st output bit in m' is a 0. If you look below the second 00, you see a second solid line- this tells you the second output bit is a 0, and SO on. So, the function of a convolutional decoder is really quite simple. It looks at V, then looks at the trellis diagram and searches it until it's found the output path in the trellis u' closest to V. From this '' it decides on and outputs m'. Channel Coding and Decoding: Part 2-Convolutional Coding and Decoding time 0 time 1 time 2 time 3 received: V = (00 O difference O difference 1 difference one possible path Total 1 different a 2nd possible path Total 2 different a 3rd possible path Total 3 different 1 difference 1 more difference 1 more difference Decide: u'= bits sent = (00 00 00) time 0 time 1 time 2 time 3 u'=(00 = solid line indicates solid line indicates input bit is o input bit is o input bit is o Decide: m' (000) Figure 7.7 (a) Deciding on closest path in trellis (3 paths shown) (b) determining output bits at convolutional decoder Chapter Seven Example 7.2 For the convolutional coder described by the trellis diagram of Figure E7.2, determine the output of the channel decoder when the channel decoder receives V = (11 11). Solution: The trellis diagram is drawn over two times in Figure E7.3. Look- ing over at this figure, we see that the output of the trellis coder can be (11 11) when it follows the shaded path. This tells us that the input bits that were sent must have been m = (00), since: the best path corresponds to two solid lines, each solid line indicating an input bit of 0. Figure E7.3 Trellis diagram over 2 times 7.2.2 The Viterbi Algorithm One thing I haven't yet mentioned- - if you have received, for example, V = (00 00 01 11 10 00 10 00 00 11 11 11 01 10 01 01 01 11 11 01), then you have to search through the trellis to find the path closest to this V. But that search is a long one. Luckily, a fellow named Viterbi presented a simple way to look through the trellis. The Viterbi Algo- rithm (VA for short) lets you (or better yet, your computer or DSP c