Critères BIC et AIC pour les chaînes de Markov caches Application aux Communications Numériques

Critères BIC et AIC pour les chaînes de Markov caches

Application aux Communications Numériques

Noura Dridi Yves Delignon  Wadih Sawaya 

Institut Mines Telecom/Telecom Lille, LAGIS UMR CNRS 8219 Cité Scientifique-Rue Guglielmo Marconi 59658 Villeneuve d’Ascq Cedex, France

Page: 
383-400
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DOI: 
https://doi.org/10.3166/TS.31.383-400
Received: 
N/A
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

This paper aims at developing both the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) for selecting the order of hidden Markov Chain (HMC) and for selecting HMC parametric models. Since AIC and BIC selection methods require the independence of the data, the proposed AIC and BIC methods are based on the observed data and the estimated hidden process. Order selection algorithms and model selection algorithms coupled to blind estimation methods are subsequently studied in the frame of wide band communication systems. Performances of algorithms are assessed with respect to both the size of the samples and the shape of the channel in terms of root mean square error of the channel and of bit error rate. Finally, the relevance of the blind estimation joint to a model selection is compared to the blind estimation of combined models. 

Extended Abstract

Model selection methods have been used in various signal processing areas such as remote sensing image, image compression or digital communication. Amongst the numerous selection methods, the Akaike and the Bayesian information criteria are the most cited one. The first is based on the minimization of the KullbackLeibler divergence, while the later maximizes the posterior probability. Both of them assume the independence of the observed data. In digital communication, the emitted signal is received through a channel modelled by a finite impulse response filter with additive Gaussian noise. So, blind receiver consists in estimating both the channel coefficients, the noise power and the transmitted symbols. When dealing with supervised estimation, a priori informations about the channel length and its shape are taken into account in order to guide the algorithm to the true channel and to estimate the transmitted symbols. In the absence of a priori information, in addition to symbols, both coefficients and the order of the channel are arbitrary. Most of usual blind estimation algorithms consist in estimating only the channel and the symbols, assuming known the channel length or its shape. In case of the joint channel estimation and symbol detection, the couple of hidden process and observed one are modelled as a hidden Markov channel (HMC) so that the observed data don’t respecttheindependencehypothesis.WeproposetodevelopAICandBICcriteriafor HMC model by exploiting the observed data and the estimated hidden process. We present results of both the order model selection method and parametric shape model selection method in the framework of blind channel estimation and symbol detection. Performance results attest the relevance of including a model selection method in terms of root mean square error of the channel and of bit error rate.

RÉSUMÉ

Dans cet article, nous proposons de développer les critères d’Information d’Akaike (AIC) et Bayesien (BIC) pour sélectionner l’ordre des chaînes de Markov cachées (CMC) et pour la sélection de modèles CMC. Les critères de sélection asymptotiques d’Akaike (AIC) ou Bayesien (BIC) devant respecter l’indépendance des données, nous proposons dans le cas des modèles de Markov cachés d’appliquer les critères sur les données observées conditionnelles aux données cachées préalablement estimées. Les algorithmes de sélection de modèles et d’estimation aveugle sont par la suite développés dans le cadre desc ommunications numériques large bande. Les performances de ces critères sont évaluées au regard de la taille de l’échantillon et de la forme du canal en termes de taux de bonne sélection et de taux d’erreur binaire. En particulier, la pertinence de l’estimation aveugle avec sélection de modèles est comparée à l’estimation aveugle de modèles combinés. 

Keywords: 

hidden Markov chain, AIC, BIC, channel estimation.

MOTS-CLÉS

chaînes de Markov cachées, AIC, BIC, estimation du canal.

1. Introduction
2. Sélection de Modèles pour les Chaînes de Markov Cachées
3. Application à la Problématique d’Estimation du Canal et Dedétection de Symboles
4. Sélection de l’Ordre du Modèle
5. Sélection de CMC
6. Résultats
7. Conclusion
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