Related papers: Information-Set Decoding for Convolutional Codes
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
In this work, we develop convolutional neural generative coding (Conv-NGC), a generalization of predictive coding to the case of convolution/deconvolution-based computation. Specifically, we concretely implement a flexible…
This paper presents a novel post-quantum cryptosystem based on high-memory masked convolutional codes. Unlike conventional code-based schemes that rely on block codes with fixed dimensions and limited error-correction capability, our…
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of…
Image restoration, including image denoising, super resolution, inpainting, and so on, is a well-studied problem in computer vision and image processing, as well as a test bed for low-level image modeling algorithms. In this work, we…
For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known…
We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
We consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
Cryptographic check values (digital signatures, MACs and H-MACs) are useful only if they are free of errors. For that reason all of errors in cryptographic check values should be corrected after the transmission over a noisy channel before…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
Information set decoding (ISD) algorithms are the best known procedures to solve the decoding problem for general linear codes. These algorithms are hence used for codes without a visible structure, or for which efficient decoders…
This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x in R^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably…
We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code…
In diffusion based molecular communication, the intersymbol interference (ISI) is an important reason for system performance degradation, which is caused by the random movement, out-of-order arrival and indistinguishability of the…