0737 B06110349 pdf Error Correction Application of CRC in the RFID System Yanbin Zhang School of Information Engineering Zhengzhou University Zhengzhou, China Abstract—The application of CRC in the ra.
Error Correction Application of CRC in the RFID System Yanbin Zhang School of Information Engineering Zhengzhou University Zhengzhou, China Abstract—The application of CRC in the radio frequency the bit error rate and frame error rate of data transmission identification protocol ISO15693 is analyzed Based on CRC, the multiple bits error correction function is realized in the decode Ċ Application of CRC in the RFID system process of Manchester Code The error correction principle and realization technique are described in detail The selection of In the RFID protocol of ISO15693, the frame format of the data transmission is as figure 1, which uses the CRC code to check error 5HTXHVW)UDPH decision threshold and error correction bits is analyzed The simulation and application results prove the validity of the multiple bits error correction algorithm Key words- cyclic redundancy check; error correction; multiple bits 62) )ODJ &RPPDQG 3DUDPHWHU 'DWD &5& (2) error; frame error probability 5HVSRQFH)UDPH ĉ.Introduction 62) )ODJ &RPPDQG 3DUDPHWHU &5& (2) Fig Data transmission frame format in ISO15693 The basic idea of the CRC is the linear codes theory At the transmission end, the r bits check codes, i.e CRC codes, are generated at the defined rule according to the k bits binary transmitted codes sequence The check codes are then attached to the transmission data At last, the new k r bits binary codes are transmitted At the receive end, the check is done according to the rule between information codes and the CRC codes to make sure if there are some errors in the transmission process The 16 bits CRC CCITT generator polynomial is Radio Frequency identification (RFID) is a technology using radio frequency method to have contactless dual communication to reach the target of data transmission and information exchange In the process of data transmission, the received data may be different from the transmitted data for the reason of noise and interfere To detect the rightness of the transmitted data, cyclic redundancy check code (CRC) is used in the RFID protocol of ISO15693 CRC is a kind of high g ( x) x16 x12 x (1) The analysis tool of CRC codes is the polynomial theory of modern algebra, suppose performance and easily realized error detection code which can identify the transmission errors at high reliability The m( x ) x r research work about CRC coding is carrying out around the p ( x) g ( x) q ( x) (2) error detection application CRC code is usually used as error Where, m( x ) is the information polynomial with the detection but not error correction, but reference proved that frame by itself This paper proposes a method of combining length of k , k < 32767, r =16; s ( x) is the codes transmission polynomial with the length of n , n k r ; r ( x) is the received codes polynomial with the check and judge process to realize the multiple bits error length of n ; e( x) is the error polynomial with the length correction based on CRC code The technique is used in the of n ; p ( x) is the quotient polynomial; q ( x) is the residue polynomial, and the highest term degree is little CRC code has the ability of one bit error correction per data RFID reader based on the protocol of ISO15693 to improve _ 978-1-61284-109-0/11/$26.00 ©2011 IEEE than r The both sides of formula (2) plus the residue polynomial q ( x ) get m( x ) x r q ( x ) Let (4) s ( x) p ( x) g ( x) q ( x) q ( x) p( x) g ( x) m( x ) x q ( x ) r The judge of high error probability is determined by the selection of VD If VD is too big, the recorded position may be too much, which introduces the calculation burden to the error correction processing If VD is too small, some (3) errors may not be corrected Here we take the binary PAM signal as an example to analyze the selection of VD The p ( x) g ( x) aim of the analysis is to select the proper parameter VD so r ( x ) s ( x ) e( x ) p ( x ) g ( x ) e ( x ) (5) If e( x) , then r ( x) p ( x) g ( x) can be divided exactly by g ( x) , which is the CRC principle that the errors can be corrected with proper calculation quantity Suppose that the two signal waves are s1 (t ) g (t ) g (t ) respectively Where g (t ) is zero except for the zone of d t d Tb with the energy of H b If and s2 (t ) ċ PRINCIPLE OF ERROR CORRECTION the two signals have the same probability and the transmitted signal is s1 (t ) , the received signal after The detail method which realizes the ability of multiple bits error correction using cyclic redundancy check codes is as follows First, the bits with high error probability are recorded in the process of threshold judge When the CRC result of the data frame is wrong, the proper recorded bits are turned over, and the CRC result is calculated again If the check result is right, the error correction ability is realized Suppose that the judge threshold is Vth , and the Hb n demodulation is r Where n denotes the additive gauss noise with the zero mean and the covariance V n2 of N / Then compares r with the threshold zero based on the judge rule of correlation measurement If r ! , the judge result is s1 (t ) ; if r , the judge result is s2 (t ) The two probability density functions are: amplitude after demodulation of the received signal is Vi exp((r H b ) / N ) S N0 P (r | s1 ) When Vi Vth VD , it is supposed that the error probability of the judge is high and the bit position is recorded Suppose that M positions, i.e., p1 , p2 , pM exp((r H b ) / N ) S N0 P (r | s2 ) are recorded in the whole judge process The CRC value is calculated after the judge of the data frame If the check result is error, error correction begins The number of error bits should be set before the error correction processing If (6) (7) In the case that the transmitted signal is s1 (t ) , the error probability of r P (e | s1 ) J it is J bits error, the CM combinations should be got about the M recorded bits Then the corresponding J bits are turned over and the CRC value is calculated again about every combination until the error bits are found out ³ f is P(r | s1 )dr 2S ³ f 2H b / N exp( x / 2)dx (8) Q( 2H b / N ) Similarly, if the transmitted signal is s2 (t ) , Č SELECTION OF ERROR CORRECTION H b n , the probability of r ! is r POSITION AND BITS P (e | s2 ) Q( 2H b / N ) (9) Because s1 (t ) and s2 (t ) are transmitted at the It can be seen that the error correction process is supposing the error position and calculating the CRC value again If there are too much recorded position or too many supposed error bits, the calculation quantity will be very large So it is necessary to analyze the judge of the bits with high error probability and the maximum supposed error bits A Judge of the bits with high error probability same probability, the mean error probability is Pbe 1 P (e | s1 ) P(e | s2 ) Q ( 2H b / N ) (10) 2 Let VD r VD is D Hb , D , the error probability when Pr e P (e | r D H b ) is Pbe , and the frame length is n , then the frame error probability is 1 P(e | s1 ) r D H P(e | s2 ) r D H (11) b b 2 Q((1 D ) 2H b / N ) Q( 2H b / N ) (15) The M bits error probability of the frame is CnM PbeM (1 Pbe ) n M PeM Then, the ratio of the error probability when (16) The frame error probability after one to M bits error correction is r VD to the mean error probability is Pr e Pbe (1 Pbe ) n P fe Q((1 D ) 2H b / N ) Q( 2H b / N ) Pfe Q( 2H b / N ) Pfe (1 Pre Pbe M Pem ¦P m ) (17) fe (12) And the probability of r VD is Pr TABLE The calculation results when P( r D H b ) SNR (dB) 10 11 1 P(r | s1 ) r D H P(r | s2 ) r D H b b 2 Q((1 D ) 2H b / N ) Q((1 D ) 2H b / N ) (13) The calculation results at different signal to noise ratio (SNR) are as table one when VD H b / It can be seen n =1024 Pfe Pe1 / Pfe Pe / Pfe Pfe 0.5468 0.1776 3.38e-2 3.96e-3 2.68e-4 65.62% 90.55% 98.29% 99.80% 99.98% 25.95% 8.84% 1.69% 0.19% 1.34e-4 7.06e-2 5.22e-3 3.23e-4 1.16e-5 1.82e-7 The calculation results at different SNR when the frame length n equals to 1024 are shown as table It can be seen that more than 90% errors are one bit error and two bits error when SNR ! 6dB So the correction bits can be restricted to a small range at certain frame length and SNR so that the calculation quantity is reduced greatly with the correction performance almost not affected that Pr e / Pbe is larger than 95ˁ and Pr is little than ˁ when SNR ! 6dB It shows that more than 95ˁ errors happen on the bits below 1ˁ So, proper threshold can be selected to error correction by use of CRC at certain SNR when the frame length is not too large Because the bits with high error probability are just a little part of the whole frame, the error correction processing will not introduce high calculation burden V SIMULATION RESULTS TABLE The probability at different SNR SNR Pbe Pr e / Pbe Pr e Pr (dB) 7.73e-4 7.35e-4 95.10% 8.75e-3 1.91e-4 1.86e-4 97.65% 3.85e-3 3.36e-5 3.33e-5 99.07% 1.40e-3 10 3.87e-6 3.86e-6 99.71% 3.98e-4 11 2.61e-7 2.61e-7 99.93% 8.38e-5 B Selection of error correction bits The selection of error correction bits is a key problem after getting the bits with high error probability because the error correction bits have great influence on the calculation quantity If getting P bits with high error probability from a data frame after the judge, the number of the true error bits may be one up to P In fact, there are L cases of the true error situation Where In order to display the performance of the multiple bits error correction based on the CRC, simulation is done to the 107 data frames with 1024 bits every frame at the SNR to 12 dB In the simulation, VD is selected as 1/ H b , and the number of correction bits is two The simulation results are as table It can be seen that the frame error probability is reduced greatly after error correction And the communication reliability is improved effectively The simulation results are consistent with the theoretic analysis results, which verify the effectiveness of the multiple bits error correction method based on CRC TABLE The simulation results P L ¦C m P (14) m In the practical application, the bits with high error probability are much more than the true error bits So it is necessary to analyze how many bits should be selected to be corrected at certain data length and bit error probability If the bit error probability of the transmission channel SNR(dB) Pfe Pr Pfe 10 11 0.5514 0.1802 3.45e-2 4.07e-3 2.77e-4 8.81e-3 3.89e-3 1.41e-3 4.04e-4 8.54e-5 7.24e-2 5.37e-3 3.22e-4 1.21e-5 1.00e-7 VI CONCLUTIONS The principle of CRC is introduced Then a new method which links the judge and data check is provided The method realizes the ability of multiple bits error correction using cyclic redundancy check codes The error correction principle and realization method are described in detail The key parameters design of the method is analyzed The simulation results show that the multiple bits error correction method can improve the bit error rate and frame error rate effectively The method has been used in the reader design based on the ISO15693 protocol References [1] Yang Jie, Zhu Jianfeng An Jianping Extensive Application of Using Cyclic Redundancy Check Codes to Correct the Error in Wireless Transmission Transact ions of Beijing Institute of Technology 2005, 25(8):726-729 [2] Fu Zuyun Information Theory: the Basic Principle and Applications Beijing: Publishing House of Electronics Industry, 2001 103- 108 [3] Wang Xinmei, Xiao Guozhen Errors Correct Coding: Theory and Method [M] Xi’an: Xidian University Publishing House, 2001 73- 79 [4] Kazakov P Fast Calculation of the Number of Minimum Weight Words of CRC Codes IEEE Transact ions on Information Theory, 2001, 47 (3):1190- 1195 ... process The CRC value is calculated after the judge of the data frame If the check result is error, error correction begins The number of error bits should be set before the error correction processing... 8.38e-5 B Selection of error correction bits The selection of error correction bits is a key problem after getting the bits with high error probability because the error correction bits have... selected to error correction by use of CRC at certain SNR when the frame length is not too large Because the bits with high error probability are just a little part of the whole frame, the error correction