Turbocodes: achievements and prospects

Nowadays, telecommunications are omnipresent in our environment. Whether it's satellite links, cell phones or WiFi connections, many systems exchange data over the air. However, the wave propagation environment is inherently disturbed by noise. This noise is of different kinds. It can be linked to human activities (radar stations, maritime beacons, radio, television, etc.), but it can also be of external origin (solar activity or intergalactic radiation). Radio waves are also subject to attenuation due to absorption by the propagation medium. Finally, in terrestrial applications, there are also echo phenomena where the receiver receives several copies of the radio signal, offset in time. This is the case, for example, when the main beam is reflected by objects in the environment (buildings, cars, etc.). All these factors disrupt communications and can lead to data transmission errors.

To deal with this problem, error-correcting codes were invented. The principle consists in adding redundant information to the information to be transmitted. So, if you want to broadcast a packet of symbols of size n, it is first encoded into a packet of size N > n. On the receiver's side, the received packet of size N may contain errors. But not all possible packets received correspond to a correct encoding. Decoding therefore involves first finding the most likely packet, and then extracting the useful information of size n from it. By most likely packet, we generally mean the valid packet that minimizes the number of errors or the power of the noise observed in relation to the packet of size N received.

References in square brackets are explained in the section Further information [Doc. TE 5 260].

The invention of turbocodes in 1993 has greatly modified the modern approach to error-correcting codes. Indeed, pre-existing systems were relatively complex in terms of encoding and decoding. On the other hand, from a theoretical point of view, the work carried out by Claude Shannon predicted that below a certain noise power, it was possible to obtain error-free communication systems. Existing solutions, however, operated at noise levels relatively far from this limit. Over time, this difference between theory and practice had even come to be accepted as an incompressible penalty. Turbocode-based solutions have...