2 * A convolutional code is generated by passing the information sequence to be transmitted through a linear finite shift register.* The input data to the encoder, which is assumed to be binary is shifted into and along the shift register k bits at a time. The number of output bits for each k bit sequence is n bits.R = k / n.
3 Example.Consider the binary convolutional encoder with k=1 and n=3.
4 >>> Initially, the shift register is assumed to be in the all-zero state. suppose the first input is a 1.then the output sequence of three bits is 111.suppose the second bit is 0.the output sequence will be 001.if the third bit is 1,the output will be 100,and so on.>>> There are three alternative methods that are often used to describe a convolutional code:1. Tree diagram.2. Trellis diagram.3.State diagram.
9 Decoding A message m is encoded into the code sequence c. Each code sequence represents a path in the trellis diagram.Minimum Distance DecodingUpon receiving the received sequence r, search for the path that is closest ( in Hamming distance) to r .
10 The Viterbi Algorithm: * The viterbi algorithm is used to decode convolutional codes and any structure or system that can be described by a trellis.* It is a maximum likelihood decoding algorithm that selects the most probable path that maximizes the likelihood function.* The algorithm is based on add-compare-select the best path each time at each state.
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