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Turbo Code
- 1. Turbo and Turbo-Like codes SUDHANSHUSAINI COMPUTER ENGINEERING (M.TECH) (31803121)
- 2. Content: Introduction toTurbo Codes Channel Coding Shannon’s Theory FEC Coding Schemes A Need for Better Codes Turbo Codes Turbo-Like Codes Performance Analysis Practical Issues for Turbo FEC Turbo and Turbo-Like Codes in Standards Future Trends Conclusions References
- 3. Introduction to TurboCodes In information theory, turbo codes are a class of high- performance forward error correction (FEC) codes developed around 1990–91 (but first published in 1993), which were the first practical codes to closely approach the channel capacity. Turbo codes achieve their remarkable performance with relatively low complexity encoding and decoding algorithms.
- 4. Channel Coding Toencode the information sent over a communication channel in such a way that in the presence of channel noise, errors can be detected and/or corrected. It Can be categorized into: 1. Backward error correction (BEC) 2. Forward error correction (FEC )
- 5. Shannon’s Theory Forevery combination of bandwidth (W), channel type, signal power (S) and received noise power (N), there is a theoretical upper limit on the data transmission rate R, for which error-free data transmission is possible. This limit is called channel capacity or also Shannon capacity. It sets a limit to the energy efficiency of a code. A decibel is a relative measure. If E is the actual energy and Eref is the theoretical lower bound, then the relative energy increase in decibels is
- 6. A Need forBetter Codes Energy efficiency vs Bandwidth efficiency Codes with lower rate (i.e. bigger redundancy) correct more errors.then communication system can operate with a lower transmit power, transmit over longer distances, tolerate more interference, use smaller antennas and transmit at a higher data rate. These properties make the code energy efficient. Low-rate codes have a large overhead and are hence more heavy on bandwidth consumption. Also, decoding complexity grows exponentially with code length.
- 7. FEC Coding Schemes Block Codes Convolution Codes Concatenated Codes Low-Density Parity Check Codes
- 8. Block Codes Ablock code is any member of the large and important family of error- correcting codes that encode data in blocks. Most common example 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 are used for error checking and correcting.
- 9. Convolution Codes Convolutioncodes are error detecting codes used to reliably transmit digital data over unreliable communication channel system to channel noise. The convolution codes map information to code bits , but sequentially convolve the sequence of information bits according to some rule. Convolutional codes are often described as continuous. Viterbi and soft output Viterbi are most common.
- 10. ENCODING CIRCUIT The codeis defined by the circuit, which consists of different number of shift registers
- 11. Cntd… We generatea convolution code by putting a source stream through a linear filter. This filter makes use of a shift register, linear output functions and possibly linear feedback. In a shift register, the information bits roll from right to left. In every filter there is one input bit and two output bits. Because of each source bit having two transmitted bits, the codes have rate ½.
- 12. DEFINING CONVOLUTION CODE A convolution code can be defined by using a generator matrix that describes the encoding function u → x : x = u .G For 3 information bit long sequence u = (u0 ,u1 ,u2 ) we get ((x0 (1) x0 (2) ), (x1 (1)x1 (2) ), (x2 (1) x2 (2) )) = (u0 ,u1 ,u2 ) .G
- 13. PUNCTURING OF CONVOLUTION CODES The idea of puncturing is to delete some bits in the code bit sequence according to a fixed rule. In general the puncturing of a rate K / N code is defined using N puncturing vectors. Considering a code without puncturing, the information bit sequence u =(0,0,1,1,0) generates the (unpunctured) code bit sequence xNP= (00,00,11,01,01). The sequence xNP is punctured using a puncturing matrix: PI= 1110 1001 The puncturing period is 4. Using P1 , 3 out of 4 code . The performance of the punctured code is worse than the performance of the mother code.
- 14. DECODING CONVOLUTION CODES The most probable state sequence can be found using the min-sum algorithm (also known as the Viterbi algorithm). The viterbi algorithm is used to decode convolutional codes and any structure or system that can be described by a trellis. It is a maximum likelihood decoding algorithm that selects the most
- 15. Concatenated Codes Sometimes 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
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- 17. Turbo Codes TheParallel-Concatenated Convolutional Codes(PCCC), called turbo codes, has solved the dilemma of structure and randomness through concatenation and interleaving respectively. The introduction of turbo codes has given most of the gain promised by the channel coding theorem. Turbo codes have an astonishing performance of bit error rate (BER) at relatively low Eb /No.
- 18. Turbo Encoder Theoutput stream of data consists of the systematic data, parity bits from encoder1, and parity bits from encoder2. Through the use of the interleaver, the decoder will have two independent looks at the same data, and can use both streams to decode the information sequence
- 19. Interleaver The interleaver’sfunction is to permute low weight code words in one encoder into high weight code words for the other encoder. A “row-column” interleaver: data is written row-wise and read column wise. While very simple, it also provides little randomness. A “helical” interleaver: data is written row-wise and read diagonally. 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. Odd-even encoders can be used, when the second encoder produces one output bit per one input bit.
- 21. Recursive Systematic Coders Recursive codes are typically systematic. The example encoder is systematic because the input data is also used in the output symbols. Recursive systematic convolutional (RSC) codes have become more popular due to their use in Turbo Codes.
- 22. Turbo Decoding Criterion: Forn probabilistic processors working together to estimate common symbols, all of them should agree on the symbols with the probabilities as a single decoder could do. The inputs to the decoders are the Log likelihood ratio (LLR) for the individual symbol d. LLR value for the symbol d is defined ( Berrou) as The SISO decoder reevaluates the LLR utilizing the local Y1 and Y2 redundancies to improve the confidence . Compare the LLR output, to see if the estimate is towards 0 or 1 then take HD.
- 23. Cntd… The valuez is the extrinsic value determined by the same decoder and it is negative if d is 0 and it is positive if d is 1 The updated LLR is fed into the other decoder and which calculates the z and updates the LLR for several iterations After several iterations , both decoders converge to a value for that symbol.
- 24. Turbo Product Codes The serial concatenation of block codes separated by a structured permutation (either implicit or explicit) was introduced in the 1950s. Codes with this structure are referred to as product codes. Product codes may have many dimensions but are usually restricted to 2 or 3. Applying iterative decoding to such code structures results in TPCs, and exchanging soft extrinsic information yields good performance. Iterative decoding of TPCs is performed by alternately decoding along the different dimensions of the code, where again reliability information is represented as true or approximate LLRs. Turbo Product Codes (TPCs) are based on block codes, not convolutional codes.
- 25. Construction and Decodingof TPC An elementary decoder for a single dimension of a multidimensional turbo product code
- 26. Low-Density Parity CheckCodes Any linear block code can be defined by its parity-check matrix. If this matrix is sparse, i.e it contains only a small number of 1s per row or column, then the code is called a low-density parity-check code. Basically there are two different possibilities to represent LDPC codes: ─ Matrix Representation ─ Graphical Representation A regular LDPC matrix is an binary matrix having exactly Y ones in each column and exactly ones in each row , where < and both are small compared to m. If H is low-density but the number of 1’s in each row or column aren’t constant the code is called a irregular LDPC code.
- 27. Representation Parity CheckMatrix: (with dimension “ n × m ” for a (8 ,4) code) ─ ρ = the number of 1‘s in each row ─ γ = the number of 1’s in each column For a matrix to be called low-density the two conditions γ<<n, ρ<<m must be satisfied. Bipartite Graph(so-called Tanner Graph): that means that the nodes of the graph are separated into two distinctive sets: Variable nodes(v-nodes) Check nodes(c-nodes) ─ m check nodes (the number of parity bits ─ n variable nodes (the number o bits in codeword
- 28. Turbo-Like Codes Someforms of turbo FEC do not fall neatly into any of the previous three categories and are referred to as turbo-like codes. Hybrids of turbo codes and LDPC codes fall into this category. Convolutional codes are often used as the constituent codes, resulting in serially concatenated convolutional codes (SCCCs). Decoding is performed in a manner similar to the parallel concatenated case, iteratively applying SISO decoders for each constituent code.
- 29. Performance Analysis ofTurbo Codes BER performance of cdma2000 turbo code WER performance of cdma2000 turbo code
- 30. Performance Analysis ofTurbo Product Codes BER performance of the IEEE 802.16 TPC WER performance of the IEEE 802.16 TPC
- 31. Performance Analysis ofLDPC Codes BER and WER performance of two IEEE 802.16e LDPC codes
- 32. Practical Issues forTurbo FEC Error Rate Performance and Power Savings Computational Complexity Parallelism Memory Requirements Latency Flexibility Effect on Synchronization
- 33. TURBO OR TURBO-LIKECODES IN STANDARDS 3G Wireless: 1. W-CDMA(Wideband code-division multiple-access) 2. CDMA2000 3. TD-SCDMA(Time-division, synchronous CDMA) Satellite Communications: 1. Consultative Committee for Space Data Systems (CCSDS) 2. Digital Video Broadcasting-Return Channel via Satellite 3. Digital Video Broadcasting via Satellite Second Generation Wireless Networking: 1. Wi-MAX (IEEE 802.16) 2. Wi-Fi (IEEE 802.11)
- 34. Future Trends Turboand turbo-like codes will be widely used for at least the next decade and probably substantially longer. No single class of turbo or turbo-like codes will dominate in the way that convolutional codes and Viterbi decoding did in the past. Substantial improvements in computational efficiency and reductions in unit costs are still possible. An increasing number of turbo and turbo-like codes will be tailored to different channel conditions and system designs. The success of turbo FEC has led to the application of soft iterative decoding techniques beyond channel coding.
- 35. Conclusions The adventof turbo and turbo-like codes has shown that excellent performance, closely approaching the ultimate Shannon capacity limit for an AWGN channel. It can be achieved through the soft iterative decoding of composite channel codes. Implementing and using turbo and turbo-like codes in real systems does present challenges, but tremendous progress in addressing these issues has been made, and all varieties of turbo FEC are finding application. Turbo and turbo-like codes are no longer a curiosity or novelty, but a powerful tool for improving the performance of communications systems.
- 36.