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We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
In hardware implementation of a cryptographic algorithm, one may achieve leakage of secret information by creating scopes to introduce controlled faulty bit(s) even though the algorithm is mathematically a secured one. The technique is very…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
Ultra-reliable wireless communication links require the utilization of all diversity sources of a wireless communication channel. Hadani et al. propose a two dimensional discrete symplectic Fourier transform (DSFT) as orthogonal pre-coder…
We re-examine a non-Gaussian quantum error correction code designed to protect optical coherent-state qubits against errors due to an amplitude damping channel. We improve on a previous result [Phys. Rev. A 81, 062344 (2010)] by providing a…
Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
To provide reliable communication in data transmission, ability of correcting errors is of prime importance. This paper intends to suggest an easy algorithm to detect and correct errors in transmission codes using the well-known Karnaugh…
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
We introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and…
Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information,…
A fault-tolerant quantum computer must decode and correct errors faster than they appear. The faster errors can be corrected, the more time the computer can do useful work. The Union-Find (UF) decoder is promising with an average time…
Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…
Forward Error Correction (FEC) is used ubiquitously in the communication pipeline. We explore noncooperative decoding where we aim to recover the code rate of a linear block code. We present a metric to characterize the quality of the code…
The cat code is a promising encoding scheme for bosonic quantum error correction as it allows for correction against losses--the dominant error mechanism in most bosonic systems. However, for losses to be detected efficiently without…
Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in delay--Doppler channels. In order to detect OTFS modulated data, the…