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Turbo Codes: An Introduction to Forward Error Correction Techniques
- 1. Mr. Ravindra Gaikwad Mr.Utkarsh Kumar M.Tech (ECE) Dept. of Electronics Pondicherry University Turbo codes
- 2. Outline • Introduction – Forward error correction – Channel capacity • Turbo codes – Encoding – Decoding – Application
- 3. Error correction • The key idea of FEC is to transmit enough redundant data to allow receiver to recover from errors all by itself. No sender retransmission required. • The major categories of FEC codes are – Block codes, – Cyclic codes, – Reed-Solomon codes, – Convolutional codes, – Turbo codes.
- 4. m r Channel encoder • Input message m contains k symbols. • Encoded message r contains n symbols. • n > k where extra bits are redundant bits in the codeword. • The code rate is k/n
- 5. Channel capacity • The channel capacity C of a continuous channel with bandwidth B Hertz can be perturbed by additive Gaussian white noise of power spectral density N0/2, provided bandwidth B satisfies C Blog 1 / sec bits ond P 2 N B 0 Where P is transmitted power
- 6. Turbo codes • Turbo codes were proposed by Berrou and Glavieux in the 1993 International Conference in Communications. • Performance close to the Shannon Limit. • Mix between Convolutional and Block codes. • The best code among FEC codes.
- 7. Key elements • Concatenated Encoders • Recursive convolutional encoders • Pseudo-random interleaving • Iterative Decoding
- 8. Concatenated encoding • Some times single error correction codes are not good enough for error protection • Concatenating two or more codes will results more powerful codes • Types of concatenated codes 1. Serial concatenated codes 2. Parallel concatenated codes
- 9. Parallel concatenated code input Systematic output RSC Encoder 1 RSC Encoder 2 Interleaver Parity 1 Systematic output Parity 2 One systematic and two parity bits are generated from the message stream
- 10. Serial concatenated code Outer encoder Interleaver Inner encoder
- 11. Recursive convolutional encoder mi • An RSC encoder can be constructed from a standard convolutional encoder by feeding back one of the outputs. • In coded system performance is dominated by low weight code words.
- 12. • A good code will causes low weight output with low probability • RSC will produces low weight and low probability output
- 13. Need of interleaver • Shannon showed that large block-length random codes achieve channel capacity • Only a small number of low-weight input sequences are mapped to low-weight output sequences • Make the code appear random, while maintaining enough structure to permit decoding • The interleaver ensures that the probability that both encoders have inputs that causes low weight output is very low.
- 14. Turbo decoding Conv Decoder1 Interleaver Deinterleaver Conv Decoder2 Systematic data Parity 1 Parity 2
- 15. Decoding • Turbo codes get their name because the decoder uses feedback, like a turbo engine. • Each decoder estimates the a posteriori probability (MAP) of each data bit. • Decoding continues for a set number of iterations.
- 16. • Performance generally improves from iteration to iteration, but follows a law of diminishing returns • Information exchanged by the decoders must not be strongly correlated with systematic info or earlier exchanges.
- 17. APPLICATION • Wireless multimedia – Data: use large frame sizes • Low BER, but long latency – Voice: use small frame sizes • Short latency, but higher BER • Combined equalization and error correction decoding. • Combined multiuser detection and error correction decoding.
- 18. Pros and cons • Pros – Remarkable power efficiency in AWGN and flat-fading channels for moderately low BER. – Deign tradeoffs suitable for delivery of multimedia services. • Cons – Long latency. – Poor performance at very low BER. – Because turbo codes operate at very low SNR, channel estimation and tracking is a critical issue.