Related papers: A Study on the Impact of Locality in the Decoding …
Turbo codes and CRC codes are usually decoded separately according to the serially concatenated inner codes and outer codes respectively. In this letter, we propose a hybrid decoding algorithm of turbo-CRC codes, where the outer codes, CRC…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
In this paper, we investigate the use of quaternary reliability statistics for ordered statistics decoding (OSD) of quantum codes. OSD can be used to improve the performance of belief propagation (BP) decoding when it fails to correct the…
Polar codes are capacity achieving error correcting codes that can be decoded through the successive-cancellation algorithm. To improve its error-correction performance, a list-based version called successive-cancellation list (SCL) has…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization, i.e., a cycle-free realization of the code on the…
We propose a low complexity list successive cancellation (LCLSC) decoding algorithm to reduce complexity of traditional list successive cancellation (LSC) decoding of polar codes while trying to maintain the LSC decoding performance at the…
A locally recoverable code of locality $r$ over $\mathbb{F}_{q}$ is a code where every coordinate of a codeword can be recovered using the values of at most $r$ other coordinates of that codeword. Locally recoverable codes are efficient at…
Data coding as a building block of several image processing algorithms has been received great attention recently. Indeed, the importance of the locality assumption in coding approaches is studied in numerous works and several methods are…
Electronic properties of disordered binary alloys are studied via the calculation of the average Density of States (DOS) in two and three dimensions. We propose a new approximate scheme that allows for the inclusion of local order effects…
Modern distributed computation infrastructures are often plagued by unavailabilities such as failing or slow servers. These unavailabilities adversely affect the tail latency of computation in distributed infrastructures. The simple…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
This paper studies bounds and constructions of locally repairable codes (LRCs) with multiple localities so-called multiple-locality LRCs (ML-LRCs). In the simplest case of two localities some code symbols of an ML-LRC have a certain…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
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…
In addition to a proposed codeword, error correction decoders that provide blockwise soft output (SO) return an estimate of the likelihood that the decoding is correct. Following Forney, such estimates are traditionally only possible for…
The forthcoming Versatile Video Coding (VVC) standard adopts the trellis-coded quantization, which leverages the delicate trellis graph to map the quantization candidates within one block into the optimal path. Despite the high compression…
In the problem of blind reconstruction of channel codes, the receiver does not have the knowledge of the channel code used at the transmitter and the aim is to identify this unknown channel code corresponding to the given received sequence.…
This paper presents a theoretical study of a new type of LDPC codes motivated by practical storage applications. LDPCL codes (suffix L represents locality) are LDPC codes that can be decoded either as usual over the full code block, or…