Channel Encoding and Decoding in WiMAX
Prabhakar Telagarapu1, Birendra Biswal2, J Venkata Suman3 Dept.of.ECE, GMR Institute of Technology, Rajam, Srikakulam District, AP, India, 532127 1
[email protected]
1,2,3,4
2
[email protected]
3
[email protected]
Abstract: Coding techniques is used for providing reliable information through the transmission channel to the user. In coding techniques the number of symbols in the source encoded message is increased in a controlled manner in order to facilitate two basic objectives at the receiver one is Error detection and other is Error correction. It is used to reduce the level of noise and interferences in electronic medium. The amount of error detection and correction required and its effectiveness depends on the signal to noise ratio (SNR). In digital communication, coding techniques is a broadly used term mostly referring to the forward error correction code. The advantage of forward error correction is that a back-channel is not required, or that retransmission of data can often be avoided, at the cost of higher bandwidth requirements on average. In this paper is useful for performance evaluation of physical layer of WIMAX by using Reed-Solomon coding and convolution coding scheme, cyclic prefix and interleaving for different modulation technique with respect to bit-error rate and SNR ratio.
Keywords: Error detection, Error correction code, WIMAX cyclic prefix, SN, Reed-Solomon coding
1. INTRODUCTION The main objective of this paper is to transmit the data in WIMAX with low bit e0072ror rate in the noisy environment for that we using Forward Error Correction method which is Reed Solomon coding and Convolution coding .this method is useful to reduce the bit error rate(BER) and increase the efficiency. Reed Solomon coding and Convolution coding are the two powerful error correction and detection methods to reduce the noise. In order to increase the performance of the coding technique Cyclic Prefix & interleaving techniques [1] is used .So in this paper is useful for analysis of physical layer of WIMAX with different modulation techniques like BPSK, QPSK, QAM and comparison of QPSK modulation with and without Forward Error Correction methods. Broadband Wireless Access (BWA) has emerged as a promising solution for last mile access technology to provide high speed internet access in the residential as well as small and medium sized enterprise sectors. At this moment, cable and digital subscriber line (DSL) technologies are providing broadband service in this sectors. But the practical difficulties in deployment have prevented them from reaching many potential broadband internet customers [2]. Many areas throughout the world currently are not under broadband [3] access facilities. Even many urban and suburban locations may not be served by DSL connectivity as it can only reach about three miles from the central office switch. On the other side many older cable networks do not have return channel which will prevent to offer internet access and many commercial areas are often not covered by cable network. But with BWA [4] this difficulties can be overcome. Because of its wireless nature, it can be faster to deploy, easier to scale and more flexible, thereby giving it 412
the potential to serve customers not served or not satisfied by their wired broadband alternatives. IEEE 802.16 standard [5,6] for BWA and its associated industry consortium, Worldwide Interoperability for Microwave Access (WIMAX) [10-12] forum promise to offer high data rate over large areas to a large number of users where broadband is unavailable. This is the first industry wide standard that can be used for fixed wireless access with substantially higher bandwidth than most cellular networks. Wireless broadband systems have been in use for many years, but the development of this standard enables economy of scale that can bring down the cost of equipment, ensure interoperability, and reduce investment risk for operators. The first version of the IEEE 802.16 standard operates in the 10–66GHz frequency band and requires line of sight (LOS) towers. Later the standard extended its operation through different PHY specification to 211 GHz frequency band enabling non line of sight (NLOS) connections, which require techniques that efficiently mitigate the impairment off adding and multi-path [7]. Taking the advantage of OFDM technique the PHY is able to provide robust broadband service in hostile wireless channel. The OFDM based physical layer of the IEEE 802.16 standard has been standardized in close cooperation with the European Telecommunications Standards Institute (ETSI) High Performance Metropolitan Area Network (HIPERMAN). Thus, the HIPERMAN Standard and the OFDM based physical layer of IEEE 802.16 are nearly identical. Both OFDM based physical layers shall comply with each other and a global OFDM system should emerge [9]. The WIMAX forum certified products for BWA comply with the both standards. Channel Encoding and Decoding in WiMAX
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2.. SIMULAT TION MODEL 2.1. Physical layeer setup t implemennted The structure off the basebannd part of the transsmitter and reeceiver is show wn in Figure 1. This structture correesponds to thhe physical laayer of the IE EEE 802.162004 Wireeless MAN OFDM O air inteerface. In thiss setup, we have h just implemented the mandatorry features of the t specificatiion, whille leaving thee implementaation of optioonal features for futurre work. Channnel coding part p is compossed of three stteps randdomization, Forward F Errror Correctioon (FEC) and interrleaving. FEC C is done in two t phases thhrough the ouuter Reedd-Solomon (R RS) and innner Convoluttion Code. The T comp mplementary opperations are applied in thee reverse ordeer at channnel decodingg [8] in the receiver Endd. The complete channnel encoding setup is shown in Figure F 2 whhile correesponding decooding setup is shown in Figuure 3. Through the rest of the sectionns, the individdual block of the setup willl be discuussed with impllementation techhnique.
2.2. Scrambler The scrambler perrforms random mization of innput data on each e burst on each allocation to avoiid long sequennce of continuuous oness and zeros. This T is implem mented with a Pseudo Randdom Binaary Sequence (PRBS) gennerator whichh uses a 15sttage shiftt register withh a generator polynomial of o 1+x14+x15 with w XOR R gates in feeddback configuuration as show wn in figure 4. 4
Figure 4: 4 PRBS geneerator for rand domization 3 Reed Solom mon coding 2.3 2.3 3.1 Encoder Th he randomizedd data are arrranged in blo ock format before b passsing throughh the encoder and a single 0X00 tail byyte is app pended to thee end of eacch burst. Thee implementedd RS enccoder is derivved from a ssystematic RS S (N=255, K= =239, T= =8) code usinng GF (28). T The following g polynomials are useed for code geenerator and fiield generatorr: G(( x )
(x
0
p( x)
x8
x4
) x )( x3
1
).....( x
x2
2T 1
),
02 HEX
.. (1)
1 .. (2)
The T encoder support shortened and punctured p codde to faccilitate variable block sizees and variablle error correection cap pability. A shoortened blockk of k´ bytes is obtained thrrough
Figuree 1: Simulation n Setup
Figure 2: Chaneel enco oding setup
oding setup Figure 3: Chaneel deco Chaannel Encoding and Decoding in i WiMAX
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adding 239k ´ zero bytes before the data block and after encoding, these 239k ´ zero bytes are discarded. To obtain the punctured pattern to permit T´ bytes to be corrected, the first 2T´ of the 16 parity bytes has been retained.
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fk
sk
(
N cbps 12
s. floor(
).K mod12
fk ) ( mk s
k floor ( ), k 2
N cbps
floor(12.
0,1,2,......N cbps 1
mk ) mod( s ) k N cbps
… (5)
0,1,2...N cbps1
2.4 Convolutional Encoder The outer RS encoded block is fed to inner binary convolutional encoder. The implemented encoder has native rate of 1/2, a constraint length of 7 and the generator polynomial in Equation (4.3) and (4.4) to produce its two code bits. The generator is shown in Figure 4.5.
G1
171 OCT For X…………… (3)
G2
133 OCT For Y…………… (4)
In order to achieve variable code rate a puncturing operation is performed on the output of the convolutional encoder in accordance to Table 4.2. In this Table “1” denotes that the corresponding convolutional encoder output is used, while “0” denotes that the corresponding output is not used. At the receiver Viterbi decoder is used to decode the convolutional codes.
(6) where s= ceil(Ncpc/2) , while Ncpc stands for the number of coded bits per subcarrier, i.e., 1,2,4 or 6 for BPSK,QPSK 16QAM, or 64QAM, respectively. The default number of sub channels i.e. 16 is used for this implementation. The receiver also performs the reverse operation following the two step permutation using equations respectively. fj
sj
j s. floor ( ) ( j s
12 .. f j
floor (12.
( N cbps 1). floor (12.
j ) mod ( s ) j N cbps fj
N cbps
)j
0,1....N cbps
…. (7)
0,1.... N cbps 1
… (8)
2.6 Constellation Mapper The bit interleaved data are then entered serially to the constellation mapper. The Matlab implemented constellation mapper support BPSK, grey mapped QPSK, 16QAM, and 64QAMa. The complex constellation points are normalized with the specified multiplying factor for different modulation scheme so that equal average power is achieved for the symbols. The constellation mapped data are assigned to all allocated data subcarriers of the OFDM symbol in order of increasing frequency offset index [13]. 2.7 IFFT The grey mapped data are then sent to IFFT for time domain mapping. Mapping to time domain needs the application of Inverse Fast Fourier Transform (IFFT). In our case we have incorporated the MATLAB ´IFFT´ function to do so. This block delivers a vector of 256 elements, where each complex number clement represents one sample of the OFDM symbol.
Figure 5: Convolution encoder of rate ½ 2.8 Cyclic Prefix Insertion 2.5 Interleaver RSCC encoded data are interleaved by a block interleaver. The size of the block is depended on the numbers of bit encoded per sub channel in one OFDM symbol, Ncbps. In IEEE 802.16, the interleaver is defined by two step permutation. The first ensures that adjacent coded bits are mapped onto nonadjacent subcarriers. The second permutation ensures that adjacent coded bits are mapped alternately onto less or more significant bits of the constellation, thus avoiding long runs of unreliable bits. The Matlab implementation of the interleaver was performed calculating the index value of the bits after first and second permutation using Equation respectively [14].
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A cyclic prefix is added to the time domain samples to combat the effect of multipath. Four different duration of cyclic prefix is available in the standard. Being G the ratio of CP time to OFDM symbol time, this ratio can be equal to 1/32, 1/6, 1/8 and ¼.
Figure 6: Cyclic prefix insertion
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3. SIMULATIION RESULT TS In thhis the simulattion results arre shown and discussed. In the folloowing sections, first we wiill present thee structure of the impllemented sim mulator and then we will w present the simuulation resullts both inn terms off validation of impllementation and a values for various parameters that t charracterize the performance off the physical layer. 3.1 The T Simulatoor We have h developeed the simulattor in Matlab™ ™ using moduular apprroach. Each bllock of the traansmitter, receeiver and channnel is written in separrate ´m´ file. The main proocedure call each e of thhe block in thhe manner a communicatio c on system works. The main proceddure also conttains initializaation parametters, inpuut data and dellivers results. The parameteers that can bee set at thhe time of innitialization are a the numbber of simulaated OFD DM symbols, CP length, modulation and a coding rate, r rangge of SNR vaalues. The innput data streeam is random mly geneerated. Outpuut variables are availablle in Matlabb™ workkspace while BER values for f different SNR S are storedd in text files which faacilitate to draaw plots. Eachh single blockk of the transmitter t is tested with its i counterparrt of the receiiver side to confirm that each block works perfecttly. 3.2 Physical P layerr per3forman nce results The objective behind b simulaating the phhysical layer in Matllab™ was too study BER R performancee under varyying paraameters that chharacterize thee performancee. But, in ordeer to relayy on any resuults from PH HY layer simuulation we must m havee some results that can doo some validaation in termss of geneeral trends. 3.3 BER B Plots In thhis section we have presented various BE ER vs. SNR plots for all the manddatory modulation and cooding profiless as speccified in the staandard on sam me channel moodels.
Figure 7: 7 Bit rate valuues for Differeent SNR
Chaannel Encoding and Decoding in i WiMAX
Figure 8: Bit B rate values for Different SNR for withh FEC and w without FEC Table 1: Bit rate vallues for Differrent SNR Modulation M Technique T BPSK ½ QPSK ½ QPSK ¾ 16-QAM ½ 16 6-QAM 3/4 64-QAM 6 ¾ 64 4-QAM 3/4
0
2
4
6
8
10
00.1082 0 0.5121 0 0.4391 0 0.5298 0 0.5232 0 0.5047 0 0.4863
0.0551 0.4718 0.47444 0.50999 0.51277 0.51400 0.51799
0.0141 0.1815 0.4036 0.4940 0.5079 0.5152 0.5105
0 0.0377 0.0973 0.2 2980 0.4 4953 0.5000 0.5074
0 0 0.0066 0.1090 0.3668 0.4755 0.4443
0 0 0 0.0028 0.1390 0.3143 0.4328
4. CON NCLUSION Errror detection and correctioon techniquess are essentiaal for reliable communnication over a noisy chann nel. Reed Soloomon cod des are one off the most poowerful and esssential non-bbinary errror correctingg codes for ddetecting and d correcting burst errrors. The efffect of error occur durin ng transmissioon is red duced by addding redunddancy to th he data prioor to transmission. Thhe redundanccy is used to enable decodder in b thee receiver to detect and coorrect errors. Cyclic liner block cod des are used efficiently e forr error detectiion and correcction. Th he encoder splits s the inccoming data into blocks and pro ocesses each block individdually by adding redundancy in acccordance witth a prescrribed algorith hm and deccoder pro ocesses each block individually and itt correct erroor by exp ploiting the reedundancy prresent in the received r data. The adv vantage of cyyclic codes inn that they eaasy to encodee and pro ocess a well defined d mathem matical structu ure which hass lead to very efficieent decoding scheme for them. The reed Solomon codes burst error caan be effectiveely corrected. Reed Solomon codes are efficienttly used for compact discs to corrrect which might m occur due to scratcches on the discs. d Errror detection and correctiion techniquee are essentiaal for reliable communnication over a noisy chann nel. Reed-Soloomon cod des are one most m powerful and efficient code to correcct the errrors by using this t codes in W WIMAX we can c reduce the biterrror in noisy ennvironment annd useful to prrovide the effi ficient datta to the subsscriber. And bby using the OFDM technnique, wee transmit highh data rate in llimited bandw width channel. 415
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Channel Encoding and Decoding in WiMAX
