Estimating random variables from random sparse observations

摘要: Let X 1 ,...., n be a collection of iid discrete random variables, and Y m set noisy observations such variables. Assume each observation to function subset the i s, consider conditional distribution given observations, namely μ (x ) = P{X x |Y} (a posteriori probability). We establish general decoupling principle among as well relation between , fixed points associated density evolution operator. These results hold asymptotically in large system limit, provided average number variables an depends on is bounded. discuss relevance our result applications, ranging from sparse graph codes multi-user detection, group testing.