JPL's Wireless Communication Reference Website

Chapter: Analog and Digital Transmission, Receiver Design

Convolutional coding

Contributed by Olivier Swedor, EPFL

A model of digital communication system:

The discrete source generates information in the form of binary symbols. The channel encoder adds redundancy to it according to a prescribed rule. The channel decoder in the receiver uses this redundancy to decide wich message bits were actually transmitted. The combined goal of the encoder and decoder is to minimize the effect of channel noise.
There are many different error-correcting codes. They have been classified into "block codes", or "convolutional codes", depending on wether there is a memory in the encoder or not.

In block coding, an encoder generates a n - bit code word with a k - bit message block, so code words are produced on a block-by-block basis. But if we want to process the incoming bits serially rather than in large blocks, we will use convolutional coding.

In convolutional codes, the encoding operation may be viewed as the discrete-time convolution of the input sequence with the impulse response (or generator polynomial) of the encoder. The encoder operates on the message with a "sliding window", with a length equal to its own memory.

An example of convolutional encoding:

This diagram represents a convolutional encoder that takes one bit in the input and returns two bits in the output. We can describe it by the impulse response (or the generator polynomial) of each of the two paths. The impulse response is defined as the response of a path to a symbol 1 applied to its input, with each flip-flop initially set to zero.


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JPL's Wireless Communication Reference Website 1999

Source: Applet by Olivier Swedor. The development of this page has been carried out as a semester project in the mobile communications laboratory of the Swiss Federal Institute of Technology, EPFL, Lausanne.