Problem SettingConsider a channel $C$, whose input is a binary vector $X^n = [X_1,X_2,\cdots,X_n]$, s.t $X_i \sim bern(\mu_i)$. The output of the channel is vector $Y^n = \Pi X^n + Z$, where $\Pi$ is a random permutation and $Z$ is a iid gaussian noise vector with variance $\sigma^2$. (Assume $\sigma^2 >> 1$)QuestionWhat is the capacity of this channel? $$I\big( X^n ; \Pi X^n + Z\big)$$Note: The optimization is over $\mu_i's$.PS : I have asked the same question here. But this forum seems more appropriate for this kind of question :)
Capacity of a channel with permutation and gaussian noise
reference request;pr.probability;it.information theory;permutations