Information Loss in Static Nonlinearities
In this paper, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. The authors derive an expression for the information loss depending on the input density and the nonlinearity and show that the result is strongly related to the non-injectivity of the considered system. Tight upper bounds are presented, which can be evaluated with less difficulty than a direct evaluation of the information loss, which involves the logarithm of a sum. Application of their results is illustrated on a set of examples.