Encoder for a convolutional code accepts k-bit blocks of information sequence and produces an encoded sequence (codeword) of n-bit blocks. However, each encoded block depends not only on the corresponding k-bit message block at the same time unit, but also on M previous blocks. Hence, the encoder has a memory length of m. Encoder operates on the incoming message sequence continuously in a serial manner. Code rate is again defined as r = k/n. Constraint length is defined as K = M+1, where M is number shift registers in encoder.

Encoder of Convolutional Code :
     Encoder of convolutional code has a finite state machine with M-stage shift register, n modulo-2 adder and a Multiplexer that serializes the outputs of the adders. Figure 3.1 shows an example of a convolutional encoder. For this encoder, the code rate is 1/2 and the constraint length is 3.

Figure 3.1: an example of a convolutional encoder

Representations of Convolutional Code :

Generator Polynomial of Convolutional code
      Generator polynomial of the i-th path is . The set of generator polynomial completely describes the convolutional encoder {g(1)(D),g(2)(D),…,g(n)(D)}. For the encoder in Figure 5, we have g(1)(D) = 1+D+D2, g(2)(D)=1+D2.

Code Tree, Trellis, and State Diagram
     There are three graphical descriptions of the structural properties of a convolution code, which are shown in Figure 3.2.

Figure 3.2: Code Tree, Trellis and State diagram of convolutional code

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