ing the two states. For example if the encoder changes from state '00' to '10', then the Broadband Telecommunications Technologies and Management Figure 6.15 A trellis decoder output of the encoder is '11'. At the end of the data block, two 0 tail bits ensure the state of the decoder returns to the '00' state. At each state the received bits and the branch bits are compared and their Hamming dis- tance is calculated. When two branches merge into a state the total Hamming distances of each branch (called branch metric) are compared and the branch with the lowest metric is selected as the most likely transmitted codeword, and duly decoded [6]. Example 6.6 Assume the sequence '111000' has been received. Draw and calculate the surviving branch. Answer As shown in Figure 6.16, the trellis decoder starts at state '00'. Only two transitions to states '00' and '10' are possible corresponding to data bits 0 and 1, and encoder outputs of '00' '11'. As the first received bits are '11' the Hamming distance is 2 for the top branch and 0 for the lower branch. In the second data bit interval, similar transitions may be shown and the branch metric calculated. At the end of the third bit interval the two branches converge in state '01' and the accumulated branch metrics are 0 for the lower branch and 4 for the higher branch. It is likely that the lower branch sequence was transmitted corresponding to a '110' input bit sequence. A typical BER vs EINo performance of a Viterbi decoder for a convolutional (2,1,3) code is shown in Figure 6.17. A coding gain of 3.5 dB can be observed at BER of 10-4. This equivalent to a transmission power reduction in the order of 2.2 times. As the ratio of the number of parities to data bit increases and more shift registers are used to increase the inter- relationship between more input data bits and output parity bits the performance of the convolutional codes improves, resulting in coding gains in the order of 6 dB (power savings of 4 times). A number of convolutional codes are used in various tele