Kursinformation
Coding is at the core of any modern communication system; reliable communication would not be possible without the use of coding. When digital data is transmitted from one place to another it is always prone to noise or interference occurring in the transmission medium. For this reason all modern communication systems use some error correcting codes that add redundancy to the original data in order to protect it from errors occurring during the transmission. As a simple example, assume that each data symbol is repeated three times. From the received sequence ’010’ one would then conclude that the original data symbol more likely was a ’0’ than a ’1’. In this example we are able to correct one error by decoding according to a simple majority vote. The number of correctable errors can easily be increased by increasing the number of repetitions. But increasing the amount of redundancy reduces the data rate and hence the bandwidth efficiency of the system.
Since bandwidth is a very limited and expensive resource, in a practical system we need to find more efficient codes that can correct a large number of errors by means of decoding algorithms with feasible complexity. A fundamental limit for reliable communication was derived by Shannon in 1948 in his famous coding theorem. He showed that with coding it is possible to transmit data with an arbitrary accuracy if the rate is below a characteristic parameter of the channel, called channel capacity.
This course gives an introduction to error correction coding (also called error control coding or channel coding). After taking this course you should understand the basic principles of block- and convolutional codes and how to characterize their performance, know different constructions that are most commonly used in digital communication systems and know how their encoding and decoding can be implemented in practice.
Example (picture):
QR codes use Reed-Solomon codes for error correction. This way they remain readable when getting distorted or dirty (for example by coffee spots).