Why convolutional codes

In this version of a state diagram there are only four states. Although technically, there are eight possible states for a three stage shift register 2 3 , they have been redefined into just four. To modify the states in this way, we regroup the eight possible states into four by noting that they share common values in their first two register places.

The common values found are of course 00, 01, 10, and For convenience, these in turn are labelled as states a, b, c, and d respectively. By noting how the three digit states in the table of Figure 3 start in their first two digits, column five can be completed, to identify the kind of transitions that exist. There are found to be only eight different transitions possible between the four new states.

These are shown in the state diagram of Figure 2. The working of the decoder and its error correction is illustrated here by the use of trellis graphics. See Figures 4, 5, and 6. The calculation of metrics is the same throughout the trellis; start at the leftmost zero point and work column by column to the right, calculating the metrics for every node. The best sequence of work is found to be:. Follow the example on the adjacent Figure 4 extract.

The unlabelled rows in this extract should be marked as states "a" to "d", from top to bottom. Now, assume that the intention is to calculate the metric for the node in the second column and at level two, State b. The incoming branches for this transition come from states c and d , and these both have previous totals of 2. The top branch has an edge value of 11 and the lower branch The received input r for the transition is shown at the top of the diagram as It is a memory based system, which means the output bit is dependent of the current bit being encoded as well as the previous bit stream stored in the memory.

The Simulink model with Convolution encoder and Viterbi Decoder in the punctured system provides encoding and decoding of high data rate. The puncturing technique uses standard rate one by two encoders and decoders. The main applications of convolution coding is in the deep space applications and in wireless communication systems. The transitions and the output may be effectively represented by a state transition diagram and a state table.

We can see that in the initial state, 00, when the input 1 was given, the next state became 10 and the corresponding output was In this state 10, when the input 1 was given, the next state was 11 and the encoder outputs were In the same manner we get the other transitions. Nancy Den.

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