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We compute explicit bounds in the Gaussian approximation of functionals ofinfinite Rademacher sequences. Our tools involve Stein's method, as well as theuse of appropriate discrete Malliavin operators. Although our approach does notrequire the classical use of exchangeable pairs, we employ a chaos expansion inorder to construct an explicit exchangeable pair vector for any random variablewhich depends on a finite set of Rademacher variables. Among several examples,which include random variables which depend on infinitely many Rademachervariables, we provide three main applications: (i) to CLTs for multilinearforms belonging to a fixed chaos, (ii) to the Gaussian approximation ofweighted infinite 2-runs, and (iii) to the computation of explicit bounds inCLTs for multiple integrals over sparse sets. This last application provides analternate proof (and several refinements) of a recent result by Blei andJanson.

The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6