Communications and Network, 2013, 5, 280-285 Published Online September 2013 (
Study of LDPC Coded SFH System with Partial-Band
Chao Gong2, Manxi Wang1, Daoxing Guo2, Xiaofei Pan2
1TheState Key Laboratory of Complex Electromagnetic Environmental Effects on Electronics&Information System, China
2College of communications engineering PLA University of Science &Technology, China
Received July, 2013
The application of Low Density Parity Check (LDPC) code in the anti-interference systems has drawn an increasing
attention, due to its admiring performance which is very close to the theory limit. This paper focuses on a LDPC en-
coded slow frequency hopping (SFH) communication system with partial-band interference. Firstly, a modified soft-
decision algorithm based on the utilization of interference information is proposed, and its performance is compared
with some other soft-decision methods. Secondly, with numerical simulation, the influence of code rate, code length
and the number of symbols per h ops on the p erformance of th e system with partial band noise interference is illu strated
and examined in detail. Considering the great influence of hops per symbol on the performance, interleaver should be
used and its influence on the performance is further examined by simulation. Finally, some constructive advises for the
design of LDPC coded SFH system are given. Simulation results show that, with a reasonable design, the SFH system
with LDPC code could achieve a desirable performance.
Keywords: LDPC; SFH; Soft-decision; Partial-band Interference
1. Introduction
Frequency hopping (FH) transmissions, whose carrier
frequency hops under control of a pseudorandom pattern,
is an attractive access method in wireless communication,
due to its special ability to anti interference and provides
continuous communication under a severe interference
situation [1]. In the civil communication, FH is often
used in the wireless communication system working in
unlicensed industrial, scientific and medical (ISM) band,
such as Bluetooth and ZigBee, to overcome the interfer-
ence coming from other electronic equipment working in
the same frequency band. While in the military commu-
nication, FH, which is almost to be a characteristic of
military communication system, is widely used in the
short-wave, microwave and satellite communication to
overcome intentional interference. For example, both of
America’s domain tactical wireless networks (JTIDS)
and the Milstar satellite communication system base on
frequency hopping tr ansmission [3]. Apar t from that, FH
is also used in the cognitive radios due to the available
frequency changes from time to time [4].
So far, researchers all along pay attention to the en-
hancement of FH systems’ anti-interference perfo rmance,
some useful methods, such as channel coded diversity,
interleave, are widely used. As a excellent channel code
method, LDPC, which is close to the theory limit, has
drawn an increasingly attention of researchers from
worldwide, especially its application in the FH commu-
nication. In [5], some diversity methods based on
LDPC-FH system were examined. And the paper [6]
focused on the technology of interference erasure in the
LDPC-FH communication. The performance of LDPC
encoded fast frequency hopping (FFH) system under
partial-band noise interferen ce was analyzed in paper [7],
and the performance of LDPC encoded FFH system with
partial band multitone interference was given by [8].In
this paper, we are focused on the performance of
LDPC-SFH system under partial-band noise interference.
There are some theory methods for the analysis of the
performance of LDPC, some of which is illustrated in [9],
such as density evolution, Gaussian approximate, extrin-
sic information transfer (EXIT) charts. All of those
methods pay attention to the performance of certain kind
of LDPC, rather than that of certain type of LDPC.
However, in practice, the choice of LDPC is limited to
the feasibility of hardware, code length, code rate and
code’s structure and so on, which causes the real per-
formance of LDPC has a large difference with the theory
bound. In the interference environment, the channel is no
longer to be an additive white Gaussian noise (AWGN)
channel, which makes it even more difficult for the
analysis of performance of LDPC. As the approximation
opyright © 2013 SciRes. CN
C. GONG ET AL. 281
and simplification have to be used for theory analysis,
the result will be imprecise. In the practical system de-
sign, numerical simulation with certain type available
code is a feasible and effective way for analysis. Based
on above considerations, numerical simulation is ex-
ploited in this paper for analysis of application of LDPC
on the SFH system, and some key points of designing
anti-interference communication are analyzed further.
2. System Model
The system model in this paper is shown as Figure 1.
The transmitter consists of encoder, interleaver, and
modulator and up frequency converter. By the number of
‘1’ in every row and column of check matrix, LDPC can
be divided into kinds: regular LDPC and irregular LDPC.
Generally, performance of irregular LDPC is better than
regular LDPC, which is at the cost of more complex re-
alization of hardware. With a tradeoff between perform-
ance and complexity degree of hardware realization, this
paper chooses quasi-cyclic regular binary LDPC [10] as
channel code. In the SFH system, number of symbols per
hop (SPH) is more than one, when the signal is jammed,
it will bring about burst symbol errors. If number of burst
symbol errors in a coded packet is larger than threshold
number of decoding, decoding error will occur. In order
to alleviate the burst errors influence and reduce frame
error rate In practice, the coded bit stream is interleaved
in the transmitter, making burst errors decentralize into
every packet equally. The following simulation will
show that interleaving do improved the performance of
system with short code length dramatically when the
code length is short. While it comes to long code length,
impact of interlacing is not obvious, so it can conclude
that interleaver is unnecessary for the system, and it can
be chosen depending on the length of code. In the SFH
system, FSK, DPSK, PSK is widely used, PSK has a
higher bandwidth efficiency, so BPSK is used in this
paper. Under the control of FH pattern, the modulated
signal is transmitted through the up frequency converter,
as Figure 1 shows. As the control methods of FH pattern
isn’t the content of this paper, we don’t introduce it here.
The transmitting signal is given by
(2 ),1,2,
ij ij
cei N
 (1)
where 1
is information sequence, i
is carrier
frequency, T is symbol interval, i
is initial phase per
hop, N is num ber of sy mbols per hop.
The channel model that we employ is an example of a
block-interference channel, including additive white
Gaussian noise (AWGN) and partial-band interference,
which has been used in several previous investigations of
FH communication [11]. Model of partial-band interfer-
ence is given by bandwidth-limited white Gaussian noise
with a
band rate, here
is the partial-band inter-
ference factor, and it is a constant but unknown number
for both transmitter and receiver. We assume all the
symbols in a FH time slot are jammed when the signal in
certain moment of the slot is hit by the interference sig-
nal, and vice versa. The probability of FH signal jammed
, power spectral density (PSD) of interference sig-
nal in the current time slot is 1
, and in other slot
without interference, the PSD is 0. Power of the interfer-
ence signal is in direct proportion to
N and irrelevant
. AWGN diffuse during the transmitting, and
PSD is , rate of bit power to PSD of AWGN is given
by 0b
ENR10log10(/ N)
, rate of bit power to PSD
of interference signal is given by EIR 10log10(/)
The receive signal is given by
(2 ),1,2,
ij ijijij
cenw iN
 (2)
where ij is wide-band white Gaussian noise, and
is partial-band interference.
Figure 1. Model of LDPC-SFH system.
Copyright © 2013 SciRes. CN
As Figure 1 shows, receiver consists of decoder, dein-
terleaver, demodulator and down frequency converter.
With the same FH pattern, the receiver change the FH
signal to lowpass or fixed band pass signal, and the de-
modulater estimate the carrier phase and symbol timing
in order to realize carrier and symbol synchronization,
and then the information sequence will be obtained by
soft-decision method. Signal after carrier and symbol
synchronization is given by (3),
ijij ijij
ycnwi N
   (3)
where ij , ij is wide-band white Gaussian noise and
partial-band interference after carrier and symbol syn-
chronization respectively. In this paper, we don’t focus
on carrier and symbol synchronization, so we assume
carrier phase and symbol timing are estimated correctly
in the following. Soft-decision methods will be discussed
in the following section detailedly. Deinterleaver reorder
the receive sequence to make it same as the original se-
quence, and finally channel decoder decodes the se-
quence after soft-decision. Decoding methods of LDPC
is sorted into two kinds: hard-decision and soft-decision.
Generally speaking, performance of soft-decision meth-
ods is better than those of hard-decision. Considering the
complexity of hardware realization, modifying-mini-
mum-sum soft-decision method [12], which has low
complexity for hardware realization and good perform-
ance close to the optimum method, is used in this paper.
3. Modifying Soft-decision
The probability of transmitting signal should be propor-
tional to the value of soft-decision for modifying-mini-
mum-sum soft-decision method (MMSSD). Without in-
terference, ij maintain its probability statistic charac-
teristic, which could give probability of transmitting sig-
nal directly, so the sequence can be decoded with di-
rect-decision (DD). While there is interference with the
received signal, the probability statistic characteristic of
ij with and without interference will be different, so it
will represent different probability of transmitting signal
in the two conditions. In this case, probability of signal
can’t archive from ij directly, which lead to drastic
deterioration of performance is DD method is used. As
Figure 2 shows, when
, performance based on
direct soft-decision is very close to that the method with
perfect channel side information (PCSI). However, with
the decreasing of
, the performance will deteriorate
drastically. To solve above problem, we can estimate
ENR of signal in every hop, and then modify the soft-
decision value accordingly. In [12], a simple square sig-
nal to noise ratio estimator is introduced, where the esti-
mator is given by (4)
ij ij
With the estimated value of ENR in ith FH time slot,
we can modify value of soft-decision with (5)
ijij i
When the EIR is low, it is imprecise to estimate the
EIR by above method, however, simulation suggests that
the precision of the estimation can meet the need of
LDPC-SFH system, and comparing with DD, we have
got admirable performance improvement. Figure 2
shows three soft-decision methods’ performance, where
the vertical axis is the required value of EIR to archiv e a
packet error probability of 10-2. We found that the EIR
increases no more than 0.2dB to reduce the packet error
probability from 10-2 to 10-3. In general, most wireless
networks, such as Ad hoc network, could work normally
with a frame error rate of 10-2. The AWGN is consid-
ered in the following simulation, though PSD of par-tial-
band interf erence signal is fa r higher th an that of AWGN.
In the simulation of this paper, we as-sume . is a exact
known number and the methods of modifying the soft-
decision value are the same , when the interference signal
is known. From the Figure 2 we can see that the per-
formance of modifying the value of soft-decision based
on estimating ENR with square-ENR estimator is close
to that of PCSI.
4. Performance of Anti-interference
The following numerical simulation bases on the system
model and MMSSD introduced in above sections, which
00.1 0.20.3 0.40.5 0.6 0.7 0.8 0.9 1
P art i al B and Int erference F actor,
Signal to Interference Ratio
Figure 2. Performances of different soft-decision methods.
Copyright © 2013 SciRes. CN
C. GONG ET AL. 283
will give performance of LDPC-SFH system with dif-
ferent code rate, code length, SPH and way of interleav-
ing. In the simulation, two cases are considered: the first
is that, code length is fixed-8064, value of code rate get-
ting from 1/2, 5/8 and 7/8; the second is code rate
fixed-3/4, and code rate varying with 8064, 4032, 2016
and 1008. Performance of above cases with AWGN
channel is shown in Figure 3. In order to make a clear
analysis, here, we introduce two basic conceptions: first
is that the ˆ
corresponding to the highest value of EIR
is represented as worst partial-band interference (WPBJ)
factor, second is throughput, which is a key standard of a
system, is given by ratio of number of available source
sequences to that of encoded transmitting packet se-
quences. Besides, we also assume that it is a available
packet only when the receiving sequences are all right,
otherwise, the packet is un available.
4.1. Influences of Code Rate
Code rate is a vital factor of the performance, when code
length is fixed, with decreasing of code rate , perform-
ance is improving, which don’t result in decreasing of
system’s throughput, as Figure 4 shown, performance of
system with 1/2, 5/8, 3/4 and 7/8 code rate and a fixed
code length 8064 are given. When 1
, difference of
Interference-to-Signal (JNS) threshold of four code rate
is about 2dB, which will enlarge with decreasing of
When 0.5
, JNS threshold of LDPC with a 1/2 code
rate is lower than 0dB; when 0.2
, JNS threshold of
LDPC with a 7/8 code rate is larger than 7dB. Different
code rate have different performance with the worst par-
tial-band interference, and with increasing of code rate,
is decreasing, and so is the threshold of
00.5 11.5 22.5 33.5 4
S i gnal to Interference Rat i o
F rame Erro r Rat e
Code Rate
Code Lengt h
Code Rate
Code Lengt h
Code Rate
Code Lengt h
Code Rate
Code Lengt h
Code Rate
Code Lengt h
Code Rate
Code Lengt h
Code Rate
Code Lengt h
Figure 3. Performances of different code.
In Figure 5, throughput of differ ent co de rate is sh own.
We can see, low code rate has a stronger adaptability to
drastic change of
, and there is an inconspicuous
change of throughput, with
changing from 0 to 0.7,
when LDPC code rate is 1/2. However, when
is very
small, the throughput of code with low rate is lower
comparatively, which leads to low transmission effi-
ciency. Therefore, in practice, throughput could improve
with a proper LDPC designed depending on
, and
code length of a system could be designed depending on
throughput an d cost of hardware.
4.2. Influences of Code Length
In Figure 6, performance of LDPC with a 3/4 code rate
under 8064,4032,2016,1008 code length are shown, while
number of symbols is 336(). When
, per-
formance of the four codes are very close, difference
between maximum code length and minimum code length
00.1 0.20.3 0.40.5 0.6 0.7 0.8 0.91
P art i al B and Int erferenc e F ac tor,
S i gnal to Interference Rat i o
Code Rate
1/ 2
Code Rate
5/ 8
Code Rate
3/ 4
Code Rate
7/ 8
Figure 4. Performances of different code rate with partial-
band interference.
00.1 0.20.3 0.40.5 0.6 0.70.8 0.91
Part i al B and Interference F ac tor,
Code Rate1/ 2
Code Rate5/ 8
Code Rate3/ 4
Code Rate7/ 8
Figure 5. Throughput of different code r ate.
Copyright © 2013 SciRes. CN
is only 0.5 dB, however, which will enlarge with de-
creasing of
. After JNS of code 8064 and 4032 reach
to the highest, it will decreasing along with the decreas-
ing of
, and then JNS of 2018 and 1008 is in direct
proportion to
. The main reason of that is , short code
has a weak ability of anti-outburst-wrong, moreover, its
performance also depend o n the value of .
4.3. Influences of Symbols per Hop
Influence of symbols per hop on the performance is
shown from two aspects: on one hand, a increasing N
will exaggerate the outburst wrong, and performance of
system will also decrease, especially when
is very
small; on the other hand, amount of data processed by
ENR estimator will also increase for N’s increasing,
which lead to a more precise estimation and higher per-
formance. As Figure 7 shows, when code length is 1008,
code rate is 3/4, and , performance keeps good
with most value of 12N
, and when 0.1
, EIR reaches
to the highest. From Figure 7, we can conclude that
number symbols is another factor which should be
in a proper range during practical system design, and it is
better design when value of is chosen depending on
the change of
. In practice, there is a simpler and
available method of choosing , basing on interleaving,
which makes outburst wrong sequence dispersing into all
the transmitting packets, therefore, even with a large ,
performance still keeps a good leve l.
4.4. Influence of Interleaving
The key parameter of interleaver is the deep degree of
interleaving (), in the simulation, different values of
, which is 4, 8, and 16, are considered, while code
length is 1008 and code rate is 3/4. As Figure 8 shows,
with increasing of , performance is also increasing. In
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Part i al B and Interference Fact or,
Signal to Interference RatioEb/NI
Code Length8064
Code Length4032
Code Length2016
Code Length1008
Figure 6. Performances of different code length with par-
tial-band interference.
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91
P artial Ba nd Interference Factor,
Signal to Interference Ratio
N=16 8
N=33 6
Figure 7. Performances of different symbols per hop with
partial-band interference and code rate 3/4.
00.1 0.20.3 0.40.5 0.6 0.70.8 0.91
P artial Band Int erference F a ctor,
S i gnal to I nterference Rat i o
Figure 8. Performances of different deep degree of inter-
leaving with partial-band interference.
general, a bigger makes random wrong sequences
discrete further, which could improve the performance,
however, a bigger will also means increasing of
transmitting delay of the system. Therefore, both
and transmitting delay should be taken into consideration.
Meanwhile, a proper also depend on exact value of
code length and methods of interleaving.
5. Advises for System Design
When it comes to design a higher performance LDPC-
SFH communication system, code rate, code length,
symbols per hop and deep degree of interleaving are key
parameters. Different code rate will result in different
performance, it is better for a low code rate when
throughput of system is not considered in the design. But
a higher code rate can benefit for the throughput when
Copyright © 2013 SciRes. CN
Copyright © 2013 SciRes. CN
is small, it is advised the system’s code rate could
adjust to the change of
. As is analyzed in above sec-
tion, when
is small, it will bring about a drastic dif-
ference of EIR with different code length, so a longer
code will our best choice, however, which is only at cost
of complexity of hardware. And of cause, considering the
complexity of hardware, short will be better, when sym-
bols per hop is small and sequences is interleaved, per-
formance could also meet the need of design.
6. Conclusions
This paper focuses on the design and performance
analyses of LDPC-SFH system in partial-band interfer-
ence channel. A new soft-decision method based on the
estimation of EIR hop by hop is proposed, performance
could be improved drastically as illustrated by simulation.
The Influences of code rate, code length, symbols per
hop and deep degree of interleaving are also analyzed
with numerical simulation. Furthermore, some construc-
tive advises for practical system design are given based
on the former work. The results of this paper will be
benefit for the design of anti-jamming communication
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