Convolutional Coding

1130 Words3 Pages

Each parity bit is taken from the corresponding D FF then ran through an XOR gate that does the mod 2 addition to output the parity bit. This circuit creates a physical generator polynomial that the message is fed through, creating the encoded message.
Another method of encoding is done through a state table diagram. This is a diagram that tracks which parity bit is output depending on which state it’s in and which state it is transitioning to, which depends on the input bit received. To make our state diagram we first need to understand the parity bit equations above. We will make a 4 state diagram that makes it very simple to understand Convolutional encoding. To illustrate the example above we need a starting state, the start from which we haven’t yet received the message we want encoded. We call this state 00, which correspond to the bits we have received so far, and two bits because our constraint window is k = 3.

Starting in state 00, say we receive a 0, we will stay in this state since we received a 0 and the system is causal, making the parity bits output be 00. Now we receive a 1, we move to the next state 10, which is the order of the message bits received, and output parity bits 11. Now we’re in state 10, we receive a 0, we then move to state 01 and the parity bits will be 11. This is continued for the length of the message, at which the state diagram is reset and awaits a new message to start. You can tell that this type of encoding scheme needs two bits of memory to remember the present bit thats received and the previous bit, while the output still depends on the entered bit. This method of encoding can also be done using circuitry using shift registers and D flip flops as previously mentioned. Shift registers w...

... middle of paper ...

...can use a Trellis structure and Viterbi decoding to find the best path through the Trellis structure and choose the most likely message sent.

Works Cited

Langton, C. Coding and decoding with Convolutional Codes. Coding and decoding with Convolutional Codes, 1, 1-29.

Convolutional Codes. (n.d.). . Retrieved April 27, 2014, from http://rywei.ce.ncu.edu.tw/course/96/ACT/lect1-print.pdf

Han, Y. (n.d.). Introduction to Binary Convolutional Codes. . Retrieved April 27, 2014, from http://erdos.csie.ncnu.edu.tw/~yshan/convolutional_codes.pdf

Mathys, P. (2007, February 1). ECEN 5682 Theory and Practice of Error Control Codes Convolutional Codes. . Retrieved April 27, 2014, from http://ecee.colorado.edu/~mathys/ecen5682/slides/conv99.pdf

Convolutional Coding. (2010, October 4). . Retrieved April 27, 2014, from http://www.cs.miami.edu/~burt/learning/Csc524.142/L8.pdf

Open Document