Extremal Problems of Information Combining

In this paper we study moments of soft-bits of binary-input symmetric-output channels and solve some extremal problems of the moments. We use these results to solve the extremal information combining problem. Further, we extend the information combining problem by adding a constraint on the second moment of soft-bits, and find the extremal distributions for this new problem. The results for this extension problem are used to improve the prediction of convergence of the belief propagation decoding of low-density parity-check codes, provided that another extremal problem related to the variable nodes be solved.