, because they can reduce the fault distance below the code distance. This motivates syndrome-extraction circuits that suppress hook-error effects for…
We derive an upper bound on the reliability function of mismatched decoding for zero-rate codes. The bound is based on a result by Koml\'os that shows the existence of a subcode with certain symmetry properties. The bound is shown to…
In this paper we show that the Index Coding problem captures several important properties of the more general Network Coding problem. An instance of the Index Coding problem includes a server that holds a set of information messages…
This paper presents a method of zero-shot learning (ZSL) which poses ZSL as the missing data problem, rather than the missing label problem. Specifically, most existing ZSL methods focus on learning mapping functions from the image feature…