3.3.3 Veterbi decoder

3.3.3 Veterbi decoder :

      The equivalence between maximum likelihood decoding and minimum distance decoding for a binary symmetric channel implies that we may decode a convolutional code by choosing a path in the code tree whose coded sequence differs from the received sequence in the fewest number of places. Since a code tree is equivalent to a trellis, we may equally limit our choice to the possible paths in the trellis representation of the code.

            For example we will assume the received data and the pre described trellis as shown in figure (3.7). The figure contains only two states for more simplification in the discussion.

Figure 3.7

           

 We check each channel output with each stage. Then, we are counting the error bits and is added it to the previous path error. For a certain node, if two paths gave two different errors the bigger one is discarded. The best path is then chosen which have the minimum error.