Turbo Codes

1. Turbo Codes Azmat Ali Pasha

2. Goals of Presentation • Why Coding, Error Correction, etc? • Basic terms and concepts • Methods of handling the noise issues

3. Error Control Coding/Channel Coding • What can you do in situations where data is transmitted over a noisy channel? • Adding redundancy to information • Check code • Correct Errors

4. Transmission • Data is digitally recorded and compressed • Data is encoded by error control coding • Data is modulated from digital data to an analog signal

5. Reception • Analog signal is received and demodulated back to a digital signal • Data is processed in the Error Control Decoder • Redundancy is used to check for errors and correct them • Data is uncompressed and presented

6. Transmission Process with Coding Application Layer  Data Compression Application Layer  Data Decompression Convolutional or Turbo coding Viterbi or Turbo decoding Channel Coding Channel Decoding Modulation  Frequency Up-conversion  Power Amplification Demodulation  Frequency Down-conversion  Receiver

7. Sensitivity to Error

8. Repetition Code • Simple Repetition Code • Information Sequence {010011} • Codeword {00 11 00 00 11 11} • Code-rate = ½ • Problems with Repetition • Bandwidth Increase • Decrease the information rate

9. Channel Coding • When NOT to channel code! • Transmitter power is irrelevant • No noise in the channel • Best case Channel Coding • Shannon Limit (ideal) • Shannon hasn’t been reached yet (Turbo codes are the closest)

10. Code Performance • Bit Error Rate (BER) • Probability of any particular bit being in error in a transmission • Signal to Noise Ratio (SNR) • The ratio of channel power to the noise power • Best Case • Low BER (fewer errors in final data) • Low SNR (less power req.)

11. Coding System Comparison

12. Error Correction Codes • Block • Convolutional • Turbo code • Technically a block code • Works like both Block and Convolutional codes

13. Block Code • Most common is Hamming Code • Take a block of length, k (information sequence) • Then encode them into a codeword, the last (n-k) bits are called parity bits • Parity bits used for error checking and correcting

14. Block Code (2D Mapping) • higher minimum weight of code, higher the minimum weight between valid code words • higher weight, better decoder performance

15. Convolutional Codes • Continuous or Streaming coding • Viterbi and Soft Output Viterbi are the most common

16. Turbo Codes • Mix between Convolutional and Block codes • Require a Block code • HOWEVER, they use shift registers like Convolutional Codes

17. Turbo Codes (contd.) • Most common is the PCCC (Parallel Concatenated Convolutional Codes) • Produce high weight code words • Interleaver shuffles the input sequence, uk, in such a way that it produces a high weight

18. Turbo Code Decoder • It requires a soft output decoder • Soft-output • Assign a probability to decoded information (eg. 1 with a 80% likelihood) • Outperform hard decision algorithms • MAP (Maximum A Posteriori)

19. Iterative Decoding

20. Turbo Decoding • Cycle will continue until certain conditions are met • The decoder circulates estimates of the sent data like a turbo engine circulates air • Once the decoder is ready, the hard decision is made

21. Error Corrections Old and New

22. Uses • Cell Phone • Satellite Communication • Dial-up Communication • RF Communication (AutoID? WiFi?)

23. Questions, Clarifications, and Comments • Turbo Coding Method? • Business Implications? • Reduced Power Requirements • Higher Bandwidth (lower redundancy)