A (n -1) A (n ) Y (n -1) A (n ) 0s B (n ) 1 Look-Ahead Transformation B (n ) 0s Y 1 Y (n -2) 0s B (n -1) Y (n ) Y Y (n ) 1 A (n ) 0s B (n ) 1 Y (a) A (n -1) 2 2 A (n ) B (n ) C (n ) 2 2 2 D (n ) 2 B (n ) C (n ) 0 s 2 1 Y 2 2 B (n -1) 2 0 Y 2 2 B (n ) C (n ) 2 2 2 D (n ) 0 1 2 2 0 1 2 0 2 2 3 2 2 1 Y 2 0 2 2 0 s 2 2 s 2 1 Y Y (n ) 2 3 s 2 2 Y (n -4) 2 2 C (n -3) Y 1 Y 2 2 3 D (n -2) 2 2 Y s 3 2 0 s 0 2 2 2 B (n -3) 2 2 3 2 2 D (n ) 2 Y 2 2 C (n ) 2 1 2 D (n -1) B (n ) s 1 Y 3 A (n ) 2 C (n -2) 2 Y 3 B (n -2) 2 2 s s 1 2 3 2 0 2 2 3 2 2 Y 2 0 s 2 2 C (n -1) A (n ) 2 3 1 2 s 2 2 2 1 2 D (n ) A (n -3) 2 2 3 2 A (n ) 0 A (n -2) D (n -3) 2 2 0 s 2 1 s 1 Y Y 2 2 2 2 3 3 Feed-Forward Section Feedback Section (b) Figure 11: The digital DFE look-ahead transformation applied to (a) a one-tap PAM-2 DFE with LF = 2 and (b) a one-tap PAM-4 DFE with LF = 4. 44 su m m E r 2 0 18 IEEE SOLID-STATE CIRCUITS MAGAZINE