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Blind Estimation of Block Interleaver Parameters using
Statistical Characteristics
Jinwoo Jeong1 , Youngkyun Jeon1 and Dongweon Yoon1
1 Dept of Electronic and Computer Engineering, Hanyang University
04763 Seoul, Korea
dwyoon@hanyang.ac.kr
Abstract. In digital communications systems, interleavers are used to stir bits
of channel coded data to robust against burst error in noisy channel. However,
in non-cooperative context such as signal intelligence system(SIGINT) and
spectrum surveillance systems, interleaver may act as encryptor to 3rd party
listener who has no information about the interleaver parameters used in
transmitter. Therefore, blind estimation of interleaver parameter is necessary in
non-cooperative context to reconstruct the original data sequences. In this
paper, a blind estimation method is proposed which can blindly estimate
interleaving period of block interleaver from block coded and block interleaved
data sequence using statistical characteristics.
Keywords: interleaver, block code, gauss elimination, signal intelligence
1 Introduction
Blind detection involves estimation of many transmission parameters, such as
modulation, source code, channel code, interleaving, and scrambling types. This is a
tremendous work, so in this letter we focus only on the blind detection of interleaving.
For a non-cooperative context such as signal intelligence system(SIGINT) and
spectrum surveillance systems, interleaving acts as an encryption process to a receiver
who lacks information about the parameters of the interleaver [1], [2]. Such an
interleaved sequence can be regarded as an unknown sequence, and to decode it, the
parameters of the interleaver must be estimated using a blind detection method.
Some previous works provided a method for estimating the period of block
interleaved sequence of block coded data, using Gaussian elimination with the linear
characteristic of block channel coding in the interleaved sequence [3], [4]. However,
the methods of [3] and [4] are based on the assumption that the number of received
data approaches infinity.
In this paper, we propose a new method which can estimate the period of the block
interleaver with unknown block interleaved sequence of the limited length as an
extension of the previous works [3] and [4]. In section 2, briefly review the system
model of the previous works [3] and [4], and propose a new blind estimation method
with unknown block interleaved sequence of the limited length. In section 3, verify
through computer simulation and conclude in section 4.
Advanced Science and Technology Letters Vol.139 (FGCN 2016), pp.51-56
http://dx.doi.org/10.14257/astl.2016.139.10
ISSN: 2287-1233 ASTL Copyright © 2016 SERSC
2 Estimation of the Period of a Block Interleaver
Block channel coding methods such as Hamming, Reed-Solomon, Golay, BCH, and
LDPC generate redundant bits as linear combinations of message bits, and these
redundant bits and message bits form a code word. After block channel coding, there
is linearity between redundant bits and message bits in a code word. Interleaving
reorders all the bits of a code word. After interleaving, however, all bits of the
interleaved code words still retain their linearity and exist within an interleaving
period because the interleaving period is an integer multiple of the length of the code
word [1], [5]. In addition, the bit location order of interleaved bits is the same for
every interleaving period. These characteristics are used as clues of estimating
interleaving periods [3], [4].
Assume a block interleaver with interleaving period N . To estimate N , previous
research used the following method [3], [4]: First, make the analytical matrix
( , )eH N M , loading column by column with data blocks which are the interleaved
sequence divided by an arbitrary estimated interleaving period, where eN is an
arbitrary estimated interleaving period, and M is the number of columns. If eN is
an integer multiple of N , redundant bits and message bits are aligned in the same
row in ( , )eH N M , respectively, and the linearity between the rows of redundant bits
and message bits can be seen in ( , )eH N M , since the order of interleaved data bits is
the same for every interleaving period. After that, apply Gaussian elimination to
( , )eH N M and examine the number of ‘1’ bits. The algorithms of [3] and [4] are
efficient for a very large value of M , since they are proposed with the assumption
that M approaches infinity. In actual non-cooperative contexts, however,
intercepting an enormous amount of signal data is impracticable.
To overcome this shortcoming, we propose a new approach that can estimate the
interleaving period with block interleaved sequence of block coded data of the limited
length in noiseless and noisy channels.
First, make the analytical matrix ( ,2 )e eH N N by loading data blocks column by
column as shown in Fig. 1, where shaded areas represent redundant bits and plain
areas represent message bits. Note that the number of columns of the analytical matrix
is just double eN instead of M approaching infinity.
(a) eN is an integer multiple of N (b) eN is not an integer multiple of N
Fig. 1. Analytical Matrix ( ,2 )e eH N N for the estimation of interleaving period.
Advanced Science and Technology Letters Vol.139 (FGCN 2016)
52 Copyright © 2016 SERSC
As shown in Fig. 1 (a), if an arbitrary estimated interleaving period eN is an
integer multiple of the original interleaving period N , the redundant bits and
message bits are aligned in the same row of ( ,2 )e eH N N , respectively. On the other
hand, as shown in Fig. 1 (b), if eN is not an integer multiple of N , there are no such
aligned rows.
We then apply Gaussian elimination to the analytical matrix ( ,2 )e eH N N . Fig. 2
depicts a Gaussian eliminated analytical matrix ( ,2 )e eL N N in a noiseless channel
when (16, 11) Hamming code is assumed and the original interleaving period
48N as an example, where dots represent ‘1’ bits, and blank spaces represent ‘0’
bits.
(a) eN is an integer multiple of N (b) eN is not an integer multiple of N
Fig. 2. Scatter diagram of ‘1’ and ‘0’ bits for Gaussian eliminated analytical matrix
( ,2 )e eL N N
As shown in Fig. 2 (a), if eN is an integer multiple of the original interleaving
period 48N (i.e., eN =48), rows of redundant bits are eliminated (note the blank
band across the bottom third of the diagram).
Otherwise, as shown in Fig. 2 (b), if eN is not an integer multiple of the original
interleaving period 48N (in this case eN =47), there are no eliminated rows
because the redundant bits and message bits are not aligned in the same row in the
analytical matrix ( ,2 )e eH N N , respectively.
To verify whether or not an arbitrary estimated interleaving period eN is an
integer multiple of the original interleaving period N , we count the ‘1’ bits and ‘0’
bits, and analyze the ratio of the ‘1’ bits to ‘0’ bits in the right-hand square portion
(dashed line in Fig. 2) of ( ,2 )e eL N N . We define the ratio of ‘1’ bits to ‘0’ bits of the
the right-hand square portion as
Advanced Science and Technology Letters Vol.139 (FGCN 2016)
Copyright © 2016 SERSC 53
Number of '1' bits in the right-hand square
Number of '0' bits in the right-hand square
1( )
21
{ ( )} ( )2
( )
2{ ( )} ( )
2
e
e e e
e
N Rank H
N N Rank H N Rank H
Rank H
N Rank H Rank H
r
r
(1)
where ( )Rank H is the number of row which is not eliminated by Gaussian
elimination and r is the code rate.
By observing , we can decide whether or not eN is an integer multiple of N . If
eN is an integer multiple of N , the value of is not near to 1. And if eN is not an
integer multiple of N , the minimum value of is near to 1 in a noiseless channel,
since probabilities of ‘1’ bits and ‘0’ bits of the the right-hand square portion are
equally 1/2 as Fig. 2 (b)
For example: The code rate of a convolutional code may typically be 1/2, 2/3, 3/4,
5/6, 7/8, etc., corresponding to that one redundant bit is inserted after every single,
second, third, etc., bit. Therefore, when eN is an integer multiple of N , the values
are from 0.33 to 0.78. The code rate of the Reed Solomon block code denoted
RS(204,188) is 188/204, corresponding to that 204 - 188 = 16 redundant bytes are
added to each block of 188 bytes of useful information. So, the value of is 0.856.
3 Simulation Results
In this section, we validate the proposed blind deinterleaving process by showing
simulation results in a noisy channel. We assume a binary symmetric channel and run
1,000 Monte Carlo simulations for each BER. And channel codes from MIL-STD
110B are used, therefore, we set 0.6th as the threshold for detection.
Channel codes for fixed-frequency operation of MIL-STD 110B are shown in Table
1.
Advanced Science and Technology Letters Vol.139 (FGCN 2016)
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Table 1. Channel codes, fixed frequency operation
Data rate (bps) Effective code rate Method for achieving the code rate
4800 (no coding) (no coding)
2400 1/2 Rate 1/2
1200 1/2 Rate 1/2 code
600 1/2 Rate1/2 code
300 1/4 Rate l/2 code repeated 2 times
150 1/8 Rate 1/2 code repeated 4 times
75 1/2 Rate 1/2
Fig. 3 shows detection probabilities of interleaver parameters in a noisy channel,
where the dotted vertical line represents the border of practical BER range (BER of
10-3). Note that the BER of 10-3 is reasonable, because it denotes the uncoded case
before channel decoding.
Fig. 3. Detection probabilities of interleaver parameters ( 0.6th ).
Fig. 3 depicts the detection probabilities of interleaver parameters for various code
rates. We adopt 1/2, 1/4, and 1/8 code rates and standard block interleavers. As shown
in Fig. 3, the proposed algorithm is more robust in a noisy channel when the channel
code rate is small.
Through computer simulations, we know that the proposed algorithm can almost
perfectly estimate the interleaver parameters in practical communication systems
having performance requirements of BER below 10-3.
Advanced Science and Technology Letters Vol.139 (FGCN 2016)
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4 Conclusion
In this paper, we presented a blind deinterleaving process that can reconstruct
unknown interleaved sequence of block coded data. We first made the analytical
matrix ( ,2 )e eH N N with data of the limited length in noiseless and noisy channels.
We then Gaussian eliminated the the analytical matrix ( ,2 )e eH N N and observed
the value of . From ( )Rank H and eN , the code rate r could also be estimated.
Through computer simulations, we presented detection probabilities for various
channel code rates and interleaver types, and found that, in a noisy channel, our
method could almost perfectly estimate interleaving periods over a practical BER
range. Our results can be applied to unknown signal reconstruction for various cases
of practical interest.
Acknowledgement. This work was supported by the research fund of Signal
Intelligence Research Center supervised by Defense Acquisition Program
Administration and Agency for Defense Development of Korea.
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Advanced Science and Technology Letters Vol.139 (FGCN 2016)
56 Copyright © 2016 SERSC