Optimized BER Performance of Asymmetric Turbo Codes over AWGN Channel

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1 International Journal of Computer Application ( ) Optimized Performance of Aymmetric Turbo Code over AWGN Channel M.Srinivaa Rao Pvpit, JNTU Kainada Andhra Pradeh, India. G.Vijaya Kumar Pvpit, JNTU Kainada Andhra Pradeh, India. P.Rajeh Kumar, Ph.D Pvpit, JNTU Kainada Andhra Pradeh, India. ABSTRACT The performance of the turbo code can be improved by varying parameter uch a bloc ize, code polynomial tructure and contraint length. Thi paper propoe a new aymmetric turbo code that conit of parallel concatenated component code with mixed type generator polynomial and alo different contraint length. Thi cheme optimize the performance of aymmetric turbo code of both Waterfall region at lower SNR and error-floor region at higher SNR. The imulation reult how better performance of aymmetric turbo code for bloc ize of 28, 52 bit, code-rate of /2 and Maximum-A-Poteriori (MAP) decoding algorithm over AWGN channel with BPSK modulation by uing MATLAB. Keyword Aymmetric turbo code, bit error rate, contraint length, code-rate, error-floor and waterfall.. INTRODUCTION In 993, turbo code are introduced by Berrou, Glavieux and Thitimajhima. Thee code are introduced a one of the mot powerful error control code which were the firt practical code to cloely approach the channel capacity. They are baically contructed by two or more parallel Recurive Sytematic Convolutinal (RSC) code, which are lined by a peudo-random interleaver [][3]. The bit error rate () performance curve of turbo code can be divided into waterfall region and error-floor region. The waterfall region ha a teep lope at lower SNR for a long bloc of information and error-floor region ha a hallower lope at higher SNR caued by codeword of mall weight [2]. The turbo code can be divided into two type baed on their generator polynomial tructure and contraint length. The turbo code baically ue the identical component code nown a ymmetric turbo code which have ame contraint length and generator polynomial []. The ymmetric turbo code have either a good waterfall performance or a good error floor performance, but not both. The parallel concatenated code which ue non-identical component code nown a aymmetric turbo code. It ha not only different contraint length but alo different generator polynomial [8]. The reulting aymmetric turbo code ha both good waterfall and error-floor performance [2][7]. The decoding of a turbo code can be done in an iterative way uing Maximum a poteriori (MAP) algorithm []. In thi paper, we conider BPSK (Binary Phae Shift Keying) modulation over AWGN channel. Thi paper propoe the new aymmetric turbo code, which conit of a parallel concatenated turbo code that ue the mixed type of the component code with different not only the contraint length but alo the generator polynomial. We can oberve the optimized performance in the both waterfall region and the error floor region by applying the propoed aymmetric turbo code. 2. ASYMMETRIC TURBO CODES 2. Aymmetric Turbo Encoder A turbo encoder i contructed by a parallel concatenation of two identical component code, which are lined by a peudorandom interleaver. Fig. how a turbo encoder (rate /2) tructure with two RSC encoder. Here trelli termination or truncation i performed on RSC encoder. Trelli termination i performed on the firt RSC encoder, which return it memory content to zero tate, while trelli truncation i performed on the econd RSC encoder that leave it memory tate open. Fig.. Generic Turbo Encoder Puncturing i a technique ued to increae the code rate. A rate /3 encoder i converted to a rate /2 encoder by multiplexing the two coded tream. The multiplexer can chooe the odd indexed output from the output of the upper RSC encoder and it even indexed output from the lower one. 8

2 International Journal of Computer Application ( ) LLR can be compoed into 3 independent term a: Ld Laprid Lc d Le d (2) Where L aprid i the a-priori information, L c d i the channel meaurement, and L e d i the extrinic information exchanged between the component decoder. The available extrinic information from one decoder will be a-priori information for the other decoder at the next decoding tage. Where L and L in Fig.3 repreent the extrinic e2 e2 information from decoder to decoder2 and decoder2 to decoder repectively [5][6]. MAP algorithm calculate the LLR for each information bit a: Fig.2 Bloc Diagram of aymmetric turbo encoder with K=5, K2=4 and R=/2 Fig.2 how the aymmetric turbo encoder with the code rate /2, which conit of 37,2 8 encoder and 5,7 8 encoder, Where K and K2 are contraint length of turbo encoder and turbo encoder2, repectively and R i the code rate for the turbo code 2.2 Aymmetric Turbo Decoder In a typical turbo decoding ytem (ee Fig. 3), two decoder operate iteratively and pa their deciion to each other after each iteration [4]. S, S S S S S (3) L d ln 0 S, S S S S S Where α i the forward recurion, β i the bacward recurion, γ i the branch metric, and i the trelli time. Forward recurion are calculated from trelli time K= to, K=N where N i the number of information bit in one data frame. Recurive calculation of forward tate metric i performed a: S S S S 0, j j (4) Similarly, the bacward recurion are calculated from trelli time K=N to, K= a: S S S S 0, j j (5) Branch metric are calculated for each poible trelli tranition a: S, S C PS S i 2 exp N 0 Y p p i Y i, S, S (6) Fig.3. Iterative Turbo Decoding Each decoder operate not only on it input but alo on the other decoder incompletely decoded output. Here, Encoded information equence i tranmitted over an AWGN channel, and a noiy received equence Y i obtained. Every SISO decoder determine the Log-Lielihood Ratio (LLR) for the ith data bit d a: L d P d log P d Y 0 Y () Where i (0, ), C i a contant, and p are the encoded ytematic data bit and parity bit, and Y and p Y are the received noiy ytematic data bit and parity bit repectively. 3. PRPOSED ASYMMETRIC TURBO CODES The propoed aymmetric turbo code that ue parallel concatenated component encoder with mixed type of generator polynomial and different contraint length. Turbo code with larger contraint length will achieve good performance and have better free ditance but the computational complexity increae. It i neceary to decreae the contraint length of one of the component encoder in order to obtain good performance and reduce decoding delay. Table. how different type of aymmetric turbo code with different contraint length and generator polynomial. Here P 9

3 International Journal of Computer Application ( ) and NP decribe primitive and prime polynomial for component encoder. G and K repreent the feedbac generator polynomial and the contraint length of each component code, repectively. There are four type of turbo code from each component code: (NP, P) turbo code, (P, NP) turbo code, (P, P) turbo code, (NP, NP) turbo code. Here (P, P) turbo code ue primitive polynomial for the feedbac polynomial of all the component code, and (NP, NP) turbo code ue prime polynomial for the feedbac polynomial of both the component code but performance i imilar to the conventional turbo code. (P, NP) and (NP, P) ue primitive and prime (non-primitive) polynomial for the feedbac polynomial of each component code. Table. Different type of aymmetric turbo code with the different contraint length turbo code have better the performance in waterfall region at low SNR and error-floor at high SNR compared to the other turbo code. Here in fig.4 (NP, P) turbo code performance i uperior to (P, NP), (NP, NP) turbo code and inferior to primitive type i.e., (P, P) turbo code performance. MAPdecoder: Code-rate= 0.5 and Bloc length =28 MAP decoder: Code-rate= 0.5 and Bloc length =52 If we ue primitive polynomial a one of the feedbac generator polynomial of the component encoder which how degrading waterfall performance at lower SNR and lower error-floor at higher SNR. If we ue non-primitive (prime) polynomial a one of the feedbac generator polynomial which how better waterfall performance at lower SNR. So, propoed aymmetric turbo code i a combination of primitive and prime generator polynomial. The component encode with primitive generator polynomial may increae the free ditance in order to reduce error-floor and component encoder with prime generator polynomial may optimize the ditance pectrum to improve water-fall performance [2]. 4. SIMULATION RESULTS In thi paper, everal combination of aymmetric turbo code have been tudied in order to determine their performance. All imulation were performed for aymmetric turbo code with code rate of /2 over AWGN channel, with a BPSK modulation, bloc ize of 28,52 and contraint length K are 3, 4 and 5. Fig.4 how the performance curve for mixed type of aymmetric turbo code with the ame contraint length K=3, K2=3 and bloc ize of 28 and 52. The imulation reult of fig.4 and fig.4 how that both primitive type Fig.4 performance curve for the bloc ize of 28 and 52(K=3, K2=3) Fig.5 how the performance curve for the four type of aymmetric turbo code with diff. contraint length K=5, K2=3 and with the bloc ize of 28, 52. The imulation reult of fig.5 and 5 how that (NP, P) and (P, P) turbo code have better the performance in both waterfall and error-floor region. The performance of (NP, NP) and (P, NP) turbo code are inferior to (NP, P) and (P, P) turbo code. So, it i the bet method to ue one component encoder a primitive feedbac generator polynomial and other a non-primitive polynomial for aymmetric turbo code. 0

4 International Journal of Computer Application ( ) MAPdecoder: Code-rate= 0.5 and Bloc length =28 MAPdecoder: Code-rate= 0.5and Bloc length =28 K=3,K2=3 K=3,K2=4 K=4,K2=3 K=4,K2=4 MAPdecoder: Code-rate= 0.5 and Bloc length =52 MAP decoder:code-rate= 0.5 and Bloc length =52 K=3,K2=3 K=3,K2=4 K=4,K2=3 K=4,K2=4 0-6 Fig.5 performance curve for the bloc ize of 28 and 52 (K=5, K2=3) 0-6 Fig.6 performance of (P, P) turbo code with diff. contraint length 3, 4 for bloc ize of 28 and 52 Fig.6 how the performance of aymmetric turbo code with different combination of contraint length K=3, 4 for the bloc ize of 28 and 52. The imulation reult of fig.6 and 6 how that performance of ymmetric turbo code with K=K2=4 i lightly uperior to aymmetric turbo code with K=3, K2=4 or =4, K2=3. The performance of aymmetric turbo code with K=4, K2=3 i very cloe to ymmetric turbo code with contraint length K=K2=4. By decreaing the contraint length of econd component encoder how better performance when compared with aymmetric turbo code with different contraint length. Fig.7 how the performance both primitive type aymmetric turbo code with different combination of contraint length K=3, 4, 5 for the bloc ize of 28 and 52. The imulation reult of fig.7 and 7 how that performance of aymmetric turbo code with K=3, K2=5 i inferior to turbo code with K=5, K2=3. So, it i better to deign aymmetric turbo code with larger contraint length for firt component encoder. Performance of turbo code with K=K2=5 i lightly uperior to aymmetric turbo code with K=4, K2=5 or =5, K2=4.

5 International Journal of Computer Application ( ) 0-6 MAPdecoder: Code-rate= 0.5and Bloc length =28 MAPdecoder: Code-rate= 0.5 and Bloc length =52 K=3,K2=5 K=4,K2=5 K=5,K2=3 K=5,K2=4 K=5,K2=5 K=3,K2=5 K=4,K2=5 K=5,K2=3 K=5,K2=4 K=5,K2=5 Fig.7 performance of (P, P) turbo code with diff. contraint length 3, 4, 5 for bloc ize of 28 and CONCLUSION In thi paper, the propoed aymmetric turbo code are contructed with different contraint length and mixed type of generator polynomial. The propoed cheme optimize the performance in both waterfall and error-floor region with the ue of primitive and non-primitive polynomial alternatively. So, finally we concluded that the performance of aymmetric turbo code i uperior to conventional ymmetric turbo code. But the turbo code with larger contraint length will increae delay and computational complexity. Thi aymmetric turbo code widely ued in mobile 3G communication ytem. 6. REFERENCES [] C.Berrou, A.Glavieux, and P.Thitimajhima, Near Shannon limit Error- correcting coding and decoding: Turbo code International Conference on Communication (ICC), pp , May 993. [2] O.Taehita, O.M. Collin, P.Maey, and D.J. Cotello, A note on aymmetric turbo code, in IEEE International Sympoium on Information Theory (ISIT), p.79, Augut 998. [3] C.Berrou and A.Glavieux, Near optimum error correcting coding and decoding: Turbo code, IEEE Tranaction on communication, pp , October 996. [4] S.Pietrobon, Implementation and performance of a turbo/map decoder Int. Jour. of Satellite Communication, 998, pp.4-7. [5] P.Roberton, E.Villebrun, and P.Hoeher, A comparion of optimal and ub-optimal MAP decoding algorithm operating in the log domain in IEEE International Conference on Communication, pp , Seattle, USA, June 995. [6] P.Roberton, P.Hoeher, and E.Villebrun, Optimal and ub-optimal maximum a poteriori algorithm uitable for turbo decoding, European Tran on Telecomm. vol.8, no.2, March-April 997, pp [7] K.Ramaarny, B.Balarihna and M.Siddiqi, A new cla of aymmetric turbo code for 3G ytem, Int. J. Electron. Commun, June 2006, pp [8] P.Maey and D.Cotello, New development in aymmetric turbo code, in Proc 2 nd International Sympoium, Sept. 2000, pp IJCA TM : 2