![References
[1]. C. E. Shannon, “A Mathematical Theory of Communication,” Bell Systems Technical
Journal 27 (July, Oct. 1948): 379–423, 623–56.
[2]. C. Berrou , A. Glavieux , and P. Thitimasjshima , “Near Shannon Limit Error-Correcting
Coding and Decoding: Turbo-Codes,” Proceedings of the IEEE International Conference on
Communications (May 1993, Geneva, Switzerland): 1064–70.
[3]. By Kenneth S. Andrews, Dariush Divsalar , Sam Dolinar “The Development of Turbo and
LDPC Codes for Deep-Space Applications” IEEE | Vol. 95, No. 11, November2007
[4]. L. R. Bahl, J. Cocke, F. Jelink, and J. Raviv, “Optimal Decoding of Linear Codes for
Minimizing Symbol Error Rate,”IEEE Transactions on Information Theory 20 (March 1974):
284–7.
[5]. John G. Proakis and Masoud Salehi, ”Digital Communications”, 5th edition, 2014](https://image.slidesharecdn.com/turboppt-200406181757/85/simulation-of-turbo-encoding-and-decoding-20-320.jpg)
simulation of turbo encoding and decoding
- 1. Simulation of Turbo Encoder and Decoder COURSE NO. EL-490B Mohd Raushan Raza 15LEB051 Gulafshan 15LEB352 DEPARTMENT OF ELECTRONICS ENGINEERING ALIGARH MUSLIM UNIVERSITY,ALIGARH 2018-19
- 2. Contents Introduction Turbo Encoder Convolutional Encoder Interleaver Puncturing Decoding Techniques Applications Conclusion References
- 3. Introduction Turbo codes, which belong to a class of Shannon-capacity approaching error correcting codes, are introduced by Berrou and Glavieux in 1993 Turbo codes can come closer to approaching Shannon’s limit than any other class of error correcting codes. A turbo code is formed from the parallel concatenation of two convolutional codes separated by an interleaver. Turbo code is a type of convolution code.
- 4. Turbo Encoder The fundamental turbo encoder is built using two identical convolutional encoder with parallel concatenation. The two encoders are separated by an interleaver. The input data stream and the parity outputs of the two parallel encoders are then serialized into a single turbo code word.
- 5. Convolutional Encoder Encodes the entire data stream, into a single codeword. Maps information to code bits sequentially by convolving a sequence of information bits with “generator” sequences. does not need to segment the data stream into blocks of fixed size. Initialize the memory before encoding the first bit (all-zero). Clear out the memory after encoding the last bit (all-zero).
- 6. Convolutional Encoder (cont.) It accepts an input stream of message and generates encoded output streams to be transmitted. For one input bit the encoder generates more than one output bits. Memory based system It consists of: i. Shift registers ii. Modulo-2 adders iii. Generator polynomials
- 7. Interleaver The interleaver is a very important constituent of the turbo encoder. Turbo encoder consists of interleaver unit which can be used to increase the BER performance by varying the interleaving size. In turbo code, interleaver unit is a random block that is used to rearrange the input data bits with no repetition. Interleaver unit is used in both encoder and decoder part. At the decoder side after passing the encoded data from first decoder some of the errors may get corrected, then we again interleaver, this first decoded data and pass through the second decoder. Here, remaining error may get correct. Like this, we are repeating the process for more number of times.
- 8. Interleaver (cont.) The purpose of the interleaver is to offer each encoder an uncorrelated or a “random” version of the information, resulting in parity bits from each RSC that are independent. How “independent” these parity bits are, is essentially a function of the type and length/depth of the interleaver. It spreads the bursty error pattern and also increases the free distance .Thus, it allows the decoders to make uncorrelated estimates of the soft output values. The convergence of the iterative decoding algorithm improves as correlation of the estimates decreases.
- 9. Types of interleaver There are certain types of interleavers. “row-column” interleaver in which data is written row wise and read column wise. While very simple, it also provides little randomness. In helical” interleaver data is written row-wise and read diagonally. In an odd-even interleaver first, the bits are left uninterleaved and encoded, but only the odd-positioned coded bits are stored. Then, the bits are scrambled and encoded, but now only the even positioned coded bits are stored. In pseudo-random interleaver defined by a pseudorandom number generator or a look-up table. Matrix interleaver. Algebraic interleaver.
- 10. Puncturing Puncturing is a technique used to increase the code rate. Puncturing is elimination of some bits of a codeword before of sending out it and replacing zero instead of these bits before of decoding. Puncturing is a tradeoff between code rate and system performance. Because due to puncturing code rate improves but the same time code performance degrades due to less number of information bits transmitted. Some of puncturing patterns are unsuitable and degrade the performance of turbo code.
- 11. Types of puncturing Odd –even puncturing by choosing or selecting odd values from encoder one and even values from encoder second. Puncturing patterns: puncturing matrix P of period p applied to a turbo code having N output branches can be represented by: All four matrices have a period of four (p = 4) and a total number of punctured bits equal to 4.
- 12. Result
- 13. Result
- 14. Result
- 15. Turbo decoder
- 16. Turbo decoding techniques After encoding, the entire n-bit turbo code word is assembled into a frame, modulated, transmitted over the channel, and decoded. 1. SOVA ( Soft Output Viterbi Algorithm) 2. MAP (Maximum A Posteriori )
- 17. BCJR Maximum a posteriori probability (MAP) decoding. Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm (1974). Decoder inputs: Received sequence r (soft or hard). A priori L-values La(ul) = ln(P(ul = 1)/P(ul = -1)). Decoder outputs: A posteriori probability (APP) L-values L(ul) = ln(P(ul = 1| r)/P(ul = -1|r)) > 0: ul is most likely to be 1 < 0: ul is most likely to be -1
- 18. Applications Now they are incorporated into standards used by NASA for deep space communications (CCSDS), digital video broadcasting (DVB-T), and both third-generation cellular standards (UMTS and cdma2000). Mobile Radio Digital video Military applications Deep space communications
- 19. Conclusion Turbo codes are one of the first practical codes to closely approach the Shannon capacity. Turbo codes are efficient in reliable data transfer over bandwidth or energy constrained links. Turbo codes achieve their remarkable performance with relatively low complexity encoding and decoding algorithms. Due these reasons turbo codes are preferred for deep space communications.
- 20. References [1]. C. E. Shannon, “A Mathematical Theory of Communication,” Bell Systems Technical Journal 27 (July, Oct. 1948): 379–423, 623–56. [2]. C. Berrou , A. Glavieux , and P. Thitimasjshima , “Near Shannon Limit Error-Correcting Coding and Decoding: Turbo-Codes,” Proceedings of the IEEE International Conference on Communications (May 1993, Geneva, Switzerland): 1064–70. [3]. By Kenneth S. Andrews, Dariush Divsalar , Sam Dolinar “The Development of Turbo and LDPC Codes for Deep-Space Applications” IEEE | Vol. 95, No. 11, November2007 [4]. L. R. Bahl, J. Cocke, F. Jelink, and J. Raviv, “Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate,”IEEE Transactions on Information Theory 20 (March 1974): 284–7. [5]. John G. Proakis and Masoud Salehi, ”Digital Communications”, 5th edition, 2014
- 21. Thank You…