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458 IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 9, NO. 3, JULY 2012

Theory and Performance Evaluation ofGroup Coding of RFID Tags

Yuki Sato, Jin Mitsugi, Osamu Nakamura, and Jun Murai

AbstractRadiofrequency identification (RFID) is an automaticidentification technology which identifies physical objects individ-ually according to their unique identifiers (ID) recorded in eachRFID tag. Many business processes require the integrity verifica-tion of a group of objects in addition to individual object identifica-tion. This paper proposes group coding of RFID tags with whichwe can verify the integrity of groups of objects by writing paritycheck data to the memory of RFID tags. It was revealed by sim-ulations and experiments that we could determine the number ofmissing RFID tags up to 10 with accuracy over 99% when we write96 bits of the checksum data to 20 RFID tags. The whole durationof group decoding measured in the experiment was approximately2 to 3 s. The time to compute group encoding and decoding was

in the order of several milliseconds and thus negligible. The RFIDinventory accounts for the majority of the duration.

Note to PractitionersCurrent RFID features fast identificationof many physical objects. However, the integrity check of a groupof objects is usually done by looking up a packaging list or a ship-ment list in EDI, which requires a network connection. Our pro-posed group coding of RFID tags can perform the group in-tegrity check without a network connection. In addition, when theintegrity of the group is infringed, the group coding can determinethe number of RFID tags missing from the group. These featuresof group coding can reduce the cost of looking up shipment listsand locate missing RFID tags. The accuracy of the determinationis controlled by adjusting the size of data written in each RFIDtag. Adopters of group coding can select the optimal performance

of group coding from the requirements of the accuracy and con-straints like memory consumption of RFID tags.

Index TermsGroup coding, group of things, integrity, radiofrequency identification (RFID).

I. INTRODUCTION

RFID, radio frequency identification, is an automatic iden-tification technology which is composed of RFID tags, in-

terrogators, and associated information systems. RFID enablesus to identify not only line-of-sight objects but also non-line-of-sight objects automatically and swiftly. We also can write datato RFID tags memory. These features make RFID different

from other existing automatic identification techniques such asbarcode.

Manuscript received August 30, 2011; accepted January 30, 2012. Date ofpublicationApril17, 2012;date of current versionJune 28, 2012.Thispaperwasrecommended for publication by Associate Editor C. Floerkemeier and EditorS. Sarma upon evaluation of the reviewers comments. This research is a collab-oration with the Network Innovation Laboratory, Nippon Telegraph, and Tele-phone Corporation. This work was supported by GS1 EPCglobal and NIFTYCorporation.

The authors are with Auto-ID Laboratory, Keio University, Endo 5322, Fu-jisawa, Japan, 2520816 (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TASE.2012.2193125

Fig. 1. Usage scenario of group verification system.

RFID identifies a physical object using its unique ID recordedin the RFID tag. On the other hand, in many business processessuch as incoming shipment inspection, not only identity of indi-vidual objects but also the integrity of a group of objects needsto be verified. Fig. 1 shows an example usage scenario for groupverification in an RFID portal. A group of RFID tagged objectson a pallet passes through the portal. If the integrity of the groupis verified, we can just let the pallet go. When the integrity is notverified, we stop the pallet and redo the scan to confirm that ob-jects have gone missing during transportation and handling. Wemay search for missing objects after consulting the shipment

list. Automatic verification of the integrity and the determina-tion of number of missing objects can reduce the time and costof such process. The determinated number of missing objectsprovides the useful information to locate missing objects.

In existing RFID systems, such group verification is done bylooking up the list of grouped objects, such as the AdvancedShipment Notification (ASN), after individual identification.This type of verification usually requires a network connectionto retrieve the list of grouped objects. However, verification ofthe integrity of a group is required not only in a network-reach-able environment but also in an offline environment. Thismotivated us to establish a method to verify the integrity of agroup of objects without a network connection.

Group verification of RFID tagged objects has been studiedfrom the perspective of security. Juels [1] introduced a yokingproof by chaining the message authentication code (MAC) withan external verifier. Other researches ([2][6]) essentially im-prove the yoking proof or generalize the yoking proof to a groupof multiple RFID tags. Inoue [7] introduced a systematic schemewhich detects failure to read of RFID tags based on a statis-tical analysis of reading results from multiple readers. Potdar[8] proposed an integrity-check method which uses total weightof grouped objects and reading result of RFID tags. All of these

approaches require an external verifier or database.This paper proposes a group verification method which does

not require access to such external verifier or database, allowing

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SATO et al.: THEORY AND PERFORMANCE EVALUATION OF GROUP CODING OF RFID TAGS 459

us to eliminate the requirement for a network connection. Wesee a similarity between this group verification problem andforward error correction in packet-level coding ([9][12]). Bytreating an RFID tag as a packet, missing RFID tags are treatedas packet loss in an erasure communication channel. Therefore,we named our proposal group coding of RFID tags [13].

This paper proposes group coding of RFID tags and eval-

uates its performance both by numerical simulations and ex-periment. This paper is an improved version of [13] where weproposed the fundamental theory and the functional verifica-tion. We enhance the performance evaluation with additionalnumerical simulation and improved experiment in this paper. InSection II, the theory of group coding is explained for complete-ness. In Section III, the evaluation of group coding is introduced.Section IV concludes this paper.

II. THEORY OF GROUP CODING

A. Fundamental Group Coding

Fundamental group coding is composed of group creationand group verification. The procedure of group creation is asfollows.

1) The interrogator collects the unique IDs of all RFID tagsbelonging to the group which the operator want to create.

2) Group coding software calculates the hash of each uniqueID with a hash function. The hash function is used in orderto avoid the situation that sequential IDs are used in thegroup encoding procedure.

3) A group ID is calculated as the bit-by-bit XOR of allhashes.

4) The calculated group ID is written to each RFID tags usermemory, so each RFID tag records both its own unique IDand group ID.

By writing multiple group IDs to user memory, a single RFIDtag can belong to multiple groups.

The procedure of group verification is as follows.1) The interrogator collects the unique IDs of all detected

RFID tags and the group IDs written in the user memoryof these RFID tags.

2) The collected unique IDs are sorted by group ID.3) Group coding software calculates the hash of each unique

ID which belongs to a group. The hash function must be

the same to the one used in the group creation procedure.4) The bit-by-bit XOR of all hashes in the group is calculated.

The result is referred to as the calculated group ID.5) Group coding software compares the calculated group ID

and the written group ID. If there is no RFID tag missingfrom the group, the two group IDs will be the same. On theother hand, if these group IDs are different, there are someRFID tags missing from the group.

These two algorithms are shown in Figs. 2 and 3, respectively.Fundamental group coding may incur a false positive

which means that the integrity of the group is verified in spiteof missing RFID tags. A false positive occurs when the XOR ofthe hashes of missing RFID tags unique IDs is coincidentally

equal to zero. We computed the probability of a false positiveanalytically and verified it via numerical simulation.

Fig. 2. Algorithm of fundamental group coding: group creation.

Fig. 3. Algorithm of fundamental group coding: group verification.

Naturally, when only one RFID tag is missing, the calculatedgroup ID will give a false positive only when the hash of themissing RFID tag

(1)

Suppose the hash function generate uniformly distributedhashes, this probability is given by the following equationfor bits of an hash:

(2)

When two RFID tags and are missing, a false positive occurswhen

(3)

that is, when

(4)

The probability of this condition is

(5)

Likewise, the probability of false-positiveness against missingRFID tags, , is generally given by the following equation:

(6)

For example, with the hash function which generates 16 bitsof a hash, the probability of false positive becomes

. This probability becomes negligible with a suf-ficiently large , the bit-length of hashes.

This probability of a false positive is verified with a numericalsimulation. In this simulation, a unique ID of each RFID tagwhich belongs to a group is 96 bits and generated randomly.

The simulator removes a designated number of RFID tags andcomputes the XOR of all hashes of removed RFID tags unique

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Fig. 4. Probability of false-positiveness of fundamental group coding.

IDs. If the result of the computation is zero, we record this as afalse positive. We executed this simulation process 1000 times

for different numbers of missing RFID tags (the number varyingfrom 1 to 40). Because CRC-5, which generates 5 bits of hash,

is used as the hash function for this simulation, the probabilityof a false positive is theoretically . Therefore, it isexpected that a false positive occurs about 31 times out of 1000trials on average. The result of this simulation is shown in Fig. 4,and this result agrees well.

This robustness against false positives is a feature of thegroup coding of RFID tags compared with packet-level codingin erasure communication channels ([9][12]). A regularpacket-level coding requires probabilistic decoding such as amessage passing decoder. Because the false positive can benegligible, we can extremely relax the complexity of group

decoding to determine the number of missing RFID tags, whichwe describe in Section III.

B. General Group Coding

By applying multiple fundamental group codings to a groupof RFID tags, we can determine the number of missing RFIDtags. This is what we referred to as general group coding. Gen-eral group coding divides a target group of RFID tags into mul-tiple overlapping subgroups, and the fundamental group codingis applied to each of the subgroups. Therefore, each RFID tagrecords all group IDs of its subgroups in its user memory. Thisprocedure is referred to as group encoding. When some RFID

tags are missing from the group, general group coding can de-termine the number of RFID tags missing from the group usingthe information obtained from the existing RFID tags. This pro-cedure is referred to as group decoding.

If we want to check the number of missing RFID tags froma group, a simple method is just writing the sequence numberand the total number of grouped RFID tags to each RFID tagsmemory. However, this simple method has a drawback. Whenwe want to add some RFID tags to existing group, we mustrewrite all RFID tags information because the total numberchanges. On the other hand, in general group coding, the ad-dition of new RFID tags to existing group can be done onlywith choosing some existing RFID tags and creating some new

subgroups containing these existing RFID tags and new RFIDtags. Comparing the method using the sequence number and the

Fig. 5. Example of division into subgroups.

total number, this independency from the total number of gen-eral group coding also has an advantage on the security, i.e., thetotal number of RFID tags cannot be obtained directly.

1) General Group Encoding: Group encoding starts by di-viding the main-group into multiple subgroups. This division to

subgroups can be expressed with a matrix equation. Thedivisionof a main-group of RFID tags into subgroups is expressedwith the following equation. is the hash of th RFID tag in

main-group, and is the group ID of th subgroup

...... (7)

In this equation, is an -column, -row matrix composedof 0 and 1, that defines the structure of subgroups. Becauseis similar to the generation matrix in coding theory, we namedthis matrix the group generation matrix.

For example, suppose that 5 RFID tags are apportioned tothree subgroups. Subgroup 1 contains RFID tags 1, 2, 3, and 4,subgroup 2 contains RFID tags 4 and 5, and subgroup 3 contains

RFID tags 1, 2, and 5, as shown in Fig. 5. The group ID of eachsubgroup is calculated as follows:

(8)

(9)

(10)

In this case, the group generation matrix becomes

(11)

The number of 1 in each column is proportional to thememory consumption of each RFID tag. The number of 1 ineach row, on the other hand, is the number of RFID tags in asubgroup. We examine the effect of the population of the groupgeneration matrix in Section III.

2) General Group Decoding: When some RFID tags aremissing from the main-group, some subgroups lose their in-

tegrity. Equation (7) can be rearranged to express these incom-plete subgroups as follows:

(12)

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In this equation, represents the array of group IDs of sub-groups which preserve their integrity, and represents that ofsubgroups which lose their integrity. Similarly, representsthe array of hashes of RFID tags read by the interrogator, and

represents that of RFID tags missing from the group. Thegroup generation matrix is separated to four partial matrices,

, , , and , in accordance with these four arrays,

, , , and .In (12), of course, , , and are known. can be

treated as a zero matrix because the false-positiveness of the fun-damental group coding can be practically ignored as explainedin the previous section. Array and partial matrix areavailable because remaining RFID tags belonging to these sub-groups records these information. Therefore, and arethe only unknowns in this equation. The product of these twounknown terms, , can be calculated as follows:

(13)

Because is an array of linear combinations of the mu-

tually independent hashes of the missing RFID tags unique IDs,the number of missing RFID tags can be determined as the rankof .

Let us take a group of RFID tags whose group generationmatrix is given by (11) as an example. When RFID tags 2 and4 are missing from this group, all subgroups lose their integrity.This situation is shown in the following equation:

(14)

is computed as follows:

(15)

In this case, the rank of this array is 2, and it is equal to thenumber of missing RFID tags.

III. EVALUATION OF GROUP CODING

A. Evaluation of the Determination Accuracy of the Number

of Missing RFID Tags

1) Theoretical Analysis of the Performance of General GroupCoding: As mentioned above, the accurate determination of

general group coding can be done only if the rank of the matrix

is equal to the number of missing RFID tags. is

an array of mutually independent hashes of missing RFID tags

unique IDs, so the rank of is equal to that of .

There are two cases where the rank of this matrix is dif-

ferent from the number of missing RFID tags.

Case 1: When does not have enough rows, these

rows can not be decomposed to each missing RFID tags

information by a linear algebra. The rank of becomes

smaller than the number of missing RFID tags and the

determination of general group coding gives a smaller

number than the number of actually missing RFID tags.For example, suppose the main-group which contains

five RFID tags and whose group generation matrix and

subgroup IDs are represented by the following equation:

(16)

When RFID tags 1, 2, and 3 are missing from this group,

this equation is changed as follows:

(17)

In this case, the rank of is two although three RFID

tags are actually missing.

Case 2: A subgroup cannot be detected if all RFID tags be-

longing to this subgroup are missing. When all subgroupswhich an RFID tag belongs to are not detected, the group

generation matrix loses the column of this missing RFID

tag. In this case, the rank of becomes smaller than the

number of missing RFID tags and the determination fails

because of the lack of the information about that missing

RFID tag. For example, suppose that a group contains 5

RFID tags and whose group generation matrix and sub-

group IDs are represented by following equation:

(18)

When RFID tags 1, 2, and 5 are missing from this group,

this equation is changed as follows:

(19)

The subgroups and cannot be detected because all

RFID tags belonging to these subgroups, RFID tags 1, 2,

and 5, are missing. In this case, the rank of is twoalthough the number of missing RFID tags is actually three.

The probability of these problems can be reduced by in-

creasing the number of subgroups. is a partial matrix of the

group generation matrix , so the probability of these problems

is affected by this matrix. By increasing the rank of the group

generation matrix, the probability of the first determination

failure can be reduced, and we can achieve this requirement

with a sparse group generation matrix, which contains many

0 s. The second determination failure can be mitigated with a

sufficient spread of the information of each RFID tag to other

RFID tags, and we can achieve this requirement with a dense

group generation matrix, which contains many 1 s. However,

the wide spreading of subgroup actually results in the lossof the rank of group generation matrix. Therefore, the group

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TABLE ICONDITIONS OF THE NUMERICAL SIMULATION: PATTERN I

generation matrix should be designed to balance these twotrade off requirements.

2) Numerical Simulation: We evaluated the performance of

general group coding with numerical simulations. The general

procedure of the simulations is as follows.

1) The unique IDs for 20 RFID tags are generated randomly.

2) The group of these RFID tags is created with the group

encoding procedure. We used a generation matrix for

an LDPC [14], Low Density Parity Check code, as the

group generation matrix. This matrix is randomly gener-

ated under different conditions for two variables, and

(Tables I and II). signifies the number of RFID tags

belonging to each subgroup. signifies the number of

subgroups which each RFID tag belongs to. Group IDs are

calculated from 16 bits of hashes generated by CRC-16.

3) Randomly selected RFID tags are removed from the

group. is a number between 1 and 19.

4) The number of missing RFID tags is determined with the

group decoding procedure.

5) This procedure is repeated 10 000 times for every com-

bination of conditions, then the error rate of determina-

tion is calculated, counting the frequency of the determined

number differing from the actual number of missing RFID

tags.

The simulation was done with two patterns of the conditions of

group generation matrix.The first pattern is shown in Table I. The number of RFID tags

belonging to each subgroup, , is fixed at 4, and the number of

subgroups which each RFID tag belongs to, , varies between

1 and 6. From the above-mentioned analysis, it is expected that

the accuracy of the determination improves with increasing .

The result of this simulation is shown in Fig. 6. This chart

shows that the accuracy of determination increases as in-

creases. This result agrees with the analysis in Section III-A1

that the performance of general group coding becomes better

with increasing the number of subgroups. Fig. 7 shows the

maximum number of missing RFID tags which can be deter-

mined within some tolerance. For example, with four subgroupsto each RFID tag, all RFID tags record 64 bits of additional

information in the user memory, the number of missing RFID

tags can be determined up to 4 within 0.5% error rate. On the

other hand, with six subgroups to each RFID tag, all RFID tags

record 96 bits of additional information, the number of missing

RFID tags can be determined up to ten within the same error

rate.

The second pattern of the conditions is shown in Table II. In

this pattern, varies between 2 and 6, and is fixed at 4.

The result of the simulation is shown in Fig. 8. The deter-

mination accuracy of general group coding improves by de-

creasing the number of RFID tags in each subgroup from 6 to

3. If we have 2 RFID tags in each subgroup, however, the per-formance degrades. Fig. 9 shows the subset of this result with

Fig. 6. Error rate of the determination of the number of missing RFID tags bygeneral group coding: Pattern I.

Fig. 7. Maximum number of missing RFID tags which can be determinedwithin tolerance of error rate: Pattern I.

TABLE IICONDITIONS OF THE NUMERICAL SIMULATION: PATTERN II

the horizontal axis of . From these charts, it is shown that

the performance of general group coding becomes the highest

at or under the conditions of this simulation.

This result also agrees with the analysis mentioned in section

Section III-A1 that a too-sparse or too-dense matrix is not suit-

able for the group generation matrix and there is an optimal

point of the matrixs density which maximize the performanceof general group coding. On the other hand, the optimal value

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Fig. 8. Error rate of the determination of the number of missing RFID tags bygeneral group coding: Pattern II.

Fig. 9. Error rate of the determination of the number of missing RFID tags bygeneral group coding: Pattern II (horizontal axis of ).

of changes according to the total number of RFID tags be-

longing to a group. Fig. 10 shows the maximum number of

missing RFID tags which can be determined within 0.5% errorrate when the total number of RFID tags is 40. The conditions

of the group generation matrix is the same as that of the simula-

tion pattern I shown in Table I. The comparison between Figs. 7

and 10 shows that the accuracy of the determination against 40

RFID tags group is lower than that against 20 RFID tags group.

This is because the group generation matrix of a large number

of RFID tags becomes relatively sparse and, thus, the effective

coding rate is decreased.

The causes of the determination error, cases 1 and 2 described

in the previous subsection, is also evaluated in these simula-

tions. Figs. 11 and 12 shows the probability of two causes of

the determination error when 10 RFID tags out of 20 are missing

from the group constructed under the two simulation conditions,Patterns I and II shown in Tables I and II, respectively. From

Fig. 10. Maximum number of missing RFID tags which can be determinedwithin 0.5% error rate: 40 RFID tags.

Fig. 11. Probability of two causes of the determination error: Pattern I.

Fig. 11, it is clear that both probability of case 1 and 2 decrease

when the total number of subgroups increases. Fig. 12 shows

that too-dense matrix and too-sparse matrix incur many deter-

mination error caused by case 1 and 2, respectively. These re-

sults also agree to the analysis in the previous subsection. In

addition, it is also shown that there is a threshold of the density

of the group generation matrix where the determination error

caused by case 2 does not occur. In Fig. 12, this threshold is

the point at or . Because a sparse matrix produces

more subgroups than a dense matrix with the same amount of

the memory consumption, it is considered from these results that

a good group generation matrix should be the sparsest matrix as

long as the determination error caused by case 2 does not occur.

B. Experimental Evaluation of the Validity of Group Coding

Using UHF-Band RFID Interrogator

We evaluated the validity of group coding theory via two ex-

periments. The first experiment is to verify the determination

accuracy of the number of missing RFID tags. The second ex-

periment examines the speed of group coding within the RFIDtag inventory process.

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Fig. 12. Probability of two causes of the determination error: Pattern II.

Fig. 13. KU-U1601 UHF-band RFID interrogator.

1) Confirmation of the Determination Performance of the

Number of Physical RFID Tags Missing From the Group: We

implemented our proposed group coding using a commercial

UHF-band RFID interrogator KU-U1601 (Fig. 13) provided by

Panasonic System Networks Company, Ltd. This interrogator

conforms to the EPCglobal UHF Class-1 Generation-2 air

protocol [15]. In our implementation, the calculation of group

coding is computed by the computer connected to the inter-

rogator, and the program for the computation of group coding

is written in Java.

The procedure of the experiment is as follows.

1) We place 20 or 40 physical RFID tags whose unique IDs(96 bits) are generated randomly in front of the antenna of

the interrogator (Fig. 14).

2) The group of these physical RFID tags is created by the

group encoding procedure. The detailed conditions of the

group encoding are the same as those of the numerical sim-

ulation shown in Table I. This process includes writing data

to physical RFID tags user memory.

3) RFID tags are physically removed from the group ran-

domly. is the maximum number of missing RFID tags

which can be determined within a specified tolerance of

error, and it is given by Figs. 7 and 10. For example, if the

tolerance of error is 0.5% and is 6, the value of is 10,

so 10 RFID tags are removed from the group. We exam-ined the case of 0.5% and 10% determination error with

Fig. 14. Environment of the experiment.

Fig. 15. Comparison between the results of simulation and experiment (0.5%error rate: 20 RFID tags).

20 RFID tags. We also examined the case of 0.5% deter-

mination error with 40 RFID tags.

4) The number of missing RFID tags is determined by the

group decoding procedure.

5) This procedure is repeated ten times for each , and the

average from the results is calculated.

When the tolerance of error is 0.5%, we expect that the result of

this experiment will agree exactly with the numerical simulation

shown in Fig. 7 because 0.5% error rate is small against ten-timetrials. On the other hand, when the tolerance of error is 10%, it

is expected that the result of the experiment is equal to or less

than the number of missing RFID tags. Figs. 15 and 16 show

the results for the error tolerance of 0.5% case and 10% case

with 20 RFID tags, respectively. Fig. 17 shows the result for the

error tolerance of 0.5% case with 40 RFID tags. When the error

tolerance is 0.5%, the result of the experiment matches that of

the numerical simulation. When the error tolerance is 10%, the

result of the experiment is a little different where the number of

subgroups which each RFID tag belongs to is 2 and 3. Both of

them affirm the expectation and prove that group coding works

on real RFID system. The result with 40 RFID tags is also agree

with the expectation and prove that group coding also worksagainst larger number of RFID tags.

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Fig. 16. Comparison between the results of simulation and experiment (10%error rate: 20 RFID tags).

Fig. 17. Comparison between the results of simulation and experiment (0.5%error rate: 40 RFID tags).

2) Time to Perform Group Coding: In this section, we intro-

duce our evaluation of the execution speed of group coding. In

our implementation, the group encoding procedure is as follows.

1) The interrogator collects the unique IDs of the RFID tags

belonging to the group which the operator wants to create.

2) The group generation matrix is generated for the group.3) Each subgroups group ID is calculated according to the

group generation matrix using the procedure of the funda-

mental group coding.

4) The subgroups group IDs are written to corresponding

RFID tags memory.

The group decoding procedure is as follows.

1) The interrogator collects the unique IDs of the RFID tags

and written subgroups group IDs.

2) The group coding system sorts the unique IDs according to

the subgroups group ID.

3) The group coding system applies the group verification

procedure to each subgroup and calculate the elements of

.4) The rank of is calculated.

TABLE IIIDETAILED TIME DURATION OF THE COMPUTATION OF GROUP ENCODING

TABLE IVDETAILED TIME DURATION OF THE COMPUTATION OF GROUP DECODING

Fig. 18. Virtualuser memoryallocated in EPC(specialformat forthe measure-ment of the duration).

We evaluated the duration of the computation portion of these

procedures and that of the whole procedures.

The duration of the computation of general group coding

was evaluated by measuring the execution time of the func-

tions which perform this computation in the program for 20

RFID tags. To be concrete, the computation of group encoding

comprises generation of group generation matrix and calcula-

tion of subgroups group ID, and that of group decoding com-

prises sorting of subgroups group ID, calculation of the matrix

and calculation of the rank of . The computerused for this measurement is a MacBook Pro with 2.53 GHz

Intel Core 2 Duo processor. When the number of RFID tags be-

longing to each subgroup is 4, and the number of subgroups for

each RFID tag is 6, the duration of both general group encoding

and decoding is less than 2 ms. Factors constituting the duration

is shown in Tables III and IV

The whole duration of group coding, including RF commu-

nication between the interrogator and RFID tags, was also eval-

uated. KU-U1601, an RFID interrogator which we used in this

implementation, needs to initially complete an inventory to read

from and write to user memory. Consequently, reading from/

writing to RFID tags memory takes a long time. Therefore, toevaluate group coding without being disturbed by interrogator

specific performance, we stored group coding related data into

EPC bank [16] by defining a special format which uses the part

of 96 bits of EPC as virtual user memory (Fig. 18). There-

fore, the information required to perform group decoding can

be collected with inventory of RFID tags. These RFID tags

are treated by the group coding system as the RFID tags which

have16 bits of unique ID and 80 bits of user memory. Using this

system, we measured the duration of the whole group decoding

procedure for 20 RFID tags which have virtual memory banks,

as shown in Fig. 18. The result of this measurement is approxi-

mately 2 to 3 seconds, and we consider this duration to be short

enough for practical use of RFID system. When the RF com-munication protocol between the interrogator and RFID tags is

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optimized, not only the group decoding but also the group en-

coding can be done within a similar duration as in this experi-

ment using general RFID tags, which do not define the spe-

cialized virtual memory bank as shown in Fig. 18. Even if the

protocol is optimized, the majority of whole duration of group

coding is the access time to RFID tags memory. The compu-

tation of the general group coding, 2 ms, is negligible. For theindustrial adoption of group coding, a fast user memory access

protocol would be required.

IV. CONCLUSION

This paper proposes group coding of RFID tags. With our

group coding, we can verify the integrity of a group of RFID

tagged objects without an external database or verifier. In this

paper, fundamental group coding and general group coding are

introduced. Fundamental group coding can verify the integrity

of the group using a group ID as a checksum of the group.

General group coding can determine the number of RFID tags

missing from the group by using multiple subgroups which areconstructed by the fundamental group coding. The determina-

tion accuracy of 10 RFID tags missing out of 20 is 99% with

writing 96 bits of checksum data to each RFID tags memory.

The performance of general group coding, the accuracy of the

determination, can be adjusted by controlling the size of the

checksum data. The performance increases in proportion to the

number of subgroups. When the high performance is not re-

quired, we can reduce the memory consumption for each RFID

tag. In addition, even if the memory consumption of RFID tags

is the same, the coding strength of general group coding can be

affected by the structure of group codes. The parameter of group

coding should be determined with considering these characteris-

tics. This group coding can be done within a few seconds with a

laptop PC and a commercial RFID interrogator. While the com-

putation of the group encoding and the group decoding can be

done within a few milliseconds, most of the time duration is con-

sumed by the inventory and reading and writing of RFID tags.

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Yuki Sato is a senior student at Keio University,Fujisawa, Japan.

He is a Researcher at Auto-ID Laboratory Japan,Keio University. His research interests are RFID,wireless communication, information theory, andcoding theory.

Jin Mitsugi received the B.S. degree from NagoyaUniversity, Nagoya, Japan, in 1985, and the M.S. andPh.D. degrees from Tokyo University, Tokyo, Japan,in 1987 and 1996, respectively.

He had been with NTT Laboratory since 1987 pur-suing research and development on satellite commu-nication system. He hasbeen with the Auto-ID Labo-ratory, Keio University, Fujisawa, since 2004. His re-search interests are Internet of Things, applied wire-less technology, satellite communications, high per-formance computing, and operations research.

Osamu Nakamura received the B.S., M.S., andPh.D. degrees from Keio University, Fujisawa,Japan, in 1983, 1985 and 1992, respectively.

He is currently a Professor at the Faculty ofEnvironment Information Studies, Keio University.During 19901993, he was an Assistant Professor atthe University of Tokyo, Computer Center. He was incharge on constricting of the campus network of theuniversity. He moved to the Faculty of EnvironmentInformation Studies, Keio University, in 1993. He

joined the WIDE project as a board member that is

the Internet research consortium since 1987. In 2003, he joined the Auto-IDLab, Japan, as Vice Director.

Jun Murai received the B.S. degree in mathematicsin 1979,the M.S. degreein computerscience in 1981,and the Ph.D. degree in computer science from KeioUniversity, Fujisawa, Japan, in 1987.

He is Dean and Professor with the Faculty of En-vironmental Information, Keio University. He servedas Executive Director of the Keio Research InstituteatSFCfrom1999to 2005. Heis the founder ofWIDEProject, and has been served as General Director ofthe Auto-ID Labs since January of 2003.

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