CHEN et al.: MAC: MISSING TAG ICEBERG QUERIES FOR MULTI-CATEGORY RFID SYSTEMS 9949
TABLE I
S
YMBOLS USED IN THIS PAPER
that the reader executes a frame with f slots and each tag will
respond only in its replying slot.
Each slot can be classified into one of the three types: empty
slot which is not selected as the replying slot by any tag, single-
ton slot which is selected as the replying slot by only one tag
and collision slot which is selected as the replying slot simulta-
neously by multiple tags. The singleton and collision slots are
also called non-empty slots. Moreover, the size of each slot may
be different, which is determined by the length of message to
be transmitted between the reader and tag. In a slot, the tag may
need to transmit a 96-bit ID, a multi-bit long response or just
a one-bit short response, then the slot size is denoted as t
tag
,
t
l
and t
s
according to the EPCglobal C1G2 standard, respec-
tively. Table I lists the symbols with corresponding descriptions
to be used in this paper. In this paper, we adopt t
tag
= 2.4 ms,
t
l
= 0.8 ms and t
s
= 0.4 ms based on the assumption that the
transmission rate between the reader and tags is 62.5 Kbps [5],
[6], [12], [17].
B. Problem Formulation
In this paper, we consider a multi-category large-scale RFID
system which comprises a server, a reader
1
and a large amount
of tags. The storage and computation capacity of the server is
assumed to be strong enough. The reader and the server are
considered as an integrity (represented as“reader” hereinafter)
since they can be connected via a high data rate communication
link. We assume that there are l categories, which are denoted as
1
Our proposed missing tag iceberg query schemes can also work in multi-
reader scenario to cover a larger area.
C
1
, C
2
,...,C
l
. Each tag has a unique ID (96-bit) and belongs
to one of the categories. The tag cardinality of the RFID system
is n, and each category has a tag size of n
i
(1 ≤ i ≤ l), i.e.,
n =
l
i=1
n
i
. Assume there are m
i
(1 ≤ i ≤ l) missing tags in
category C
i
and the missing tag cardinality in the whole RFID
system is m, which equals
l
i=1
m
i
. We only consider the
known tags, whose IDs are known by the reader in advance. Then
the multi-category RFID missing tag iceberg query problem can
be formulated as follows: given a predefined threshold T ,an
error threshold ∈ (0, 1] and a reliability requirement δ ∈ [0, 1),
a set of categories T will be obtained satisfying the following
two constraints:
∀C
i
∈T, m
i
≥ T,Pr[m
i
≥ (1 − )T ] ≥ δ, (1)
∀C
i
/∈T, m
i
<T,Pr[m
i
≤ (1 + )T ] ≥ δ. (2)
where m
i
is the estimated missing tag cardinality of C
i
. Con-
straint (1) means that for each category in T , its estimated miss-
ing tag cardinality should be not less than the threshold T and
the probability that its real missing tag cardinality is larger than
or equal to (1 − )T should be at least δ. While Constraint (2)
means that for each category out of T , its estimated missing tag
cardinality should be less than the threshold T and the proba-
bility that its real missing tag cardinality is less than or equal to
(1 + )T should be at least δ. Note that δ and are the system
parameters, which are known in advance.
IV. B
ASIC SCHEMES
In this section we first propose the MAC-SZE scheme, which
adopts the singleton-zero estimator (SZE) to estimate the miss-
ing tag cardinality for the missing tag iceberg query. After
that we propose the MAC-HZE scheme, which adopts the
homogeneous-zero estimator (HZE). Finally, we analyze the
accuracy of the proposed MAC-SZE and MAC-HZE schemes
to determine the parameters to satisfy the constraints.
A. MAC-SZE Scheme
The MAC-SZE scheme comprises w rounds. In round k,the
reader first broadcasts f
k
,R
k
before executing a frame for
each tag to determine its response slot. Note that the reader
will use a uniform frame size among different rounds and f
k
is
set as the tag cardinality of the RFID system, i.e., f
k
= n,to
maximize the efficiency [6]. As the reader knows each tag’s ID, it
can pre-compute the responding slot of each tag. Therefore, the
reader can predict the status of each slot, i.e., empty, singleton or
collision in the current frame, which is called as expected frame
as shown in Fig. 1. After that, the reader executes the current
frame and detects whether each slot is empty or not. The reader
compares the slot status difference between the expected frame
and the executed one, based on which it can estimate missing tag
cardinality of each category. The above procedure is conducted
for w rounds, after which the set of categories T satisfying the
constraints Eqs. (1) and (2) can be obtained.
We set X
i,j,k
s→0
= 1ifinthek
th
round slot j is expected to
be selected only by one tag in C
i
and is actually an empty slot
in the executed frame, and X
i,j,k
s→0
= 0 otherwise. As shown in