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)

54 Copyright © 2016 SERSC

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)

Copyright © 2016 SERSC 55

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.

References

1. Ramsey, J. L.: ‘Realization of Optimum Interleavers’, IEEE Trans. on Information Theory,

May 1970, 16, (3), pp. 338–345

2. Garello, R., Montorsi, G.., Benedetto, S., and Canellieri, G.: ‘Interleaver Properties and

Their Applications to the Trellis Complexity Analysis of Turbo Codes’, IEEE Trans. on

Communications, May 2001, 49, (5), pp. 793–807

3. Lu, L., Li, K. H., and Guan, Y. L.: ‘Blind Detection of Interleaver Parameters for Non-

Binary Coded Data Streams’, IEEE International Conference on Communications,

Dresden, Germany, June 2009

4. Sicot, G., Houcke, S., and Barbier, J.: ‘Blind detection of interleaver parameters’, Signal

Processing, April 2009, 89, pp. 450–462

5. Andrews, K., Heegard, C., and Kozen, D.: ‘A theory of Interleavers’ (Technical Report

97-1634, Computer Science Department, Cornell University, June 1997)

Advanced Science and Technology Letters Vol.139 (FGCN 2016)

56 Copyright © 2016 SERSC