Related papers: Efficient color code decoders in $d\geq 2$ dimensi…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
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.…
Two-dimensional quantum colour codes hold significant promise for quantum error correction, offering advantages such as planar connectivity and low overhead logical gates. Despite their theoretical appeal, the practical deployment of these…
We establish and explore a new connection between quantum information theory and classical statistical mechanics by studying the problem of qubit losses in 2D topological color codes. We introduce a protocol to cope with qubit losses, which…
Surface crack segmentation poses a challenging computer vision task as background, shape, colour and size of cracks vary. In this work we propose optimized deep encoder-decoder methods consisting of a combination of techniques which yield…
In this paper, we consider quantized decoding of LDPC codes on the binary symmetric channel. The binary message passing algorithms, while allowing extremely fast hardware implementation, are not very attractive from the perspective of…
Folded Reed-Solomon (FRS) codes are a well-studied family of codes, known for achieving list decoding capacity. In this work, we give improved deterministic and randomized algorithms for list decoding FRS codes of rate $R$ up to radius…
We introduce and analyze a new type of decoding algorithm called General Color Clustering (GCC), based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under code capacity…
The surface code is the most studied error-correcting code thanks to its high threshold, simple decoding, and locality in two dimensions (2D). A key component of any code is its encoding circuit, which maps an unencoded state to the…
We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a…
Lookup table decoding is fast and distance-preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can…
The Gottesman-Kitaev-Preskill (GKP) code is an important type of bosonic quantum error-correcting code. Since the GKP code only protects against small shift errors in $\hat{p}$ and $\hat{q}$ quadratures, it is necessary to concatenate the…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further…
We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure (L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e errors and t erasures…
While 3D point clouds are widely used in vision applications, their irregular and sparse nature make them challenging to handle. In response, numerous encoding approaches have been proposed to capture the rich semantic information of point…
Quantum error correcting (QEC) codes protect quantum information from decoherence, as long as error rates fall below critical error thresholds. In general, obtaining thresholds implies simulating the QEC procedure using, in general,…
Lattice coding techniques may be used to derive achievable rate regions which outperform known independent, identically distributed (i.i.d.) random codes in multi-source relay networks and in particular the two-way relay channel. Gains stem…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…