Repeat code

The repetition code is the simplest error-correcting channel code . It repeats each transmitted symbol n times.

Example for n = 3:

Bit sequence to be coded: 10010

Coded sequence: 111 000 000 111 000

The n-fold repetition code has the distance with which errors can be corrected by rounding. If the error rate exceeds 50%, the decoder sees the correct bits as wrong and "corrects" in the wrong direction. ${\displaystyle d=n}$ ${\displaystyle \left\lfloor {\tfrac {n-1}{2}}\right\rfloor }$

All odd length binary repeat codes are perfect codes . The repetition code with length 3 corresponds to the binary (3,1) Hamming code .

literature

• Martin Bossert, M. Breitbach: Digital networks. Function groups of digital networks and system examples. BG Teubner Verlag, Stuttgart 1999, ISBN 3-519-06191-0 .
• Wilfried Dankmeier: Basic coding course. Encryption - Compression - Debugging. 3. Edition. Friedrich Vieweg & Sohn Verlag, Wiesbaden 2006, ISBN 3-528-25399-1 .
• Bernd Friedrichs: Channel coding. Basics and applications in modern communication systems. Springer Verlag, Berlin / Heidelberg 1995, ISBN 3-540-59353-5 .

Web links

• Linear Codes (accessed October 5, 2017)
• Coding Theory (accessed October 5, 2017)
• Recurrence Code (accessed October 5, 2017)