Related papers: Error correcting codes and spatial coupling

Decoding error-correctiong codes by methods of mathematical optimization, most importantly linear programming, has become an important alternative approach to both algebraic and iterative decoding methods since its introduction by Feldman…

This study focuses on the efficiency of message-passing-based decoding algorithms for polar and low-density parity-check (LDPC) codes. Both successive cancellation (SC) and belief propagation (BP) decoding algorithms are studied {in} the…

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…

This text is the extended version of a talk given at 6th Meeting of Integrable Systems and Quantum Filed Theory at Peyresq hold from June 10 2006 to June 17, 2006 at Peyresq, France. The goal of this lecture is to give a brief introduction…

Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…

These lecture notes from the 2019 Les Houches Summer School on 'Quantum Information Machines' are intended to provide an introduction to classical and quantum error correction with bits and qubits, and with continuous variable systems…

In conventional sparse representations based dictionary learning algorithms, initial dictionaries are generally assumed to be proper representatives of the system at hand. However, this may not be the case, especially in some systems…

Polar codes were introduced in 2009 and proven to achieve the symmetric capacity of any binary-input discrete memoryless channel under low-complexity successive cancellation decoding. In this thesis, we construct cyclic polar codes based on…

In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. This local-global construction is motivated by practical applications in data storage and transmission where reduced-latency…

In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information…

We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…

Spatially coupled, parallel concatenated codes (SC-PCCs) have been shown to approach channel capacity when decoded using optimal iterative methods. However, under complexity constraints such decoding strategies can result in unacceptable…

We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…

We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…

In this paper we propose a new class of spatially coupled codes based on repeat-accumulate protographs. We show that spatially coupled repeat-accumulate codes have several advantages over spatially coupled low-density parity-check codes…

We propose a new method called decoupling representation to represent Pauli operators as vectors over $GF(2)$, based on which we propose partially decoupled belief propagation and fully decoupled belief propagation decoding algorithm for…

These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory,…

Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D qubit lattice,…

This volume contains the proceedings of the Eighth Workshop on Fixed Points in Computer Science which took place on 24 March 2012 in Tallinn, Estonia as an ETAPS-affiliated workshop. Past workshops have been held in Brno (1998, MFCS/CSL…

For finite length polar codes, channel polarization leaves a significant number of channels not fully polarized. Adding a Cyclic Redundancy Check (CRC) to better protect information on the semi-polarized channels has already been…