Codes de parité à faible densité

Résumé

Dans la théorie de l'information, un contrôle de parité de faible densité LDPC est un code linéaire correcteur d'erreur, permettant la transmission d'information sur un canal de transmission bruité. LDPC est construit en utilisant un graphe biparti clairsemé. Les codes LDPC ont une capacité approchant la limite théorique. À l'aide de techniques itératives de propagation d'information sur la donnée transmise et à décoder, les codes LDPC peuvent être décodés en un temps proportionnel à leur longueur de bloc. Ces informations supplémentaires (qu'on appelle aussi contraintes) sont en fait un groupe de bits de parité, chaque bit protégeant un sous-ensemble du bloc, chaque sous-ensemble étant recouvert par d'autres sous-ensembles. Les codes LDPC ont trouvé une utilisation dans les applications exigeant le transfert d'informations fiables et hautement efficace avec peu d'information en retour. Bien que la mise en œuvre de codes LDPC ait pris du retard sur d'autres codes, notamment les turbo

Source officielle

https://fr.wikipedia.org/wiki/Codes_de_parit%C3%A9_%C3%A0_faible_densit%C3%A9

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées (100)

Publications associées

Chargement

Personnes associées (18)

Personnes associées

Chargement

Unités associées (10)

Unités associées

Chargement

Concepts associés (26)

Concepts associés

Chargement

Cours associés (4)

Cours associés

Chargement

Séances de cours associées (5)

Séances de cours associées

Chargement

New Results On The Pseudoredundancy

Zihui Liu

The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding minimum pseudoweight equals its minimum Hamming distance. By using the value assignment of Chen and Klove we present new results on the pseudocode-word redundancy of binary linear codes. In particular, we give several upper bounds on the pseudoredundancies of certain codes with repeated and added coordinates and of certain shortened subcodes. We also investigate several kinds of k-dimensional binary codes and compute their exact pseudocodeword redundancy.

2019

Chargement

Low-delay low-complexity error-correcting codes on sparse graphs

Xiao-Yu Hu

This dissertation presents a systematic exposition on finite-block-length coding theory and practice. We begin with the task of identifying the maximum achievable rates over noisy, finite-block-length constrained channels, referred to as (ε, n)-capacity Cεn, with ε denoting target block-error probability and n the block length. We characterize how the optimum codes look like over finite-block-length constrained channels. Constructing good, short-block-length error-correcting codes defined on sparse graphs is the focus of the thesis. We propose a new, general method for constructing Tanner graphs having a large girth by progressively establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) construction. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. The PEG construction attains essentially the same girth as Gallager's explicit construction for regular graphs, both of which meet or exceed an extension of the Erdös-Sachs bound. The PEG construction proves to be powerful for generating good, short-block-length binary LDPC codes. Furthermore, we show that the binary interpretation of GF(2b) codes on the cycle Tanner graph TG(2, dc), if b grows sufficiently large, can be used over the binary-input additive white Gaussian noise (AWGN) channel as "good code for optimum decoding" and "good code for iterative decoding". Codes on sparse graphs are often decoded iteratively by a sum-product algorithm (SPA) with low complexity. We investigate efficient digital implementations of the SPA for decoding binary LDPC codes from both the architectural and algorithmic point of view, and describe new reduced-complexity derivatives thereof. The unified treatment of decoding techniques for LDPC codes provides flexibility in selecting the appropriate design point in high-speed applications from a performance, latency, and computational complexity perspective.

EPFL2003

Chargement

We study coding over a class of two-user broadcast channels with additive white Gaussian noise and fading known at the receivers only. Joint decoding of low-density parity-check codes is analyzed. The message update rule at the mapping node linking the users' codes is derived and is shown to exhibit an interesting soft interference cancellation property. Good degree distributions are found using the differential evolution optimization technique and extrinsic information transfer analysis. The corresponding codes have rates close to the boundary of the achievable region for binary constrained input channels, both with and without fading. Simulation results for moderate blocklength show that the optimized codes operate within 1 dB of their thresholds.

2004

Chargement

Low-delay low-complexity error-correcting codes on sparse graphs

Xiao-Yu Hu

EPFL2003