Related papers: Finite-connectivity systems as error-correcting co…
In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…
Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick…
Fault tolerant quantum computers will require efficient co-processors for real-time decoding of their adopted quantum error correction protocols. In this work we examine the possibility of using specialised Ising model hardware to perform…
Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Theoretical framework for dealing with general symmetric…
Low-Density Parity-Check (LDPC) codes received much attention recently due to their capacity-approaching performance. The iterative message-passing algorithm is a widely adopted decoding algorithm for LDPC codes \cite{Kschischang01}. An…
Recently, Lechner, Hauke and Zoller [Science Advances, 1(9)e1500838, (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all connectivity is simulated by a spin glass with geometrically local…
Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{\rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar…
The implementation of practical error correction protocols is essential for deployment of quantum information technologies. Ways of exploiting high-spin nuclei, which have multi-level quantum resources, have attracted interest in this…
We investigate quantum error correction using continuous parity measurements to correct bit-flip errors with the three-qubit code. Continuous monitoring of errors brings the benefit of a continuous stream of information, which facilitates…
Sparse superposition codes are a recent class of codes introduced by Barron and Joseph for efficient communication over the AWGN channel. With an appropriate power allocation, these codes have been shown to be asymptotically…
Recently, a new class of codes, called sparse superposition or sparse regression codes, has been proposed for communication over the AWGN channel. It has been proven that they achieve capacity using power allocation and various forms of…
A polar-coded transmission (PCT) scheme with joint channel estimation and decoding is proposed for channels with unknown channel state information (CSI). The CSI is estimated via successive cancellation (SC) decoding and the constraints…
Consider transmission over a binary additive white gaussian noise channel using a fixed low-density parity check code. We consider the posterior measure over the code bits and the corresponding correlation between two codebits, averaged…
We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing,…
We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for…
The performance of ``typical set (pairs) decoding'' for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding, error happens when the information transmission is corrupted by an untypical noise or…
Information reconciliation (IR) corrects the errors in sifted keys and ensures the correctness of quantum key distribution (QKD) systems. Polar codes-based IR schemes can achieve high reconciliation efficiency, however, the incidental high…
This article examines the queueing performance of communication systems that transmit encoded data over unreliable channels. A fading formulation suitable for wireless environments is considered where errors are caused by a discrete channel…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
To allow for a comparison of theoretical predictions for spin chains with experimental data, it is often important to take impurity effects as well as interchain couplings into account. Here we present the field theory for finite spin…