Algorithm 1 Arimoto Blahut pseudocode for rate distortion with second order statistics constraints

Require: $p\left(\tilde{v}\right)$ Ensure: Fix $p\left(u\right),\eta ,\tau ,\mu ,\lambda \left(\tilde{v}\right)$ 1:Set $\tilde{\lambda }\left(\tilde{v}\right)=1-\lambda \left(\tilde{v}\right)/p\left(\tilde{v}\right)$ 2:Set $p(u|\tilde{v})=p\left(u\right)e^{-\tilde{\lambda }\left(\tilde{v}\right)}{e}^{-\eta {(u-\tilde{v})}^2-\tau u-\mu u^2}$ 3:Set $p\left(u\right)={\int }_{\tilde{v}}p(u|\tilde{v})p\left(\tilde{v}\right)d\tilde{v}$ 4:Set $\tau$ so that $\mathbb{E}\left(U\right)=0$ 5:Set $\mu$ so that $\mathbb{E}\left(U^2\right)=1$ 6:Go to Step 4 until convergence