1. Turbo Codes – Decoding and Applications Bob Wall EE 548

2. The Turbo Decoder Since a Turbo Code trellis would have a very large number of states (due to the interleaver), a normal decoder would be huge Instead, perform an iterative decoding process –This requires some changes to the normal decoder – instead of making a “hard” decision, it needs to make a “soft” decision

3. Decoder Decisions A “hard” decision is choosing a sequence of 0 or 1 output bits based on the input symbols. It does not take into account how likely this string of bits was. A “soft” decision produces a value in [0, 1] that corresponds to the likelihood (or log likelihood). This can be used as input to help make decisions about the transmitted sequence

4. Decoder Algorithms Normal decoding algorithms (i.e. Viterbi algorithm) find the most likely sequence of bits that was transmitted. In a turbo decoder, want to find the likelihood of each bit. This serves as the a priori probability or the reliability of each bit, to use as input to the next decoder –Optimal MAP (Maximum a Priori) – BCJR (Bahl, Cocke, Jelinek, Raviv) –Simpler - SOVA (Soft Output Viterbi Algorithm) – lose roughly.7 dB coding gain

5. Decoder Flow Simplified flow diagram (from http://www.xenotran.com/turbo_tech_error_turbo.html)

6. Block Diagram Generic Turbo Decoder extrinsic information x i y i x k y k DEC - DEC | Inter- leaver De-inter- leaver

7. Turbo Decoding Delays Delay introduced by interleaver – depending on how it is designed, some or all of a block of data must be present before encoding or decoding can begin Delay introduced by iteration You have to have some drawbacks – no free lunch!

8. Performance

9. Performance (cont.)

10. Applications Terrestrial Wireless Communications –UMTS (Universal Mobile Telecommunication Systems) Digital Video Broadcasting (DVB) CCSDS (Consultative Committee for Space Data Systems) Telemetry Standard

11. CCSDS Telemetry Standard Upgraded to specify Turbo Code as an alternative channel coding standard –Alternative to older codes: (255, 223) Reed- Solomon code, 64-state rate-1/2 convolution coder, and their serial concatenation –2.5 dB coding gain over old standard Also allows for symbol synchronization

12. Space Telemetry Symbol Synchronization – recover clock information from the signal itself Requires relatively frequent changes in signal (run lengths must be limited) Specifications suggest max run length of 64 symbols, and a minimum number of transitions in 1000 symbols of 275

13. Symbol Synchronization With turbo code specified in standard (N = 8920), simulation has shown that the max run lengths for the rate 1/2 and rate 1/3 encoders are 42 and 53, respectively, and the minimum number of transitions per 1000 symbols are 407 and 408, respectively Turbo code is very close to the ideal random code