Using the Method of Nearby Measures in Superposition Coding with a Bernoulli Dictionary

The work discussed in this presentation is motivated by the problem of decoding superposition codes when using {−1,+1}-valued dictionary elements. Under this encoding scheme, the output, Y , is a linear combination of independent Bernoulli random variables and noise. Statistical decoding then requires the study of the conditional distribution of the Bernoulli random variables given the output, Y . We find this distribution analogous to that of summands given the sum of independent random variables as studied by Cover and Campenhout and Csiszár. Motivated by this work we wish to bound the Rényi relative entropy distance between the true conditional distribution and the product of tilted distributions in order to show that events that are exponentially rare under the tilted product distribution remain rare under the true distribution.