What is convolutional code?
9.4. 3 Convolutional coding. Convolutional coding is a widely used coding method which is not based on blocks of bits but rather the output code bits are determined by logic operations on the present bit in a stream and a small number of previous bits.
Why do we use convolutional codes?
The sliding nature of the convolutional codes facilitates trellis decoding using a time-invariant trellis. Time invariant trellis decoding allows convolutional codes to be maximum-likelihood soft-decision decoded with reasonable complexity. Convolutional codes are often described as continuous.
What is difference between block codes and convolutional codes?
In block codes, the data comprises of a block of data of a definite length. However, in convolutional codes, the input data bits are not divided into block but are instead fed as streams of data bits, which convolve to output bits based upon the logic function of the encoder.
What is sequential decoding of convolutional codes?
Recognised by John Wozencraft, sequential decoding is a limited memory technique for decoding tree codes. Sequential decoding is mainly used as an approximate decoding algorithm for long constraint-length convolutional codes.
How is convolutional code generated?
Basically, convolutional code is generated by passing the information sequentially through a series of shift registers. K stands for the number of the shift registers.
What are different representations of convolution codes?
There are several methods for representing a convolutional encoder in graphical form; they include the state transition diagram, the tree diagram, and the trellis diagram. As a convention, in the state transition and trellis diagrams, a solid line represents an input 1, whereas a dashed line represents an input 0.
How are convolution codes generated?
Convolution Code is a type of channel coding that generate two bits of coded bits out of one input bit. The name convolution code comes from the way in which how each of the two output bits are generated. Mathematically they are generated by the mathematical opeartion of convolution as shown below.
Is convolutional code linear?
The turbo codes are the hybrid model of the both the linear block codes and the convolutional codes respectively. The linear block codes used in the turbo codes instead of the convolutional codes to form a turbo product code(TPC).
Which method is used most for convolutional decoding?
The most popular decoding algorithm for convolutional codes is perhaps the Viterbi algorithm. Although widely adopted in practice, the Viterbi algorithm suffers from a high decoding complexity for convolutional codes with long constraint lengths.
What is constraint length in convolutional code?
Constraint Length of Convolutional Code Constraint length, k, is the size of the shift register in the memory encoder without feedback. It means how many stages are needed for the combinational logic that produces the output bits. The shift register of size k, stores the present bit and the past (k -1) bits.
How do you decode convolutional codes?
Viterbi algorithm is utilized to decode the convolutional codes. Again the decoding can be done in two approaches. One approach is called hard decision decoding which uses Hamming distance as a metric to perform the decoding operation, whereas, the soft decision decoding uses Euclidean distance as a metric.
Which method is used for decoding of convolutional codes?
Viterbi algorithm
The convolutional coding technique is designed to reduce the probability of erroneous transmission over noisy communication channels. The most popular decoding algorithm for convolutional codes is perhaps the Viterbi algorithm.
Convolutional code is another type of error-correcting code where the output bits are obtained by performing a desired logical operation on a present bitstream along with considering some bits of the previous stream. This coding technique rather than depending on the block of bits shows dependency on bitstream.
What are the inputs and outputs of a convolutional encoder?
Consider the convolutional encoder shown below: Here, there are 2 states p 1 and p 2, and input bit (i.e., k) is represented by m. The two outputs of the encoder are X 1 and X 2 which are obtained by using the X-OR logic function.
What is a K R convolutional coding scheme?
A ( K, R) convolutional coding scheme can be described by an FSM, where K is the constraint length and R is the code rate. Similar to a mealy FSM, there are a total of 2 K coding states where output bits and the next state depend on the current state and an input bit.
What is a rate 1/r convolutional encoder?
Therefore, the code bit rate is 1/ r times the data rate and the encoder is called a rate 1/ r convolutional encoder of constraint length K. Also needed to completely define the encoder are the connections from stages in the shift register to the r summing blocks.