ALGORITHM I.

Low-rank coding optimization procedure

Input: $X_s$, $X_t$, $Y$, $\lambda$

Initialization: $Y_1=Y_2=0$, $Z=0$, $E=0$, $\rho =1.1$, $\epsilon ={10}^{-6}$

Output: $Z$, $E$, ${\mathit{\text{Loss}}}_{lr}$

while converted do

1. Fix the other variables, update $Z$ by solving (7)

2. Fix the other variables, update $J$ by solving (8)

3. Fix the other variables, update $E$ by solving (9)

4. Update the multipliers and parameters: $Y_1$, $Y_2$

5. Check the convergence conditions: ${\Vert X_t-X_{s}Z-E\Vert }_{\infty }<\epsilon$, ${\Vert Z-J\Vert }_{\infty }<\epsilon$

end while