Contents
Which is the output of a convolutional encoder?
The product of each of these n generator polynomials and the input polynomial gives rise to the corresponding output polynomial, from which the corresponding encoded output can be formed. A convolutional encoder, with k = 1, n = 2, and K = 3, is shown in Figure 10.8a.
What is the code rate of the encoder?
The code rate = k/n, is expressed as a ratio of the number of bits into the convolutional encoder (k) to the number of channel symbols output by the convolutional encoder (n) in a given encoder cycle.
How is a convolutional code different from a block code?
Convolutional code. This is in contrast to classic block codes, which are generally represented by a time-variant trellis and therefore are typically hard-decision decoded. Convolutional codes are often characterized by the base code rate and the depth (or memory) of the encoder . The base code rate is typically given as ,…
Why are convolutional codes used in digital communications?
Convolutional code. The performance of a punctured convolutional code generally scales well with the amount of parity transmitted. The ability to perform economical soft decision decoding on convolutional codes, as well as the block length and code rate flexibility of convolutional codes, makes them very popular for digital communications.
How are parity bits switched out in convolutional coding?
Two parity bits are switched out in the interval between n and n − 1 from the upper adder and then the lower one. When the next data bit arrives, the shift register moves its contents to the right. The K − 1 earlier bits, in this case two, determine the state of the encoder. They are shown in gray in Fig. 9.7. There are 2 K − 1 states.
What kind of machine is a binary convolutional code?
A binary convolutional code is a finite-state machine with 2 k ( K − 1) states. In a finite state machine, a state consists of the smallest amount of information that together with the knowledge of the input can determine the output.
How are sampling times chosen in convolutional coding?
Fig. 9.7 shows an example with K = 3, r = 2, and the generator vectors are chosen as [1 1 1] and [1 0 1]. Discrete sampling times are labeled n. The data stream enters on the left and the present bit at time n, the most recent bit n − 1 and the next earliest bit at n − 2 occupy the shift register.