Geometrical interpretation and improvements of the Blahut-Arimoto's algorithm

Ziad Naja (1) , Florence Alberge (1) , Pierre Duhamel (1)

1 L2S - Laboratoire des signaux et systèmes

The paper first recalls the Blahut Arimoto algorithm for computing the capacity of arbitrary discrete memoryless channels, as an example of an iterative algorithm working with probability density estimates. Then, a geometrical interpretation of this algorithm based on projections onto linear and exponential families of probabilities is provided. Finally, this understanding allows also to propose to write the Blahut-Arimoto algorithm, as a true proximal point algorithm. it is shown that the corresponding version has an improved convergence rate, compared to the initial algorithm, as well as in comparison with other improved versions.

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]

Ziad Naja, Florence Alberge, Pierre Duhamel. Geometrical interpretation and improvements of the Blahut-Arimoto's algorithm. ICASSP 2009 - 34th IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2009, Taipei, Taiwan. pp.2505 - 2508, ⟨10.1109/ICASSP.2009.4960131⟩. ⟨hal-00445714⟩