Trellis Coding based on RLLPUM Codes for RFID Reader-to-Tag Channel

Transcription

1 Austalian Jounal of Basic and Applied Sciences, 74: 78-77, 23 ISSN Tellis Coding based on RLLPUM Codes fo RFID Reade-to-Tag Channel Vijey Thayananthan, Ahed Alzahani & Muhaad Shuaib Queshi Depatent of Copute Science, Faculty of Coputing and Infoation Technology, King Abdulaziz Univesity, Jeddah 2589, Kingdo of Saudi Aabia. Abstact: Tellis coding techniques ae siple gaphical ethodology in the encode and decode developent in infoation theoy. When this technique is applied to patial unit eoy code PUM code, inial tellis designs with less coplex appoach ae identified using Shannon poduct theoy. Cobination of un-length liited RLL and PUM codes is called RLLPUM code, which is applicable to digital agnetic ecoding channels. Radio fequency identification RFID syste contains eade-to-tag channel, which has siila popeties as used in digital agnetic ecoding channels. In this pape, eo detection and coection ae consideed with tellis coding techniques based on RLLPUM codes. Data stoage is challenging topic with othe copeting technologies which povide a nube of benefits. We popose a technique that allows the design of PUM codes with balanced RLL popeties influenced with RFID eade-to-tag channel. Fo the esults, eo detection, coection and stoage, which could be inceased up to 5%, ae copaed. Key wods: Tellis coding, RLLPUM codes, RFID, Balanced codes, Reade-to-tag channel INTRODUCTION TRFID syste has tag and eade which is the only ain souce of enegy that allows passive tags to stoe data. Using RFID tags, easonable size of data can be stoed, but they can be extended with bigge stoage capacity with soe odifications. The RFID tag, which has any types, is used in diffeent applications. Data need to be coected befoe they ae stoed in the tag, so pope eo contol technique should be eployed in the eade-to-tag channel. PUM eo contol code is chosen because both eo coecting capability and stoage capacity needs to be ipoved in the RFID channel. Using netwoked RFID syste, stoed infoation o essage could be sent to all ove the places though the high-speed netwok linked within the faction of the second if RFID channel is eliable. Most of the edical and business applications ae involved with data stoage; theefoe, RFID syste is odified to use as data stoage. RFID s potential deands encouage e to exploe this eseach which povides bette stoage capacity without changing the bandwidth. In this pape, data stoage of RFID eade-to-tag channel based on RLL/PUM coding will be consideed with tellis design. Tellis design is constucted fo Shannon poduct discussed by Ke et al. 995 helped to educe coplexities and incease the decoding facilities. In PUM and RLLPUM coding schees, tellis appoaches ae popula coding techniques because inial tellis constuction depends on the fee distances of PUM coding. In ode to incease stoage capacity in eade-to-tag channel, PUM code is chosen because this channel has siila popeties as digital agnetic and optical stoage devices. RLLPUM code is aleady poved to ipove the above entioned channels. In the eade-to-tag channel, inductive coupling of RFID is intoduced to tansfe the enegy helped fo infoation tansission entioned by Angela et al. 2 RFID eade needs attached powe but tag can be used without sepaate powe. In this pape, lowe laye coding of infoation on inductively coupled channels is intoduced with PUM eo contol coding. Regading the encoding schees specified in counication standads fo RFID applications including data stoage, geneal counication potocols, such as NRZ, Mancheste, Unipola RZ, and Mille coding ae useful. Coding schees fo the eade to tag channel depend on RLL and othe coding constaints, Mancheste code, vaiable code etc. Abdel-haffa et al. 99. RLL codes ae used to tansfo the digital use bit stea into a sequence of binay channel sybols that ae suitable fo the specific stoage equieents. The unlength is known as the nube of consecutive identical sybols occuing in a sequence. This coespondence is oganized as follows. In the next section, we descibe the tellis of PUM codes and intoduce the basic pocedue fo constuction. In section 3, design of both the balanced and RLLPUM codes is descibed. The details of the poposed syste ae descibed. In section 4, a egula tellis design pocedue is biefly outlined. In section 5, esults of PUM and RLLPUM codes ae pesented fo the poposed codes and finally, in section 6, the conclusions ae given. Basic Infoation of Pu Codes: Coesponding Autho: Vijey Thayananthan, Depatent of Copute Science, Faculty of Coputing & I.T, King Abdulaziz Univesity, Jeddah 2589, Kingdo of Saudi Aabia. E-ail: thayananthan@live.co.uk 78

2 Aust. J. Basic & Appl. Sci., 74: 78-77, 23 The PUM eo contol codes wee invented in late 97, but its applications wee not popula at that tie because the technology wasn t poweful as we use the in potential applications. The N, K unit eoy codes use fixed delay t duing the encoding. When delay is less than infoation length t < K, it is called PUM code Lee, 976; Thoesen and Justesen, 985. Initially, it was used it fo digital agnetic ecodings. It is basically an eo contol code which povides best fee distance popeties. In this pape, linea PUM codes ae chosen as a technique because its data ates fo RFID stoage ae vey useful in potential RFID applications. Futhe, it has both block and convolutional code popeties. It has a lot of advantages such as vaiable ates, best pefoance, stoage capacity etc. but we need to optiize the coplexities which could be the ain disadvantage. Fig. : Basic idea of PUM code. As shown in Fig., the geneato atix can be oganized fo PUM code. Each atix in this Fig. is explained in the next section. Linea PUM codes wee poposed as a ethod of using the theoy of block codes fo constuction of new convolutional codes Makaian, Honay, 994; Makaian et al These codes cobine advantages of both block and convolutional codes ay be descibed as N, K convolutional codes with eoy v=. It has been shown that thee ae PUM codes with the fee distance at least as lage as those of convolutional codes with the sae infoation ates and constaint lengths Thayananthan et al Copaed with the block codes, the PUM codes have the highest possible code diension K fo a given code length N and fee code distance d fee Shaga, 995. Fo instance, the best known block code with encoded block length n = 8 bits, infoation length k = 4 bits and the iniu Haing distance d in = 4 is consideed. The PUM code chosen with sae encoded length N = n = 8, fee distance d fee = 4 and infoation length K = 6 povides 5% inceases in the infoation ate. In addition, the byte oiented natue ceated fo PUM encode akes the paticulaly attactive in stoage channels such as digital agnetic ecoding and RFID. It is anticipated that the application of PUM codes in agnetic and optical ecoding systes could povide a significant incease of the ecoding density without expensive technological advances. Howeve, known PUM codes ay not be applicable in the RFID eade to tag channel because they do not satisfy the d k and the RDS constains thus they ae not applicable to agnetic and optical ecoding channels. In this coespondence, we intoduce a technique that allows the design of the high-ate RLL and balanced eo contol codes based on PUM codes. We can also show that the axiu-likelihood decoding of these codes can be achieved with egula tellis stuctue. Tellis coding technique based on RLLPUM is intoduced fo RFID eade-to-tag channel. Details of the Poposed Syste: As shown in Fig. 2, poposed syste is oganised with RLLPUM encode and decode. The encode is depended on geneato atix and delay which should be less than K as in Fig.. 79

3 Aust. J. Basic & Appl. Sci., 74: 78-77, 23 Fig. 2: Block diaga of RFID syste with RLLPUM coding. We popose a technique that allows the design of PUM codes with soe special chaacteistics, which copoate with balanced and RLL popeties. Accoding to the popeties, the designed code can be used in the RFID channel known as a eade to tag channel. Taditionally, any counication systes, such as digital agnetic and optical stoage devices, fibeoptic and cable telecounication systes, eploys the dc-fee constained codes often efeed to as ecoding o odulation codes which tansfo the input data stea to a wavefo suitable fo the specific channel equieents Henici et al. 2. The te constained code copises the two paticula types of codes, known as the RLL and balanced codes. The RLL codes, also defined as the d k constained codes, epesent a class of codes in which the two consecutive ones ae sepaated by at least d but no oe than k zeos. The paaete d is used to contol the inte sybol intefeence between ecoded tansitions while the k paaete iposes a axiu nube of zeos that ae equied fo self-clocking puposes. The balanced codes epesent a class of constained codes with the liited value of the digital unning su RDS Makaian et al, 997. Pobles connected to the design of both the RLL and balanced eo contol codes ECC have eceived consideable attention, and a geat nube of block and convolutional ECC constained codes have been designed. Howeve, the eve existing deand fo highe ecoding densities dictates the need of highe infoation ates that cannot be achieved with the conventional block and convolutional encoding techniques. Constuction of PUM Codes: Let x, x2,... xi,.. be the sequence of infoation vectos of length k, whee index notifies the tie inteval i =, 2... Let y, y2,... yi,.. be the sequence of output code vectos of length n. The PUM encode is given as; yi xi * xi * i,2,3... Whee and ae the K N atices espectively. In equation, ank of = k. They ae pats of the geneato atix defined as Fig.. Matices ae such as 2 KN and 3 KN In equation 2, is a geneato atix of the n, k, d in basic block code. In equations 2 and 3, and ae the k n atices espectively. In equation 3, ank of depends on ank = k because is the all zeo k n atix Sidoenko et al. 996; Thayananthan et al A PUM code is odified as N, K, d code, and the oveall geneato atix equation 4 of such code is as follows: fee 7

4 Aust. J. Basic & Appl. Sci., 74: 78-77, In ode to analyze the eseach, PUM 8, 6, 4 code is illustated. To design a geneato atix fo this code, following atices ae used. It has been shown in Boli c et al. 2 that a significant pefoance ipoveent and coplexity eduction can be achieved if the PUM code is constucted based on the, Reed-Mulle RM codes. In ode to constuct the, RM code, equation 5 is used as follows...., 5 Whee is the ode of the code, is the all s ow atix of length 2, i is 2 a atix and the iniu code distance of the code ae d 2,. The coesponding PUM/RM code can be constucted fo following equations 6, 7 and 8., 6 In equation 6, = 4 and = 2 can be substituted. The top ow of in PUM 8, 6, 4 is diffeent, because it is optiized to educe the coplexity, but iniu distance would be sae. 7 ˆ 8 Whee, atix is obtained fo by intechanging the coluns. Fo equation 9, fee distance of such a code can be estiated as:, 2 2 d d fee 9 In this pape, fee distance is consideed as sae as the iniu distance fee d = in d = 4 of PUM 8, 6, 4. As entioned above, the PUM code is constucted using convolutional and block codes which depend on ode of Reed-Mulle block code ipleented fo is based on denoted by 2 k F.

5 Aust. J. Basic & Appl. Sci., 74: 78-77, 23 Constuction of Balanced Codes: In this pape, selected 8, 6, 4 PUM code is used fo designing balanced and RLL PUM code. It has unique popeties such as byte oientation, which allows the design to ipleent the suitable balanced and RLL/PUM code fo digital agnetic channel. Fo the ecent eseach, these balance code can be used in RFID channel. Futhe, this developent can be applied to nanotechnology stoage systes such as nano-optical disc and nanocoputes. PUM codes can be poposed fo futue counication applications based on RFID o nanotechnology. Assue that x, x2,... xi... and y, y2,... yi... ae infoation vectos and encoded output vectos espectively. Hee, length of infoation vecto xi { xi, xi 2,... xik } is k and length of encoded vecto yi { yi, yi 2,... yin } is n espectively. The RDS befoe the p-th sybol in the i-th code wod is defined as follows M. Boli c et al. 2, i n p p w i 2yjl 2yjl j l l p i To deteine the w, only encoded output yi, yi 2,... yin ae applied in equation. The sign of this sybol is vey ipotant in RFID channel. As in equation, sign is used at the end of the i-th code wod as: p n wi wi wi Let the encoding pocedue defined as: y i xi xi N sign wi Whee N is a vecto, which has N ones. Tellis Coding of Rll/Pu Code: Siila to the balanced PUM codes, the inial tellis fo the RLL/PUM code can be easily obtained fo the inial tellis of the paent PUM code. This could be achieved by a siple alteation of the tellis banches, accoding to the chosen odification vecto, M. In this case, the tellis design pocedue is as follows: Design the tellis diaga of the paent PUM code, by using any conventional technique 2 In the designed tellis change the labelling of all banches accoding to the chosen odification vecto, M: RLL { Pi } { Pi } M 2 RLL Whee P i and Pi epesent the i-th path in the new and the paent tellises, espectively. Tellis Constuction of 8, 6, 4 RLL/PUM Codes: Let ou ai be to design a egula tellis fo the 8, 6, 4 RLL/PUM fo the pevious sections. The pocedue to calculate the Shannon poduct of coponent tellises is illustated in the Ke et al. 995, and the inial tellis of the paent 8, 6, 4 PUM code is also shown by Thayananthan et al Fo the chosen odification vecto M = and equation 2, the tellis diaga of the designed 8, 6, 4 RLL/PUM code will have the sae state and banch pofiles with alteed labels of tellis banches. As shown in Fig. 3, tellis is odified to RLL/PUM code, which few changes fo oiginal tellis of PUM coding. In RLL/PUM case, second bit of stage 2 and 4 within indicated dashed lines is inveted accoding to the odification vecto. iven N, K PUM code with geneato atix [ PUM ] explained in the pevious section, by using the following thee concepts, we can deteine the iniu following values. They ae attainable fo i l j i l j R end, R stat andr id, which we will denote Miniu R end, Miniu R stat and Miniu R id, fo any coset of the PUM eo contol coding, and hence set a lowe bound on the axiu unlength fo the patial code. j i RL ax = MAX{R id, R end + l stat R } 2 =MAX{4, } = 6 72

6 Aust. J. Basic & Appl. Sci., 74: 78-77, 23 Fig. 3: Tellis diaga fo 8, 6, 4 RLL/PUM code Ke et al Whee, uppe index indicates diffeent states of the encode in the PUM code. Fo the above concept, we can deteine the RLL popeties which depend on paaetes d, k fo the 8, 6, 4 PUM code. Accoding to RLL theoy, paaetes of RLL ae veified though the test and tabulated in Table, whee soe selected RLL/PUM codes ae consideed. RLL paaetes of 8, 6, 4 code can be epesented as d, k =, 6. Value k RLax 6 can also be calculated fo equation 2. Fist and Repeating Tellis of RLL/PUM Codes: As fa as the softwae and hadwae designs ae concened, the epeating tellis diagas ae vey ipotant in the PUM codes. This epeating tellis stuctue can also be applied as a fist tellis diaga when the fist state of epeating tellis is consideed. Futhe, they can be utilized to select best path out of the suviving paths that detect and coect eo in the RFID eade-to-tag channel. This epeating tellis stuctue is siply alteed accoding to the type of odification vecto. As shown in Fig. 3, fist and epeating tellis of 8, 6, 4 RLLPUM code equie alteation in stage one and stage thee. In ode to coplete the siulation, fist and at least one epeating tellis ust be used but fist and thee epeating tellises ae the best option in the decoding. Tellis Decoding of RLL/PUM Codes: The eo coection fo RFID eade to tag channel is consideed with tellis coding whee coect path is selected fo decoding. The decode poga also is witten individually fo each stage. Fo the final stage of the final depth etic calculation, the iniu path is selected. In each window, the fist depth is taken as coected path; the eaining next thee depths will be oved to the next window. This final path picks up the decoded output which should be one out of 256 possibilities. The each label of the stage has 2 encoded bits. Each state has 64 diffeent weights, which is vey useful and easy to copae the path identification. Coesponding path identification and weight fo given infoation bits poduces the decoded output with eo coection. Futhe, the eo coection is depended on the fee distance as well etic calculation in the tellis. So, it will be inceased with the inceasing depths Angela et al. 2. The copute poga concened in this poject calculates eo pefoance of decoding pogas is siulated with gaphical epesentation. Even, the gaphical epesentation of this tellis is vey ipotant fo exta explanation; this poga pocedue is ainly concened and witten to analyze the esults with othe conventional decodes. As entioned in the tellis decoding algoith, this poga is divided into any sub functions which is vey easy to odify and extend with othe functions. Diffeent noisy signals have been 73

7 Aust. J. Basic & Appl. Sci., 74: 78-77, 23 added and copaed in this channel. Tellis decoding algoith inceases the eo coecting capability and bit eo ate BER pefoance when fou tellises ae used in a single window. Constucted tellis design fo 8, 4 PUM code has 256 code wods epesented by tellis path o banches. These 256 code wods ae used hee to select the iniu distance and path. Results: In ode to incease the data stoage in RFID tag, PUM coding is bette than othe known block codes. Fo the tellis diaga, coplexity can be copaed staightaway. The top pat of the tellis diaga in Angela et al. 2 can be consideed as 8, 4, 4 block. In tes of coplexity, 8, 6, 4 PUM code is 4 ties highe than 8, 4, 4 block code. Pefoance of these two codes ae alost equal; theefoe, it is still bette fo stoage than block code. Using this specific PUM code, 5% of data can be stoed as an enhanceent without changing bandwidth. Pb Against Eb/No fo 8,6,4PUM Code - had soft uncoded -2 P obability of bit eo Fig. 4: BER pefoance of 8, 6, 4 PUM coding Eb/NodB Copaison of uncoded and coded had and soft decision cuves illustate the eo pefoance. Fo the Fig. 4 and Fig. 5, we know in which diection the watefall-like cuves oe coesponding to BER pefoance ipoveent. As expected, the unquantised o had decision decoding tellis decoding has oe than.5db coding gain ove the soft decision. A high speed of eading is of attactive fo any RFID applications. High-speed eading is inteupted by nube of things such as collisions when too any RFID eades ae involved, unwanted eos intoduced duing the eading etc. In ode to aintain the high data quality, BER and data tansfe ate ae ipotant. Eo Detection in RFID: The RFID eade-to-tag channel needs soe kind of eo detection and coection techniques because noise based on inductive influences of tansfoes in RFID syste should be eoved. Copaison Between Block and PUM Coding: As shown in Fig. 6, BER pefoance of block and PUM codes is copaed though the siulations. They ae alost sae, but the coplexity of 8, 6, 4 PUM code is fou ties highe than the basic block 8, 4, 4 code. It is obvious because code ate is high. So, in ode to incease the stoage capacity in RFID tag without changing the bandwidth, 8, 6, 4 PUM codes can be used. RLLPUM Coding Selections: Fo the analysis of this eseach, tellis coded techniques based on RLLPUM codes can be chosen and constucted with RLL paaetes as given in Table. In ode to analyze stoage capacity of RFID eade-totag channel, RLL paaetes can be used with suitable odification vecto. 74

8 Aust. J. Basic & Appl. Sci., 74: 78-77, 23 Pb Against Eb/No fo 8,6,4RLL/PUM Code - had soft uncoded -2 Pobability of bit eo Eb/NodB Fig. 5: BER pefoance of 8, 6, 4 RLLPUM coding. Pb Against Eb/No fo RLL/Block & RLL/PUM Code - Block8, 4, 4 PUM8, 6,4 Uncoded -2 Pobability of bit eo Eb/NodB Fig. 6: BER pefoance of RLL/block and RLL/PUM coding. Table : RLL paaetes of soe selected codes. N, K, d fee RLL/PUM Code RLL Paaetes d, k 8, 4, 4, 6 8, 4, 6, 6 8, 4, 8, 6 8, 6, 4, 6 6, 4, 3, 6, 4, 6, 6, 5, 4,2 6, 5, 6,4 8, 6,, 75

9 Aust. J. Basic & Appl. Sci., 74: 78-77, 23 As shown in Table 2, thee diffeent types of tellis configuations have been investigated thooughly. In this investigation, tellis design with 2 bits pe banch is chosen because selected tellis coded technique has less coplexity. Fo the investigations, the tellis decoding coplexity can be tabulated as: Table 2: Copaisons of coplexities in tellis decoding. Tellis Type States Coluns Banches Copaison O additions bit/ banch bits/ banch bits/ banch Tellis design fo 8, 6, 4 RLLPUM code is investigated as in Sidoenko et al., 996; Angela et al., 2. Conclusion: In this eseach, stoage capacity can be inceased at least 5%. This inceent puely depended on the selection of the PUM coding ate. If 8, 6, 4 PUM/RLL code is used instead of odinay 8, 4, 4 block code, we can have bette pefoance and 5% stoage inceent without expanding the bandwidth. In RFID technology, the 8, 6, 4 code is vey attactive because it has byte oientation. It eans that signal pocessing would be bette than othe block codes. eneally, thee is a tade-off between pefoance and decoding coplexity. REFERENCES Abdel-haffa K.A.S., H. Webe, 99, Bounds and constuctions fo un length liited eo contol block codes, IEEE Tans Info. Theoy, IT-373: Angela, I.B., Eiik Rosnesz, uang Yangz and Øyvind Ytehus, 2. Constained Codes fo Passive RFID Counication, Depatent of Infoatics, Univesity of Begen, N-52 Begen, Noway. Boli c, M., D. Siplot-Ryl and I. Stojenovi c. Eds., 2. RFID Systes: Reseach Tends and Challenges. Wiley. Detta, U. and S.A. Shavgulidze, 992. New optial patial unit eoy codes, Electon Lette., 28: Detta, U., and U.K. Soge, 993. New optial patial unit eoy codes based on extended BCH codes, Electon Lette., 29: Henici, D., A. Kabzeva, T. Fleuen and P. Mulle, 2. Data stoage in RFID systes. Radio Fequency Identification Fundaental and applications binging eseach into pactice. Coatia, Ke, I. and M.W. Macellin, 995. A new constuction fo n-tack d, k codes with edundancy, IEEE Tans. Info. Theoy, 44: 7-5. Laue..S., 979. Soe optial patial unit-eoy codes, IEEE Tans. Infoation Theoy, 25: Lee, L.N., 976. Shot unit-eoy byte oiented binay convolutional codes having axial fee distance, IEEE Tans. Info. Theoy, 22: Lee, L.N., 977. Concatenated coding systes eploying a unit-eoy convolutional code and a byteoiented decoding algoith, IEEE Tans. Counication, 25: Makaian,., B. Honay, 994. Tellis decoding technique fo block RLL/ECC, IEE Poc., 4: Makaian,., B. Honay, V. Thayananthan, 997. Tellis Coded Quantization technique based on patial unit eoy codes, Poceedings of the 4 th Intenational Syposiu on Counication Theoy and applications, Ableside, Lake Distict, Shaga, I.B., 995. Unit-eoy codes fo continuous phase odulation in an AWN channel, IEEE Tans. Info. Theoy, IT-43: Sidoenko, V., 995. Unit Meoy/Patial Unit Meoy Codes, Lectue Notes. Sidoenko, V.,. Makaian and B. Honay, 996. Minial Tellis Design fo Linea Codes Based on the Shannon Poduct. IEEE Tansactions on Infoation Theoy, 426: Thayananthan, V., B. Honay and. Makaian, 998. Tellis Coded Quantization Technique Based on Patial Unit Meoy Codes, IEEE Intenational Syposiu on Infoation Theoy, MIT. Thayananthan, V.,. Makaian and B. Honay, 998. DSP Ipleentation and Design of Tellis Coded Quantization Technique Based on Patial Unit Meoy Codes, IEEE LOBECOM 98. Thoesen, C. and J. Justesen, 985. Bounds on distances and eo exponents of unit-eoy codes, IEEE Tans. Info. Theoy, 29:

10 Aust. J. Basic & Appl. Sci., 74: 78-77, 23 Zyablov, V.V.,.S. Makaian, S.L. Potnoy, 99. Balanced codes constuctions based on patial unit eoy codes, Poceedings of Soviet-Sweden Syposiu on Infoation Theoy, Moscow. 77