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Table 2 Numerical solution for solving (9)

From: Achievable rates optimization for broadcast channels using finite size constellations under transmission constraints

Step   Solution
Step 0   ss(0)
Step k Step 0 X X ( 0 ) where X=( x 0 , x 1 ,.., x M - 1 )
  Step P UX ( ) = arg max P UX C L ( P UX , X ( - 1 ) , s ( k - 1 ) ) ( P 1 ) X ( ) = arg max X L ( P UX ( ) , X , s ( k - 1 ) ) ( P 2 )
  Stopping |L( P UX ( ) , X ( ) , s ( k ) )-L( P UX ( - 1 ) , X ( - 1 ) , s ( k - 1 ) )| ε L
  criterion  
   s ( k ) = [ s ( k - 1 ) - β ( P - i , j p ij ( s ( k - 1 ) ) · ( x j ( s ( k - 1 ) ) ) 2 ) ] +
   where [.]+= max(.,0)
Stopping   
criterion   |s(k)-s(k-1)|≤ε s