ng through a trellis for the closest path can be a difficult task. But, in Chapters 7 and 8, we saw a handy way to do it-a way called the Viterbi algo- rithm. When you want to use the Viterbi algorithm to find the best path, just use it in exactly the same way explained in Section 8.3. Channel Filtering and Equalizers r1=1.7A r2 1.7A time O time 1 time 2 -1.5A -1.5A PATH 1 Distance = (1.7A - ( (-1.5A))2 + (1.7A - (-1.5A)) = 20.48A2 time 0 time 1 time 2 -1.5A PATH 2 Distance = (1.7A - (-1.5A))2 -(1.7A-0.5A)2 = 11.72A2 time O time 1 time 2 PATH 3 -0.5A Distance = (1.7A - 1.5A)2 - + (1.7A-(-0.5A))2 =10.32A2 - time O time 1 time 2 PATH 4 Distance2 = =1.7A-1.5A)2 + (1.7A-1.5A)2= - = 0.08A2 Figure 9.18 Looking for the closest path through the trellis Chapter Nine Example 9.4 If, after a whitening filter, the received signal is described by (E9.19) where Vo = vi =1 (E9.20) (E9.21) then figure out the output of an MLSE (using the Viterbi algorithm) when the input to the decoder corresponds to r = = (E9.22) Solution: Figure E9.1 shows the trellis diagram characterizing the received signal in Equation (E9.19). This diagram is created from Equation (E9.19) using the four steps outlined in the writing you just read. Also shown in Figure E9.1 is the application of the Viterbi algorithm to determine the best path through the trellis. For each node, the best parent is found by choosing the parent with the smallest total distance. When we get to the last nodes, we look for the node with the smallest total and we backtrack through the trellis as marked by the arrows. These arrows tell us that the output of the trellis should be (-11) (based on the branch lines of the best path). received dist2=0.01 total = 0.01 dist2 = 4.41 total = 4.42 dist2 best parent best parent =-1 (total 0.01) (total 4.42) dist2 = 16.81 total =16.81 best parent best parent (total 4.41) (total 0.02) Figure E9.1 Trellis describing received signal + Viterbi Algorithm used to get best output Channel Filtering and Equalizers 9.5.4 An Issue with Using the Whiteni