Related papers: Erasure decoding of convolutional codes using firs…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…
High-dimensional vectors have been proposed as a neural method for representing information in the brain using Vector Symbolic Algebras (VSAs). While previous work has explored decoding and cleaning up these vectors under the noise that…
We devise a scheme that protects quantum coherent states of light from probabilistic losses, thus achieving the first continuous-variable quantum erasure-correcting code. If the occurrence of erasures can be probed, then the decoder…
In this article we extend the idea of Turbo codes onto the Real Field. The channel is taken to result in block erasures and the only noise as being that due to quantization. The decoding in this case is reduced to reconstruction of the lost…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
Digital media is ubiquitous and produced in ever-growing quantities. This necessitates a constant evolution of compression techniques, especially for video, in order to maintain efficient storage and transmission. In this work, we aim at…
The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure,…
Recently, Convolutional Neural Networks (CNNs) have achieved tremendous performances on face recognition, and one popular perspective regarding CNNs' success is that CNNs could learn discriminative face representations from face images with…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
Sparse representations of images are useful in many computer vision applications. Sparse coding with an $l_1$ penalty and a learned linear dictionary requires regularization of the dictionary to prevent a collapse in the $l_1$ norms of the…
Over the past several years, we have witnessed impressive progress in the field of learned image compression. Recent learned image codecs are commonly based on autoencoders, that first encode an image into low-dimensional latent…
A Viterbi-like decoding algorithm is proposed in this paper for generalized convolutional network error correction coding. Different from classical Viterbi algorithm, our decoding algorithm is based on minimum error weight rather than the…
The successive cancellation list decoding algorithm for polar codes yields near-optimal decoding performance at the cost of high implementation complexity. The successive cancellation stack algorithm has been shown to provide similar…
In this paper, we introduce a deep learning-based decoder designed for concatenated coding schemes over a deletion/substitution channel. Specifically, we focus on serially concatenated codes, where the outer code is either a convolutional…
Image compression has been investigated as a fundamental research topic for many decades. Recently, deep learning has achieved great success in many computer vision tasks, and is gradually being used in image compression. In this paper, we…
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…
This paper considers transmitting a sequence of messages (a streaming source) over a packet erasure channel. In each time slot, the source constructs a packet based on the current and the previous messages and transmits the packet, which…