Note: Descriptions are shown in the official language in which they were submitted.
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1
INTERLEAVER AND INTERLEAVING METHOD IN A COMMUNICATION
SYSTEM
This is a divisional application of Canadian Patent Application No. 2,443,453
filed on February 6, 2003.
BACKGROUND OF THE INVENTION
Field of the Invention:
The present invention relates generally to interleaving in a communication
system, and in particular, to a method of optimizing parameters according to
an
interleaver size for partial bit reversal order (P-BRO) interleaving and an
interleaver
using the same. It should be understood that the expression "the invention"
and the like
encompasses the subject matter of both the parent and the divisional
applications.
Description of the Related Art:
While a sub-block channel interleaver designed in accordance with the IS-
2000 Release C(1xEV-DV) FM specification performs P-BRO operation for row
permutation similarly to an existing channel interleaver designed in
accordance with the
. IS-2000 Release A/B spec., the sub-block channel interleaver differs
from the channel
interleaver in that the former generates read addresses in a different manner
and requires
full consideration of the influence of a selected interleaver parameter on
Quasi-
Complementary Turbo code (QCTC) symbol selection.
Hence, there is a need for analyzing the operating principles of the sub-block
channel interleaver and the channel interleaver and creating criteria on which
to generate
optimal parameters for the channel interleavers. The optimal parameters will
offer the
best performance in channel interleavers built in accordance with both the IS-
2000
Release A/B and IS-2000 Release C.
SUMMARY OF THE INVENTION
An object of the present invention is to substantially solve at least the
above
problems and/or disadvantages and to provide at least the advantages described
below.
Accordingly, it is an object of the present invention to provide a method of
optimizing
parameters for P-BRO interleaving and an interleaver using the optimizing
parameters.
It is another object of the present invention to provide a method of
optimizing
parameters m and I according to an interleaver size for P-BRO interleaving and
an
interleaver using the same
To achieve the above and other objects, there are provided a P-BRO
interleaver and a method for optimizing parameters according to an interleaver
size for
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the P-BRO interleaver. The P-BRO interleaver sequentially, by columns,
arranges an
input data stream of size N in a matrix having 2m rows, (J-1) columns, and R
rows in Jth
column. The P-BRO interleaver interleaves the arranged data, and reads the
interleaved
data by rows. Here, N, m, J and R are given as follows:
408 7 4 24
792 8 4 24
1560 9 4 24
2328 10 3 280
3096 10 4 24
3864 11 2 1816
According to an aspect of the present invention, there is provided a method of
determining parameters m and J according to an interleaver size N for
sequentially
storing input data in a memory having a matrix having 2m rows, J-1 columns and
R rows
in a Jth column (0..<2m), and partial-bit reversal order (P-BRO) interleaving
the stored
data, the interleaver size N, and the parameters m, J, R being expressed as
N=rxJ+R,
the method comprising:
calculating a first variable a using an expression ( log2N ¨Llog2 NJ)
and a
lNJ
second variable p using an expression ( 2kg2);
comparing the first variable a with a predetermined first threshold;
comparing the interleaver size N with at least one predetermined second
threshold determined by a ratio of the second variable P;
determining the parameter J according to the comparison results; and
Llog2(¨Ni )]
determining the parameter m using an expression
According to another aspect of the present invention, there is provided an
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interleaver in a communication system, comprising:
a memory having a matrix having 2' rows, J-1 columns and R rows in a Jth
column (0..R<2'); and
an address generator adapted to partial-bit reversal order (P-BRO) interleave
addresses of the memory, calculate a first variable a using an expression
(log2N --Llog 2 N j) using an interleaver size N and a second variable 13
using an
expression ( 21-'0'2N-1), compare the first variable a with a predetermined
first threshold,
compare the interleaver size N with at least one predetermined second
threshold
determined by a ratio of the second variable 0, determine a parameter J
according to the
comparison results, calculate the parameter m using an expression [ log2(¨N)],
calculate
J
the parameter R using an expression N=2"' xJ+R, sequentially arrange by
columns an
input data stream in the matrix, P-BRO interleave the arranged data and
generate read
addresses for reading the interleaved data by rows.
BRIEF DESCRIPTION OF THE DRAWINGS
The above and other objects, features and advantages of the present invention
will
become more apparent from the following detailed description of preferred
embodiments
thereof when taken in conjunction with the accompanying drawings, in which:
Fig. 1 illustrates P-BRO interleaving when N=384, m=7 and J=3 according to an
embodiment of the present invention;
Fig. 2 illustrates distances between read addresses after P-BRO interleaving
when
N=384, m-7 and J=3 according to an embodiment of the present invention;
Fig. 3 illustrates P-BRO interleaving when N=408, m=7, J=3 and R=24 according
to an embodiment of the present invention;
Fig. 4 illustrates the minimum intra-row distance after P-BRO interleaving
when
N=408, m=7 and J=3 according to an embodiment of the present invention;
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Fig. 5 is a block diagram of an interleaver to which an embodiment of the
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present invention is applied;
Fig. 6 is a flowchart illustrating a first example of the optimal interleaver
parameters determining operation according to an embodiment of the present
invention;
and
Fig. 7 is a flowchart illustrating another example of the optimal interleaver
parameters determining operation according to an embodiment of the present
invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Several preferred embodiments of the present invention will be described in
detail with reference to the accompanying drawings. In the drawings, the same
or similar
elements are denoted by the same reference numerals, even though they are
depicted in
different drawings. In the following description, a detailed description of
known
functions or configurations incorporated herein have been omitted for
conciseness.
Hereinbelow, a description will be made of P-BRO interleaving to which
various embodiments of the present invention are applied, as well as the
principle of
determining parameters for optimal P-BRO interleaving in accordance with
embodiments of the present invention.
Fig. 5 is a block diagram of a P-BRO interleaver to which an embodiment of
the present invention is applied. Referring to Fig. 5, an address generator
511 receives an
interleaver size N, a first parameter m (i.e., Bit Shift), a second parameter
J (i.e.,
Up_Limit) and a clock signal Clock, and generates read addresses to read bit
symbols
from an interleaver memory 512. The parameters m and J are determined in an
higher-
layer controller (not shown) and provided to the address generator 511, or
determined
according to the interleaver size N in the address generator 511. The
interleaver memory
512 sequentially stores input bit symbols at write addresses corresponding to
count
values of a counter 513 in a write mode, and outputs bit symbols from read
addresses
received from the address generator 511 in a read mode. The counter 513
receives the
clock signal Clock, generates a count value, and provides it as a write
address Write
ADDR to the interleaver memory 512.
As described above, the P-BRO interleaver writes input data sequentially in
the interleaver memory 512 in the write mode and reads data from the
interleaver
memory 512 according to read addresses generated from the address generator
511. For
=
-
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details of the P-BRO interleaver, reference is made to Korea Patent
Application /4o.
1998-54131, filed on December 10, 1998, the entire contents of which are
expressly
incorporated herein. =
In operation, the' address generator 511 generates a read address Ai for
symbol permutation by
Ai = 2"1 ( i mod J) + BRO õ,(Li / J
...............................................................................
. (1)
where 1, . N-1 and N=2"`x.J.
In Eq. (1), N denotes the size of an interleaver input sequence and m and J
are interleaver parameters called Up Limit and Bit Shift, respectively.
Fig. 1 illustrates P-BRO interleaving when N=384, m=7 and J=3. Referring
to Fig. 1, an interleaving matrix has r rows starting from index 0 and .1
columns starting
from index 0. After step 101, the row index and column index of a symbol in
the
.resulting matrix are expressed as Lin] and (i mod J), respectively.
Therefore, after 2'(i
mod J)+ Li/J, an ith symbol in an input sequence has a number corresponding to
an
Lia_lth row and an (I mod J) column as its read address. J symbols are in each
row and
the distance between symbols is T" in the row.
The row index Lill] is BRO-operated in step 102. If the distance between
symbols in adjacent rows of the same column is row distance dmõ the BRO
operation of
the row indexes results in a row permutation such that two minimum row
distances drõõ
are 2'2 and 2", as illustrated in Fig. 2. Thus, after r(i mod J)+ BRO,Ii/JJ,
the ith _ =
= symbol in the input sequence has a number corresponding to a BROli/Jith
row and an
(i mod J)th column as its read address in the third matrix from the left.
In summary, a read address sequence is generated by row permutations of a 2mxJ
matrix
in the P-BRO interleaver. The row-permuted matrix is read first by rows from
the top to
the bottom, then subsequently reading each row from the left to the right.
For clarity of description, the distance between adjacent addresses in the
same row is defined as "intra-row distance dint:. IfJ#1, di0.3.2"1. If J=1,
there is no
intra-row distance.
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The distance between adjacent addresses in different rows, that is, the
distance between the last address in a row and the first address in the next
row is defined
as "inter-row distance dnõ..". dinõ is one of a plurality of values calculated
from a
function of the parameters m and J. When m and J are determined, the resulting
minimum inter-row distance din, is defined as dinm,b1õ.
Since two minimum rows distances dr. are 2"' and
If J = I , d in:, = d = 2'2
row ,
Else, d:itir = (J ¨ I)= ¨23"-' =,(2-J-3)=2"-'
....................................................................... (2)
The reason for computing d ............ by Eq. (2) when .I#1 is apparent in
Fig. 2 If
J=1, which implies that the interleaving matrix has only one column, Cin, is
dr7õ,." , that
is,
As described above, the interleaver parameters m and J are used as the
numbers of rows and columns in a read address sequence matrix and parameters
for a
function that determines distances between read addresses. Consequently, the
characteristics of the P-BRO channel interleaver depend on the interleaver
parameters m
and J.
Before presenting a description of a method of determining sub-block
channel interleaver parameters that ensure the best interleaving performance
according
to an embodiment of the present invention, the purposes of channel
interleavers in the
IS-2000 specifications, Releases A/B and C will first be described. Following
that, the
interleaver parameter determination will then be described separately in two
cases:
N=rxJ; and N=rxJ+R.
The purpose of chamiel interleaving in the 1S-2000 specification, Release
A/B, is to improve decoding performance, which is degraded when fading
adversely
influences successive code symbols, through error scattering resulting from
symbol
permutation. To improve decoding performance, interleaving must be performed
such
=that the distance between adjacent addresses (inter-address distance) is
maximized.
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Meanwhile, the purpose of sub-block channel interleaving as described in the
IS-2000 specification, Release C, is to allow a QCTC symbol selector at the
rear end of
an interleaver to select appropriate code symbols according to a coding rate
and thus
ensure the best performance at the coding rate, as well as to scatter errors
through
symbol permutation. To achieve this purpose, interleaving must be performed
such that
inter-address distances are maximized and are uniform.
Accordingly, to satisfy the requirements of the channel interleaver of the IS-
2000 specification, Release A/B, and the sub-block channel interleaver of the
IS-2000
specification, Release C, an interleaver must be designed so that a read
address sequence
is uniformly permuted by interleaving. This is possible by determining the
interleaver
parameters m and j that maximize a minimum inter-address distance and minimize
the
difference between inter-address distances.
= As
stated before, the inter-address distances are categorized into the intra-row
distance d and the inter-row distance di The intra-row distance is a function
of m
and the inter-row distance is a function of m and J. Since there are a
plurality of inter-
row distances, a minimum inter-row distance <in, is calculated. A minimum
inter-
address distance is always 212 when J is 1, and the smaller of the minimum
inter-row
distance d and the minimum intra-row distance dbim," when J is not 1. The
difference between inter-address distances is 24 when J is 1, since the intra-
row
distance dinõ., is 0, and is equal to the difference between the intra-row
distance dinfra and
the minimum inter-row distance dbini,"õ when J is not 1.
This can be expressed as follows:
If J=1, 10-2'21= 2' 2 ,
Else, Id¨clitl=12m ¨(2- J ¨3 )= 2'11=12 J 2'
=
= (3)
Since N=2"xJ, 2' is replaced by Nil in Eq. (3), it follows that
N
IfJ=1, 2'2 =-1 =¨= 0.25¨
4 J J
Else,
2 J J
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..............................................................................
(4)
When 3=3 in Eq. (4), the difference between inter-address distances is
minimized. Thus
Id,õõa ¨cl:rie.nri =0.166667N.
Table 1 below illustrates changes in inter-read address distances as m
increases when N=384. When J=3, a maximum difference between inter-address
distances is minimized, 64 and a minimum inter-address distance dmin is
maximized, 128.
Table
Td
ditnra "
her d Ira d I rain dmi"
4 24 16 360 344
16
384 5 12 32 336 304
32
6 - 6 64 288 224
64
7 3 128 192 64
128
The method of determining optimal interleaver parameters when N=rxJ has
been described above. Now, a method of determining optimal interleaver
parameters
when INI=2"xJ+R will be described. Here, R is the remainder of dividing N by
2. Thus
R is a positive integer less than 2".
Fig. 3 illustrates P-BRO interleaving when N=408, m=7, 3=3 and 12.#0.
Referring to Fig. 3, similarly to the case where R=0, numbers in a row-
permuted matrix
after step 302 are read as read addresses by rows from the top to the bottom,
reading
each row from the left to the right, as described in step 303. Since R#0, the
number of
columns is 3+1, and numbers are filled in only R rows of a (J+1)th column with
no
numbers in the other (r¨R) rows.
In summary, when a read address sequence is generated by a
row
permutation of a rxJ matrix, each row including J or J+1 elements in the P-BRO
interleaver. The row-permuted matrix is read by rows from the top to the
bottom,
reading each row from the left to the right.
Furthermore, when R#0, the interleaver parameters in and J are determined
such that a minimum inter-read address distance is maximized and the
difference
between inter-read address distances is minimized.
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An inter-row distance cli is a function of m, 2 irrespective of whether R=0 or
R#0.
However, while the minimum inter-row distance diat, is a function of m and J
when
R=0, it is a function of m, J and R when R*0.
The minimum inter-row distance is determined according to J by Eq. (5) and
Eq. (6).
When J =1,
For 0 <3-2'2, dr" =2'2
For3-2n1-2.SR<2", dinmInter = 2"1-1
...............................................................................
(5)
When .1 *1,
For 0 <H <2"e4 , d = -1)-2m - = (2J -3)-
. .
For 2"" R <3.2'2, dit ===--, (.1 -1)= - (-2'2) = (4J - 3). 2'2
For 3-2'2 R <2'", d, = J 2' = (2J -1) = 21"-1
. .. (6)
Fig. 4 illustrates how Eq. (6) is derived when m=7 and J=3. Referring to Fig.
4, when 0..12.<2'1, the inter-row distance between two adjacent rows having a
row
distance dmõ of 2, the last column of the upper row being empty, is a minimum
inter-
row distance (d, (2J (2J -3)= ). When 2""_SR<3=2", the inter-row
distance
between two adjacent rows having a row distance d,, of 2'2, the last column of
the
upper row being empty, is a minimum inter-row distance (diZer." = (4J -3)=
2'2).
When 3.2'25.R<T", the inter-row distance between two adjacent rows having
a row distance kw of 22 and elements in the last columns, is a minimum inter-
row
distance ( dre, = (2J -1)=
). For example, if R=0, the minimum inter-row distance is
192, as indicated by reference numeral 401. If R=64 (2n"), the minimum inter-
row
distance is 288, as indicated by reference numeral 402. If R=96 (3-2'2), the
minimum
inter-row distance is 320, as indicated by reference numeral 403. In the same
manner, Eq. =
(5) can be derived when J=1.
.Table 2 below illustrates changes in the interleaver parameters J and R, the
intra-row
distance dint., the minimum inter-row distance ti"" , and the minimum inter-
read
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address distance d. as m increases, with respect to six encoder packet (EP)
sizes as
described in the IS-2000 specification, Release C.
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=
= =
Table 2
m J R did ¨ d! ernin n(dm)
3 51 0 8 , 396 , 388 , 8 400
4 25 '8 16 388 372 16 392
408 5 , 12 24 , 32 368 336 , 32 376
6 6 24 64 288. 224 64 344
24 128 192 6.4 na 280
8 1 152 256 64 192 64 40 ,
4 49 8 16 772 756 16 776
24 24 32 752 720 32 760
792 6 12 24 64 672 608 64 , 728
7 6 24 128 576 448 128 664
3 24 _ 256 324 122 256 536 ,
9 1 280 512 128 384 128 104
5 48 24 32 1520 1488 32 1528
6 24 24 64 1440 1376 64 1496
1560 7 12 24 128 1344 1216 128 1432
8 6 24 256 1152 896 256 1304
2 3 24 512 768 256 5.12 1048
1 536 1024 256 768 256 232
6 36 24 64 2208 2144 64 2264
7 18 24 128 2112 1984 128 2200
2328 8 9 24 256 1920 1664 256 2072
12 2 218 1024 512 512 512 232
11 1 280 2048 512 1536 512 512
6 48 24 64 2976 2912 64 3032
7 24 24 128 , 2880 , 2752 128 2968
3096 8 12 24 256 2688 2432 256 2840
9 6 24 512 2304 1792 512 2584
12 3 24 1024 1536 512 1024 2072
6 60 24 64 3744 3680 64 3800
7 30 24 128 3648 3520 128 3736
3864
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8 15 24 256 3456 3200 256 3608
9 7 280 512 3200 2688 512 3352
3 792 1024 2560 1536 1024 2840
1 1816 2048 1024 1024 1024 1024
As described above, similarly to the case where R=0, optimal interleaver
parameters are selected which maximize a minimum inter-address distance and
minimize the difference between inter-address distances.
5
In Table 2, the minimum inter-read address distance dim in the eighth column
is the smaller of the intra-row distance di and the minimum inter-row distance
dr.:.
Hence, parameters that maximize the minimum inter-read address distance drmn
can be
obtained by selecting a row having the maximum value in the eighth column. For
EP
10 sizes of 2328 and 3864, three rows and two rows satisfy this
condition. In this case, rows
that satisfy another condition of minimizing the difference between inter-read
address
c/4 must be selected. They are shown in bold and underlined in Table 2. The
validity of this condition is apparent by comparing the rows having the
maximum Om in
terms of n(crm) in the last column. Here, n(crin) indicates the number of
address pairs
having a minimum inter-address distance en'.
Rows marked in bold and underlined in Table 2 satisfy the above two
conditions for selecting optimal interleaver parameters. As noted, once the
second
condition is satisfied, the first condition is naturally satisfied. For
reference, it is made
clear that the intra-row distances dimTa and the minimum inter-row distances d
listed
in Table 2 are equal to those computed on P-BRO-interleaved read addresses.
Table 2
covers both cases of dividing N by 2' or J with no remainder and of dividing N
by 2' or
J with a remainder R (i.e., N=2NI+R (0.5.12.<2n)). Here, interleaver
parameters shown in
bold and underlined are optimal for each EP size.
When N=2N(J-1)+R (05R<2'), that is, N is divided by 2mor I either with no
remainder or with a remainder R, optimal interleaver parameters for each
interleaver size
N are listed in Table 3. The description made in the context of I is also
applied when J is
replaced by (J--1).
=
Table 3
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408 7 4 24
792 8 4 24
1560 9 4 24
2328 10 3 280
3096 10 4 24
3864 11 2 1816
The above description has provided a method of selecting interleaver
parameters expected to offer the best performance when, for example, a channel
interleaver built in accordance with the IS-2000 Release A/B specification,
and a sub-
block channel interleaver built in accordance with the IS-2000 Release C
specification
are used.
As described above, the optimal interleaver parameters are those that
maximize an inter-address distance and at the same time, minimize the
difference
between inter-address distances when generating read addresses in a channel
interleaver.
Consequently, interleaver parameters for sub-block channel interleaving in
circumstances wherein a sub-block channel interleaver is built in accordance
with the IS-
2000 Release C specification are values in the rows in bold and underlined in
Table 2.
While interleaver parameters selection has been described for the sub-block
channel
interleaver built in accordance with the IS-2000 Release C specification, it
is obvious
that the same thing can also be applied to systems of other standards.
Fig. 6 is a flowchart illustrating an optimal interleaver parameters
determining operation according to an embodiment of the present invention.
Particularly,
.this operation is concerned with the computation of Id ¨ d1 . An optimal (m,
J)
that minimizes id ¨dr',1 is selected by computing Id inõõ drõ:1 ,changing (m,
J).
Referring to Fig. 6, when an interleaver size N, and parameters m and J are
given in step 601, a parameter R is calculated by subtracting 2'4 from N in
step 603. In
step 605, it is determined whether J is 1. This is a determination, therefore,
of whether
an interleaving matrix has a single column or not. If 5 is 1, the procedure
goes to step
607 ("Yes" path from decision step 605) and if J is not 1, the procedure goes
to step 621
("No" path from decision step 605) . In step 607, it is determined whether R
is 0(i.e., =
whether N is an integer multiple of 2"). On the contrary, if R is 0 (("Yes"
path from
decision step 607) , an intra-row distance dintr., is set to 0 in step 609. If
R is not 0 ("No"
path from decision step 607) , dimra is set to 2`" in step 617.
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After clintra is determined, it is determined whether R is less than 3x2"" in
step
611. If R is less than 3x2"' ("Yes" path from decision step 611) a minimum
inter-row
distance ci:::: is set to 2' in step 613. If R is equal to or greater than
3x2'2 ("No" path
from decision step 611) d imnil: is set to 2t"-' in step 619. After <it is
determined,
= fri,õõa ¨d[1 is calculated in step 615.
Meanwhile, if./ is not 1 in step 605, di is set to 2' in step 621 and it is
determined whether R is less than 2"' in step 623. If R is less than 2'"--'
("Yes" path
from decision step 623) d int is set to (2.1--3)x2' in step 625 and then the
procedure
goes to step 615. If R is equal to or greater than 2" ("No" path from decision
step 623),
it is determined whether R is less than 3x2"" in step 627. If R is less than
3x2" ("Yes"
path from decision step 627) , 01,t is set to (4J-3)x2" in step 629. If R is
equal to or
greater than 3x2' ("No" path from decision step 627) , d:,'", is set to (2.I--
1)x2'1 in
step 631 and then the procedure goes to step 615.
Optimal interleaver parameters m and J are achieved for a given N by computing
!dew. ¨ d , .1 , changing (m, 3). If3 is one of 1, 2 and 3, a logical formula
that facilitates
selection of J without the repeated computation can be derived.
With a description of a logical equation deriving procedure omitted, the
logical equation is
If log 2N ¨Llog, N j< log 2 3 ¨ I =0.5849625,
For(-3 .21-42N-1 ..c. N < I - 2i42N -I, j = 3,
4
For I . 211 :=NJ 5.N <(-3)-21-1
1 82N, J = 2,
2
For(¨3 -21-h:2Ni < N <2 = 21-1 gINJ, J = I.
2
Else if log 2N ¨1_10g 2 N j?.. log 2 3 ¨ 1 = 0.5849625,
For 1 = 21-41g'N J < N <(-13-)= 21-kg2N J , J =2,
2
For(-3)= 21-43 N J < N <(-7- 2160g2NJ , J =3,
2 4
For(-7)-21-43NJ < N < 2 = 211 47N-1, J = I.
4
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...............................................................................
(7)
From an optimal J from Eq. (7), an optimal m is calculated by
-
= Llog2(-1
...............................................................................
(8)
The selection of optimal interleaver parameters by the simple logical
equations is
summarized below and illustrated in Fig. 7.
1. An optimal J is obtained by Eq. (7) for a given N; and
2. m is calculated by computing Eq. (8) using N and J.
Fig. 7 is a flowchart illustrating an optimal interleaver parameters
determining operation according to another embodiment of the present
invention.
Referring to Fig. 7, when N is given, a variable a is calculated by
log 2N ¨Llog 2 NJ and a variable fl is calculated by 21mg2N-1 in step 701.
Decision step
703, determines whether a is less than a first threshold, 0.5849625. If a is
less than the
first threshold ("Yes" path from decision step 703), another decision is made,
whether N
is less than 13 in decision step 705. If N is equal to or greater than 13
("No" path from
-decision step 705) , the procedure goes to step 707. On the contrary, if N is
less than 0
("Yes" path from decision step 705) , J is determined to be 3mn step 713.
Meanwhile, decision step 707 determines whether N is less than (3/2)43. If
N is less than (3/2)43 ("Yes" path from decision step 707) ,J is determined to
be 2 in
step 711. Otherwise, J is determined to be 1 in step 709 ("No" path from
decision step
707) .
If a is equal to or greater than the first threshold in step 703 ("No" path
from
decision step 703) , a decision is made whether N is less than (3/2)xf3 in
decision step
.
.
= 717. If N is less than (3/2)x13 ("Yes" path from decision step 717) , J
is determined to be
2 in step 721. Otherwise, decision step 719 determines whether N is less than
(7/4)43.
If N is less than (7/4)43 ("Yes" path from decision step 719) , J is
determined to be 3 in
step 723. Otherwise, J is determined to be 1 in step 725 ("No" path from
decision step
719) .
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As described above, optimal m and J can be calculated simply by the logical
equations using N. The optimal m and J are equal to m and J resulting from
repeated
computation using different (m, J) values as illustrated in Table 2. This
obviates the need
for storing optimal m and J values according to N values.
When N=2328, for example, optimal m and J values are calculated in the
procedure illustrated in Fig. 7 or by Eq. (8) to Eq. (10), as follows.
a = log2N .1=
log22328 ¨Llog2 2328j= 11.1848753 ¨ 11 =0.1848753.
= 2110g2 N = 21log2 23281 ==
z 2048.
a 0.5849625 and = 2048 = 2328 < (12) = 13 = 3072. Thus J = 2.
m =1L10g2.111 Liog2(l 2328
) =Llog21164 j= 10, R = A r - 21" = J = 2328 ¨ 21 = 2 = 280.
2
For reference, Eq. (7) is derived as follows.
In each case depicted in Fig. 6, Eq. (5) and Eq. (6), Id ¨ d.1 is determined
by
A. When J=1,
A-1. If R=0, Id ¨ ditHO - 2'21= 2'2
A-2. If O<R<3=2"2, n,ra- 2m-21= 3. 2m-2
A-3. If 3.22_5..R<2m, dr,ZI =12m - r-'1= 2""
B. When J*1,
B-1. If 0...c.R<TTh-1, Id,õõ,, d:::,H2m -(2J -3). 2'11=12J - 51- 2""1
B-2. If 2"1...R<3.22, Idõ,õa !=12m -
(4J .3). 2m1 =14J 7I.22
B-3. If 3 2m--2..R.<2m, I =12m -(2J - 1) = 2m41=12J - 31. 2'1
. ....- .
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Since N=211'.1.4-R and 0.1Z<-2m, J=2'1<(J+1)-2m. When this is divided by .1
and then
subject to a log base 2 operation,
N.
m ..<_log2(¨)<log2r)= 21= m+ log 2(1 + J-1)< m+ 1
J J
4
Thus, m = log2( -1--' -.1 . Using m = log2 ¨N , .1 can be expressed as a
function of N for
J
J
all the cases of A and B.
A'. When J=1, since m =Llog 2 NJ, R = N ¨ 2'n = N ¨ 21'n2 N -I . Then the
cases A-1, A-2 and A-3 can be expressed as functions of N. It therefore
follows that:
A'-1: If N = 21/0 N -1 , Id ¨ d:::,.1= 2"" =(.--41-). 2I-kg 2 NJ
If 2110z: NJ N <(1- 21) 12 NJ 4 Id.intro . ¨d1=(1- 211 g3N-1 1 mter
4
A'-3: If (-7) = 21-1`12NJ ... N < 2 = 21-h'gz N i Idintra . ¨ en I=N= 21-kg2N-
1
4 1 niter 2
1) I
B'. When J#1, since m = [log2 (¨)j, R= N ¨J = .2'n = N ¨J - 2ILlo -g,( i ".
j
Then the cases B-1, B-2 and B-3 can be expressed as functions of N instead of
R.
Therefore,
1/4 I
B'-1: If J = 2L " 1 " < N <(J +1. 21.-11
- ,
2
51 11 41J
'dint, ¨dit1=1J ¨..-i-1- 2 '
2082 ¨ N ( 3) 1-kg7
B'-2: If I./ +-1)- 21-1 (N)i J+¨= - 2(1)1
4 ,
. 11c. 14)1
Id int;a ¨ ditirl+ --7-1. 21-g:(- I Li .
4
N
? l, ¨ , l, Eli
B'-3: If (J+1=21 og -("L_ N<Q+1)-21-og4"
,
,
4
Id imrd ¨ d:::-1=1.1 --421 2L7)1
µ
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=
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B". When J=2, since Llog2(1=Llog2 N - 1 j=Llog N j- I ,
2
(5 õ
B"-1: If 21-kg2Ni N < ' 2 Lkg 2 N j -
dist I= 1 = 211'3:2N-1
rttra Inter
4
55 N 11
B"-2: If (-)= 21- ''gz N <(¨). 21 82N j Id
4 8 tra ter 8
11
B"-3: If (-8)= 21 i"2,v.' 5_ N <(-3)- 211'2N , infra - d:::rI -41 = 21-1"2"
2
B"'. When J=3,
llog2N j- 2, if log2N -Llog 2Nj< log, 3 - I ,
since ilog2()j={
3 [log-2N j- I,
otherwise
if log2N -11og 2 N j< log2 3
- 1 =0.5849625 ,
3 N 7 I I
B"'-l': If (-4)- 21"= N <(-)= 2t1"2N , - d ,7,4"1= = 211"'N
8 tr ter 8
N 5
13'"-2': If (-7 ). t g 2 j :5- N
<(1-16)= 211"2N I , id imra - dm I= ¨5 211"2"
8 16
B"'-3': If ()= 21-4N2 N < 211"2Ni , - d:1" I= -3 -Pg2Ni
7--6
fret ter 8
15 if log2N -Llog N j?_ log2 3 - 1=0.5849625 ,
7 ow
B"-l": If (-3)=21-kg2N3 5_ N <b-)- 21"2 , hara - d ;ad,' I= 21-
1"2x
2 4
B"-2": If( = .21142Ni N <(L-5)= 211"21'i -
df'an I= = 211"21vJ
4 8 , infra inter
8
B"-3": If (-1-1- 21' :2 NJ 5_ N < 2 = 21-1"2N , - I= -3 21' NJ
8 tra ter 4
IfJ is 4 or more, this case is neglected because Idinfro inter
d
I cannot be less
that Idiaõ,, -dinterj
in any of the cases where J=1, 2, and 3.
Eq. (7) is obtained by selecting a case having a minimum Idi,,õõ umnierl
among the cases of A'-1, A'-2, A'-3, B"-1, B"-2, B"-3, B'"-1', W"-2', and 13'"-
3'.
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Similarly, Eq. (8) is obtained by selecting a case having a minimum '1 "ter
among
the cases of A'-1, A'-2, A'-3, B"-1, B"-2, B"-3, B"-1", W"-2", and W"-3".
In accordance with the embodiments of the present invention as described
above, interleaver parameters m and J are simply optimized according to an
interleaver
size N, for P-BRO interleaving.
While the invention has been shown and described with reference to
certain preferred embodiments thereof, it will be understood by those skilled
in the art
that various changes in form and details may be made therein.
