A convolutional
code is described by a set of rules by which the encoding of k data bits into n-coded data
bits is defined. Convolutional codes are characterized by three parameters: k the number of input
data bits, n the number of output data bits, and K the number of input data bits involved in the
calculation of the current output coded bits.
The ratio of k/n is typically called the code rate, this ratio determines the amount of additional
redundancy inserted into the code word. Since k is always less than n, the code rate will always be
less than unity. The smaller the code rate the more parity bits are inserted into the data stream. Two
differences over the block codes are noted as: The value of n does not define the length of the code
word and the convolutional encoder has memory. What this says is that the convolutionally encoded
bit stream is not only a function of the present input data bit, but also a function of the previous K 1
input bits.
The name ???convolutional??? is used because the output of this FEC encoder can be viewed as the
convolution of the input bit stream and the impulse response of the encoder. Which we will show is a
time invariant polynomial.
State Machines and Trellis Diagrams.
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