We study the convergence behavior of turbo decoding, turbo equalization, and turbo bit-interleaved coded modulation in a unified framework, which is to regard all three principles as instances of iterative decoding of two serially concatenated codes. There is a collection of measures in the recent literature, which trace the convergence of iterative decoding algorithms based on a single parameter. This parameter is assumed to completely describe the behavior of the soft-in soft-out decoders being part of the iterative algorithm. The measures observe different parameters and were originally applied to different types of decoders. In this paper, we show how six of those measures are related to each other and we compare their convergence prediction capability for the decoding principles mentioned above. We observed that two measures predict the convergence very well for all regarded decoding principles and others suffer from systematic prediction errors independent of the decoding principle.

Abstract-An investigation of the relationship between the sensitivity coefficients and the K-matrix of n-port networks is presented. The results available on the K-matrix and the adjoint network approach for sensitivity computations will form the basis of the discussions. THE P-MATRIX ONSIDER a resistive n-port network N. Let 4 = C {gi} denote the column matrix of edge conductances of N. We shall denote by Jo. = {gio} the nominal value of @., The sensitivity coefficient matrix P = [pii] with respect to the Y-matrix of N will be defined as follows: Pij = 218 =Oo I where yii is the short-circuit driving-point admittance across port i of N. Pij will be referred to as the sensitivity coefficient of yii with respect to the conductance gj. It may be seen that the matrix P is of order it x e, where e is the number of edges in N. Without any loss of generality the graph of the network N may be assumed to be complete by permitting edges with zero admittances. It follows from the results of [l], [2] that where vkj (a,‘) is th e voltage across conductance gk when port j(i) is excited with a source of unit voltage and all the other ports are short-circuited. This is illustrated in Fig. 1. Hence we get Pik IO = 80 = Cvk’12 (3) as a consequence of the no amplification property of resistive networks pik I 1. Let the port configuration T of N be in p parts Tl, T,, * *., Tp. Let the set of vertices in Ti be denoted by l$. Let To be a tree of N such that T c To. We shall denote by qi thef-cutset of N with respect to the branch of T correspond-ing to the port i. If port i is in Tk, it may be seen from (3)