2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168639Loop Calculus introduced in [Chertkov, Chernyak '06] constitutes a new theoretical tool that explicitly expresses the symbol Maximum-A-Posteriori (MAP) solution of a general statistical inference problem via a solution of the Belief Propagation (BP) equations. This finding brought a new significance to the BP concept, which in the past was thought of as just a loop-free approximation. In this paper we continue a discussion of the Loop Calculus. We introduce an invariant formulation which allows to generalize the Loop Calculus approach to a q-are alphabet.5 pages, 2 figures, proceedings of ISIT '07, misprints correctedInformation TheoryStatistical Mechanicstext