TURBO CODE - TURBO CODE AN AN ERROR CORRECTING CODE...

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Unformatted text preview: TURBO CODE : AN AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT GUIDED BY PREPARED BY PROF (MRS) N Y DESAI, Head, ECED SOUNAK SAMANTA, Roll No 42, Div - B 20 TH MARCH 2006 ELECTRONICS ENGINEERING DEPARTMENT ENGINEERING DEPARTMENT SARDAR VALLABHBHAI NATIONAL INSTITUTE OF TECHNOLOGY ICHCHHANATH, SURAT – 395 007 The authors acknowledges all the materials are taken from Standard Text Books. OUTLINES OUTLINES BASIC BASIC COMMUNCATION MODEL CONCEPTS BEHIND ERROR CORRECTION AND DETECTION SHANNON LIMIT SHANNON LIMIT STATISTICAL CODEC CONCEPTS TURBO CODING PRINCIPLE TURBO CODING PRINCIPLE PRACTICAL ISSUES OF TURBO CODE WHY ARE TURBO CODES SO POPULAR? WHY ARE TURBO CODES SO POPULAR? TURBO CODES PERFORMANCE ANALYSIS APPLICATION OF TURBO CODES APPLICATION OF TURBO CODES 2 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B BASIC BASIC COMMUNCATION MODEL QPSK, QAM, AES, DES INFORMATION SOURCE SOURCE ENCODER JPEG, MPEG, ZIP ENCRY PTOR CHANNEL ENCODER ENCODER BLOCK BLOCK, CONVOLUTIONAL, MODUL ATOR CHANNEL TURBO CODE INFORMATION SINK SOURCE DECODER DECRY DECRY PTOR CHANNEL DECODER DEMODUL ATOR 3 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B RECAPITULATION RECAPITULATION OF OF BASIC BASIC CODING THEORY CONCEPT CONCEPT 4 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B ⎢ d min − 1⎥ ⎢2⎥ ⎣ ⎦ CONCEPT CONCEPT BEHIND ERROR CORRECTION & DETECTION CORRECTION DETECTION Error Correcting Capability tc = (dmin-1)/2 (d Error Detecting Capability Detecting Capability td = (dmin-1) dmin = Minimum Hamming Distance 5 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B HAMMING WEIGHT w(U) NUMBER OF NON-ZERO ELEMENT IN NONCODE WORD HAMMING DISTANCE d(U, V) DISTANCE d(U V) NUMBER OF UNCOMMON ELEMENT BETWEEN TWO CODE WORDS BETWEEN TWO CODE WORDS !!! IMPORTANT OBSERVATION !!! d(U, V) = w(U + V) 6 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B Contd……… Contd……… From Property of Linear Code, Li if U and V both are code words and W= U+V then W must be a code word d(U, V) = w(U + V) = w(W) !!! Conclusion !!! Maximum Minimum Hamming Distance = Maximum Weight of Codeword 7 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B !!! !!! SHANNON LIMIT !!! Signific ance PB 1 ½ Uncoded BPSK 10-1 Shannon Limit -1.6 dB 10-2 BIT ERROR PROB 10-3 Low Bit Error Low SNR 10-4 10-5 -5 0 5 10 Eb/No (dB) Ultimate Achievement !! Achievement !! 8 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B Acc to Shannon, Only Random Codes approaches Shannon Limit Random Codes Shannon Limit “Almost all codes are good, except those we can think of.” Turbo Code is Randomly Structured Code Purely Random Codes : Approaches Shannon Limit Approaches Shannon Limit Not Easily Decodable Purely Structured Codes : Structured Codes Not Not Approaches Shannon Limit Easily Decodable Easily Decodable Merit Demerit Demerit Merit 9 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B STATISTICAL STATISTICAL CODEC CONCEPT Maximum Likelihood Decoding U(m) = All possible transmitted sequence All possible transmitted sequence Z = Received sequence Maximum Likelihood Decoder is an optimal decoder that chooses U(m’) if P (Z | U(m’)) = max P (Z | U(m)) Over all U(m) where P(Z | U(m)) is Probability of received sequence is Z assuming U(m) is transmitted assuming U(m) is transmitted 10 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B Soft vs. Hard Decision Soft decision = Hard decision + Confidence Level Trade off : More Bits to be transmitted from Demodulator Likelihood of s2 p(z|s2) 000 001 010 0 Likelihood of s1 p(z|s1) 011 100 101 110 111 1 z (T) 8 level Soft Decision 2 level Hard Decision level Hard Decision 11 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B P(d = i | x) = P( x | d = i) ⋅ p(d = i) p ( x) A Posteriori Probability (APP) & Priori Probability P( x | d = i ) ⋅ p(d = i ) APP = P(d = i | x) = p ( x) 12 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B Maximum A Posteriori Probability (MAP) H1 > P(d = +1| x) P(d = −1| x) < M p ( x) = ∑ p ( x | d = i ) P (d = i ) H2 i =1 H1 > p(x | d = +1) ⋅ P(d = +1) p(x | d = −1) ⋅ P(d = −1) < H2 13 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B TURBO TURBO CODING PRINCIPLE 14 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B CONCEPT OF INTERLEAVER CONCEPT OF INTERLEAVER Channel Error Category Without Memory Isolated Error With Memory e.g. Multipath Faded Ch !! Burst Error !! Interleaver is used to is used to spread out the errors occurring in Burst !! 15 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B CONCEPT OF PUNCTURING CONCEPT OF PUNCTURING Puncturing is the process of deleting some redundant bits is the process of deleting some redundant bits from the codeword according to a puncturing matrix. In simple case, MUX ing operation 11 10 c11,c12 01 P= s1,s2 c21,c22 {s1,c11} {s2,c22} {s 16 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B Turbo Code Structure Turbo Code Structure Turbo Code Convolutional Turbo Code Code Block / Product Turbo code code Parallel Concatenated Convolutional Codes Serial Concatenated Convolution Codes Concatenated Convolution Codes Hybrid Concatenated Concatenated Codes 17 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B PCCC PCCC Encoder dk Xk ak D D D RSC1 (37,21) Y2k a k Randomness Y1k interleaver D D D Concatenation of RSCs of RSCs D RSC2 (37,21) delay Structureness Yk Interleaver D High Weight Code word Output 18 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B PCCC PCCC Decoder Significance of of Name “Turbo” Feedback Loop for Iteration Π-1 Zk Xk Yk DEC1 Y1k Π Π DEC2 Y2k :: Interleaver Π-1 :: De-Interleaver DEMUX / INSERTION BLOCK BLOCK Π-1 Hard Decision OUTPUT 19 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B Turbo Decoding Algorithm Turbo Decoding Algorithm Mainly Two Algorithm was proposed : •LOG MAP ALGORITHM (BAHL or BCJR) OPTIMAL FOR BIT ERROR PERFORMACE IMPLEMENTATION OF ALGORITHM IS COMPLEX •SOFT OUTPUT VITERBI ALLGORITHM (SOVA) OPTIMAL FOR SYMBOL ERROR PERFORMACE IMPLEMENTATION OF ALGORITHM IS SIMPLE 20 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B SOVA SOVA DECODING ALGOITHM SOVA = VITERBI DECODING + SOFT OUTPUT HARD DECISION VITERBI ALGORITHM Input bit bi m First Code Symbol u1 Output branch word word u2 Second Code Symbol 21 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B t1 a=00 00 00 t2 11 00 t3 11 t4 00 11 11 11 b=10 t5 00 11 10 10 t6 00 11 11 u1 10 10 10 10 10 c=01 Input bit m u2 01 01 d=11 Input bit 0 Input bit 1 bit 10 01 01 10 01 01 01 10 a,b,c,d = state of last two FFs Data on transition shows output 22 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: U: Z: t1 1 11 11 2 00 1 01 01 t2 1 0 01 01 t3 00 1 00 1 00 10 t4 1 01 01 t5 1 00 1 t6 00 a=00 0 11 1 1 11 11 1 1 b=10 1 11 11 1 1 11 11 11 1 11 c=01 10 0 d=11 20TH MARCH 2006 1 11 2 10 2 1 11 0 10 2 10 0 10 0 10 10 10 2 2 10 2 0 10 10 10 0 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B 0 10 10 2 23 m: 1 1 0 1 1 …… Z: 11 01 01 10 01 …… t1 2 t2 t3 t4 t5 t6 a=00 0 b=10 c=01 d=11 24 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: 1 1 0 1 1 …… Z: 11 01 01 10 01 …… t1 2 t2 t3 1 1 t4 t5 t6 a=00 0 1 b=10 2 c=01 0 d=11 25 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: 1 1 0 1 1 …… Z: 11 01 01 10 01 …… t1 2 t2 t3 1 t4 1 t5 t6 a=00 0 1 1 1 b=10 2 2 c=01 0 0 0 d=11 2 26 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: 1 1 0 1 1 …… Z: 11 01 01 10 01 …… t2 t1 t3 t4 t5 t6 3 a=00 0 1 b=10 3 1 2 c=01 0 0 0 d=11 2 2 27 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: 1 1 0 1 1 …… Z: 11 01 01 10 01 …… t2 t1 t3 t4 t5 0 a=00 0 t6 1 1 b=10 1 1 1 2 0 c=01 0 2 0 2 0 d=11 2 28 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: 1 1 0 1 1 …… Z: 11 01 01 10 01 …… t2 t1 t3 t4 t5 t6 1 a=00 0 b=10 1 1 1 1 2 0 c=01 3 0 0 0 d=11 2 2 29 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: 1 1 0 1 1 …… Z: 11 01 01 10 01 …… t2 t1 t3 t4 t5 t6 1 a=00 0 1 b=10 1 1 1 1 2 1 0 0 c=01 0 2 0 0 0 d=11 2 2 30 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: 1 1 0 1 1 …… Z: 11 01 01 10 01 …… t2 t1 t3 t4 t5 1 a=00 0 t6 2 1 b=10 1 2 1 0 c=01 0 2 0 0 0 d=11 2 1 31 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B SOFT SOFT OUTPUT 0,1 1,1 0,1 0,7 1,1 7,7 √13 √41 0,0 1,0 t1 0,0 7,7 0,0 t2 1,0 5,4 0,0 t1 7,0 √41 t2 √13 32 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B PRACTICAL ISSUES PRACTICAL ISSUES OF OF TURBO CODE 1.Error Floor 2. Latency 3. Complexity & Memory Size 33 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B ERROR ERROR FLOOR Flattening out BER curve at higher SNR for PCCCs out BER curve at higher SNR for PCCCs Remedies • Use of Asymmetric of Asymmetric Turbo Code ( Two different RSCs ) • Best Method is to use SCCCs is to use SCCCs or HCCCs Source:: “Performance Characteristics of Turbo Codes”, Virginia Tech SCCCs : good at High SNR PCCCs : good at Low SNR good at Low SNR HCCCs is best but Structure will be more complex 34 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B LATENCY LATENCY Due to Large Interleaver Size and Iteration Si It • For Example, Turbo code uses 65536 bits of Interleaver code uses 65536 bits Interleaver For Speech Transmission, bit rate = 8 kbps To store bits in the Interleaver, it takes time 65,536 / 8000 = 8.192 Sec !!! Great Delay !!! • Normally, in wireless/speech services 40 ms delay acceptable so Interleaver size =0.04 x 8000=320 Interleaver Size Small : Less Randomness Interleaver Size Large : Delay Size Large Delay 35 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B TURBO TURBO CODE PERFORANCE ANALYSIS ANALYSIS GENERATOR GENERATOR POLYNOMIAL (CONSTRAINT LENGTH OF TURBO ENCODER) NUMBER NUMBER OF ITERATIONS BLOCK BLOCK SIZE INTERLEAVER DESIGN INTERLEAVER DESIGN 36 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B GENERATOR GENERATOR POLYNOMIAL Increasing the constraint length of Turbo encoders do give better performance albeit to encoders do give a better performance albeit to a minuscule extent, whereas complexity minuscule increases lot so experimentally optimum increases a lot so experimentally optimum constraint constraint length is 3 to 5. 37 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B EFFECT EFFECT OF NUMBER OF More Iterations ITERATION ITERATION Latency Less Iterations Less Performance Gain Max 18 Iterations, though 6 will suffice will suffice 38 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B NUMBER NUMBER OF BLOCK SIZE Block Size is same as Interleaver Size 39 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B APPLICATION APPLICATION •Deep Space Exploration Wh Where Delay can be tolerated & Power is crucial issue •Mobile Communication with Low Latency Interleaver •Terrestrial Digital Video Broadcast (DVB Broadcast (DVB-T) Standard Standard 40 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B CONCLUSION CONCLUSION ** Turbo Code approaches Shannon Limit ** Turbo Code approaches Shannon Limit !!! No Doubt !!! IS IT AN END TO CODING THEORY ?? 41 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B m: 1 1 0 1 1 …… U: 11 01 01 00 01 …… Z: 11 01 1 01 1 10 1 01 …… t6 1 a=00 t1 2 0 t2 t3 1 t4 1 1 1 b=10 t5 2 1 1 1 2 2 0 c=01 0 d=11 0 0 2 2 2 0 0 0 2 42 20TH MARCH 2006 TURBO CODES : AN ERROR CORRECTING CODE APPROACHES SHANNON LIMIT by SOUNAK SAMANTA, Roll No – 42, Div - B ...
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