Related papers: Information-Set Decoding for Convolutional Codes
Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In this work, we leverage this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local…
We propose application-layer coding schemes to recover lost data in delay-sensitive uplink (sensor-to-gateway) communications in the Internet of Things. Built on an approach that combines retransmissions and forward erasure correction, the…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol…
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.…
This paper investigates data compression that simultaneously allows local decoding and local update. The main result is a universal compression scheme for memoryless sources with the following features. The rate can be made arbitrarily…
We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes and message-passing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
Quantum convolutional coding is a technique for encoding a stream of quantum information before transmitting it over a noisy quantum channel. Two important goals in the design of quantum convolutional encoders are to minimize the memory…
Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target…
The rapidly improving performance of modern hardware renders convolutional codes obsolete, and allows for the practical implementation of more sophisticated correction codes such as low density parity check (LDPC) and turbo codes (TC). Both…
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to…
In source coding, either with or without side information at the decoder, the ultimate performance can be achieved by means of random binning. Structured binning into cosets of performing channel codes has been successfully employed in…
In this paper, we introduce DICOD, a convolutional sparse coding algorithm which builds shift invariant representations for long signals. This algorithm is designed to run in a distributed setting, with local message passing, making it…
Consider the case where a programmer has written some part of a program, but has left part of the program (such as a method or a function body) incomplete. The goal is to use the context surrounding the missing code to automatically 'figure…
Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in DNA-based data storage systems where the inner code decoding, which generally has…
We convert Stern's information set decoding (ISD) algorithm to the ring $\mathbb{Z}/4 \mathbb{Z}$ equipped with the Lee metric. Moreover, we set up the general framework for a McEliece and a Niederreiter cryptosystem over this ring. The…