- Email: [email protected]
Information Hiding Capacities in Multiple Antennas Channel Coding System
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 1848 – 1853 www.elsevier.com/locate/procedia
Advanced in Control Engineering and Information Science
Information Hiding Capacities in Multiple Antennas Channel Coding System Liquan Chena, Miao Lu a a. Research Center of Information Security, Southeast University, Nanjing, 210096，China
Abstract In this paper, the basic principles and requirements for information hiding used in channel coding system are presented and analyzed. An information hiding scheme based on LDPC code is proposed to be implemented in Alamouti coding MIMO system. The capacities of information hiding used in channel coding system and multiantenna channel coding system are theoretically analyzed, and validated by the numerical calculation results.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [ CEIS 2011] Key words: Information hiding; Channel coding; LDPC code; Alamouti; Hiding capacity
1. Introduction Information hiding technology, which has many advantages over encryption technology, is becoming a hotspot in the field of information security. With the increase of users and business in future communications, the shortage of spectrum resource seems to be a serious problem. Pursuing higher frequency spectrum efficiency for expanding system capacity has become an urgent challenge. The spacetime code, proposed in recent years, is one of techniques for improving wireless spectrum efficiency effectively. Furthermore, channel coding, with a rigorous mathematical structure, can improve the reliability of transmitted information by adding redundancy. Many information hiding algorithms have been applied to single channel communication system. Under the background of rapid development of Multiple-Input Multiple-Output (MIMO) technology, the applicabilities and effects of information hiding algorithms in MIMO systems need to be studied deeply. Therefore, the research of information hiding
* Corresponding author. Tel.:+86-25-8379-5822 ext. 810; Fax.: +86-25-8379-5822 ext. 800. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.344
2
LiquanLiquan Chen and Miao ProcediaEngineering Engineering00 15(2011) (2011)000–000 1848 – 1853 Chen ，et Lu al/ /Procedia
technology based on channel coding in the multiple antenna system with space-time coding, has important scientific significance. Hiding capacity is one of the difficulties in the theory of information hiding. In practical applications, the control of hiding capacity is an inevitable requirement for information concealment and has instructional significance of seeking better hiding schemes. Thus, the research of channel coding and information hiding capacity in MIMO system has practical significance. 2. Information Hiding Theory and Channel Coding Technology The main research topics of information hiding are how to hide secrets into another public carrier with redundancy, and then deliver the confidential information through the carrier in an open environment. Compared with encryption technology, information hiding technology avoids complex processes of encryption and decryption to ensure the security of information [1]. LDPC(Low Density Parity Code), put forward by Gallager in 1962, is a linear block code defined by sparse check matrix. The decoding method of LDPC is an iterative algorithm based on the thought of message delivery. The most important distinction between LDPC decoding and traditional error correction decoding is that the decoding complexity is lower, the hardware implementation is simpler, and the design optimization is relatively easier [2],[3]。 MIMO system is a communication system where the sender and receiver use multiple antennas in order to improve the system capacity and the spectrum efficiency, without any increase in bandwidth[4]. The purpose of STC technology is to improve the transmitting rate in wireless channel by joint encoding from aspects of space and time. Coding redundancy is mapped to a two-dimension space-time plane in order to reduce harmful effects of frequency and time selective fading caused by wireless multipath transmission, and to achieve a data transmission with high speed and reliability [5]. The simplest STBC scheme, named Alamouti, is a space-time code where the system equips with 2 transmitting antennas and can provide fully launch diversity gain [6]. 3 Information Hiding Capacity Based on Channel Coding in the Multiple Antenna System 3.1 The Theory of Hiding Capacity Based on Channel Coding in Single Channel Communication System Considering the correction ability of channel coding, we must make sure that the overall effect of embedded information and channel noise is no more than the range of correction ability. Thus, we can receive source information without distortion and extract secret information correctly at receiver[7],[8]. The basic theory of hiding capacity is the following: Error produced by channel is plus by capacity of encoding secret information. Subtracts error derived from secret should be equal or lower than information error correction ability of channel coding. Block code as an example, the derivation is as follows[9]: Supposing that, C 0 ：source data streams；
(n1，k1，t1 ) ：channel coding scheme of source information; C = (c1，c2 ...c N ) ：encoded carrier data of C0 ； m0 = (m01，m0 2...m0 M 0 ) ：secret data stream； (n2，k 2，t 2 ) ：error correction coding method of secret information； m = (m1，m2 ...mM ) ：encoded secret information；
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Liquan Chen and/Miao Lu / Procedia Engineering (2011) 1848 – 1853 Author name Procedia Engineering 00 (2011)15 000–000
3
N is the number of blocks; M means the length of encoded secret information; Pe represents the BER of channel; M0 means the length of secret information. Then: N ⋅ n1 ⋅ Pe + M − M ⋅ Pe ≤ N ⋅ t1 (1) N ⋅ t1 − N ⋅ n1 ⋅ Pe M≤ 1 − Pe N ⋅ t1 − N ⋅ n1 ⋅ Pe ⎡ C0 ⎤ t1 − n1 ⋅ Pe M max = (2) =⎢ ⎥ 1 − Pe ⎣ k1 ⎦ 1 − Pe (3) k M 0 max = M max × 2 (4) n2 ⎡ C ⎤ t − n ⋅ Pe k 2 M 0 max = ⎢ 0 ⎥ ⋅ 1 1 ⋅ n2 ⎣ k1 ⎦ 1 − Pe The result of M 0 max is the upper limit of information hiding capacity based on channel coding.
(5)
3.2 Information Hiding Structure in Multiple Antennas Alamouti Channel Coding System Considering the multi-antenna system based on Alamouti coding scheme, the implementation of information hiding is shown in Figure1. Firstly, the system takes LDPC-encoded data as the carrier for secret information, conducts the process of error correction coding for secret information, and hides the secret information into the carrier according to the embedding algorithm. Next, the operation of modulation and space-time coding on the hiding carrier are completed. Finally, the receiver gets the original secret information with error correction decode after space-time decodes and demodulation at receiver.
Fig. 1. The information hiding structure in multi- antenna Alamouti channel coding system
3.3 Analysis of Information Hiding Capacity in the Multiple Antennas System The basic theory here is the same as those described in section 3.1. Assumption 1： BPSK modulation is assumed to be used in Alamouti space-time coding scheme. It’s assumed that channels between antennas are Quasi-static flat Raleigh fading channels whose decay coefficient remains
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LiquanLiquan Chen and Miao ProcediaEngineering Engineering00 15(2011) (2011)000–000 1848 – 1853 Chen ，et Lu al/ /Procedia
4
the same in an interval of a frame. The decay coefficients are complex Gaussian random variables whose mean and variance of each dimension are 0 and ½, respectively. Noise signals are also a complex Gaussian random variables whose mean and variance are 0 and N 0 /2, respectively. Total launch powers are Es, which are not related to the transmitting antennas and are distributed to each transmitting antenna equally; Channel information is known to the receiver; Receive correlation is only concerned. Assumption 2： { x1，x2 } ：a pair of modulated independent signals;
{r1，r2 } ：receiving signals in two time buttress;
The derivation is as follows. The ruling signal is gotten with a principle named MRC [10]: ~
(6)
*
x1 = h1 ⋅ r1 + h2 ⋅ r2
(
2
= h1 + h2 (7) ~
2
)⋅ x + h 1
*
x2 = h2 ⋅ r1 − h1 ⋅ r2
(
2
= h1 + h2
(9)
*
2
* 1
⋅ n1 + h2 ⋅ n2
*
⋅ n1 − h1 ⋅ n2
*
*
)⋅ x + h 1
2
(8) *
So, receiving SNR is defined as： S~ E 2 2 2 x γ o = 1 = h1 + h2 ⋅ s = h1 + h2 N~ N0
(
)
(
2
)⋅ γ
s
x1
(10) According to formula (6-10), SNR at receiver is proportional to the SNR at transmitter if the channel is determined. Therefore, the research of SNR at receiver can be simplified to that at transmitter. According to literature [11] and [12], the transmission BER of BPSK modulation signal in multiantenna system is equivalent to that: 2 2 ⎛ ⎞ P2b = Q⎜ h1 + h2 ⋅ 2γ s ⎟ ⎝ ⎠ (11) Where: ⎛ x ⎞ E 1 ⎟⎟，γ s = s Q(x ) = ⋅ erfc⎜⎜ (12) 2 N0 ⎝ 2⎠
(
)
So, according to the formula(1)-(5), the maximum capacity of hiding information is that: ⎛ E ⎞ 2 2 t1 − n1 ⋅ Q⎜ h1 + h2 ⋅ 2 ⋅ s ⎟ ⎜ N 0 ⎟⎠ k 2 ⎡C ⎤ k ⎝ M 0 max = M max ⋅ 2 = ⎢ 0 ⎥ ⋅ ⋅ , n2 n2 ⎛ E s ⎞⎟ 2 2 ⎣ k1 ⎦ ⎜ 1− Q h1 + h2 ⋅ 2 ⋅ ⎜ N 0 ⎟⎠ ⎝ (13) n1 in formula(13) is the length of the block in channel coding. According to formula (13), the information hiding capacity in multi-antenna system is related to the channel coding scheme, channel decline coefficient, and the launch SNR.
(
(
)
)
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Liquan Chen and/Miao Lu / Procedia Engineering (2011) 1848 – 1853 Author name Procedia Engineering 00 (2011)15 000–000
4. Numerical Calculations and Validation The parameters of numerical calculation are set next, assuming that each dimension of channel decay coefficient is a complex Gaussian random variable. The mean and variance are 0 and ½, respectively. Each dimension of noise signal is also a Gaussian variable whose mean and variance are 0 and ½, respectively. Transmitting power Es is normalized to 1. The length of code stream is 2400 bits. We use (400, 12, 24) regular LDPC codes and BPSK modulation, while the power of modulation signal is normalized to 1. The results are shown in Table 1and Table 2. Table 1. The comparison of information hiding capacity in single antenna system and multiple antennas system Hiding capacity
Embedded rate
Single antenna 1*1
38.95 bit
1.6%
Multiple antennas 2*1
52.52 bit
2.2%
According to Table 1, the scheme of two transmitting antennas with space-time code can improve the hiding capacity to some extent in comparison to that of one transmitting antenna under the same conditions. Table 2. The relationship between information hiding capacity and launch power in multiple antennas system
Launch power/w
Hiding capacity
1
52.52 bit
2
66.81 bit
4
68.74 bit 69.84 bit
6
Table 2 shows that increasing launch power can help improve hiding capacity when the number of antennas is fixed. However, when the launch power reaches a certain value, the increase of capacity is not obvious. The above phenomenon is related to Alamouti scheme whose spatial multiple gains are not obvious compared to diversity gain. 5 conclusions This paper puts forward an information hiding scheme in multi-antenna channel coding system with Alamouti coding method and gives the derivation and analysis of information hiding capacity. Along with the development of MIMO technology, the information hiding technology in encoded channel based on MIMO system will certainly obtain a widespread application and development. References [1] W. Chang, W. Liu. Overview of Information Hiding Technology. China Science and Technology Information, 2010, 26(3). [2] R. G. Gallager. Low-density parity check codes [J]. IRE Trans. on Information Theory, 1962, IT-8: 21-28. [3] D. J. C. MacKay and R. M. Neal. Near Shannon limit performance of low-density parity-check codes [J]. Electronics Letter, 19 96, 32(18): 1645-1646. [4] I. E. Telatar. Capacity of Multi-antenna Gaussian Channels. European Trans on Telecom, 1999, 10(6): 1-29. [5] Tarokh V, Seshadri N, CalderbankAR. Space-time codes for high data rate wireless communication: Performance criterion and code construction [J].IEEE Trans. Inform. Theory, 1998, 44: 744-765. [6] Alamouti S M A simple transmitter diversity scheme for wireless communications[J].IEEE, JSAC, 1998, 16(10): 1451-1458. [7] Weixiang Wang, Yujun Liu, Wenxiong Li. The Implementation of Channel Coding Information Hiding Based on LDPC Codes
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LiquanLiquan Chen and Lu Procedia / ProcediaEngineering Engineering0015(2011) (2011)000–000 1848 – 1853 ChenMiao ，et al/
. Journal of Information Engineering University, Mar. 2006, 3(7). [8] W. X. Wang, Y. J. Liu. The Research of Information Hiding Technology Based on Channel Coding. Television Technology, 2 006, 3. [9] Xuehu Yan. The Information Hiding Capacity Model Based on Error Correction Code. Computer Engineering, 2010, 36(3). [10] Dingfa Gong, Xuerong Qian, Yanming Chen. The Performance Research of Alamouti Space-time Coding Scheme. Journal of Chongqing University of Posts and Telecommunications (Nature Science Edition). 2008, 2(20). [11] Prokis J G. Digital Communication [M]. Fourth Version. Beijing: Electronic Industry Press, 2003. [12] Simon M. K, Alouini M. S. Digital Communication Over Fading Channel: A unified Approach to Performance Analysis [M]. New York: Wiley, 2000.
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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 1848 – 1853 www.elsevier.com/locate/procedia
Advanced in Control Engineering and Information Science
Information Hiding Capacities in Multiple Antennas Channel Coding System Liquan Chena, Miao Lu a a. Research Center of Information Security, Southeast University, Nanjing, 210096，China
Abstract In this paper, the basic principles and requirements for information hiding used in channel coding system are presented and analyzed. An information hiding scheme based on LDPC code is proposed to be implemented in Alamouti coding MIMO system. The capacities of information hiding used in channel coding system and multiantenna channel coding system are theoretically analyzed, and validated by the numerical calculation results.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [ CEIS 2011] Key words: Information hiding; Channel coding; LDPC code; Alamouti; Hiding capacity
1. Introduction Information hiding technology, which has many advantages over encryption technology, is becoming a hotspot in the field of information security. With the increase of users and business in future communications, the shortage of spectrum resource seems to be a serious problem. Pursuing higher frequency spectrum efficiency for expanding system capacity has become an urgent challenge. The spacetime code, proposed in recent years, is one of techniques for improving wireless spectrum efficiency effectively. Furthermore, channel coding, with a rigorous mathematical structure, can improve the reliability of transmitted information by adding redundancy. Many information hiding algorithms have been applied to single channel communication system. Under the background of rapid development of Multiple-Input Multiple-Output (MIMO) technology, the applicabilities and effects of information hiding algorithms in MIMO systems need to be studied deeply. Therefore, the research of information hiding
* Corresponding author. Tel.:+86-25-8379-5822 ext. 810; Fax.: +86-25-8379-5822 ext. 800. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.344
2
LiquanLiquan Chen and Miao ProcediaEngineering Engineering00 15(2011) (2011)000–000 1848 – 1853 Chen ，et Lu al/ /Procedia
technology based on channel coding in the multiple antenna system with space-time coding, has important scientific significance. Hiding capacity is one of the difficulties in the theory of information hiding. In practical applications, the control of hiding capacity is an inevitable requirement for information concealment and has instructional significance of seeking better hiding schemes. Thus, the research of channel coding and information hiding capacity in MIMO system has practical significance. 2. Information Hiding Theory and Channel Coding Technology The main research topics of information hiding are how to hide secrets into another public carrier with redundancy, and then deliver the confidential information through the carrier in an open environment. Compared with encryption technology, information hiding technology avoids complex processes of encryption and decryption to ensure the security of information [1]. LDPC(Low Density Parity Code), put forward by Gallager in 1962, is a linear block code defined by sparse check matrix. The decoding method of LDPC is an iterative algorithm based on the thought of message delivery. The most important distinction between LDPC decoding and traditional error correction decoding is that the decoding complexity is lower, the hardware implementation is simpler, and the design optimization is relatively easier [2],[3]。 MIMO system is a communication system where the sender and receiver use multiple antennas in order to improve the system capacity and the spectrum efficiency, without any increase in bandwidth[4]. The purpose of STC technology is to improve the transmitting rate in wireless channel by joint encoding from aspects of space and time. Coding redundancy is mapped to a two-dimension space-time plane in order to reduce harmful effects of frequency and time selective fading caused by wireless multipath transmission, and to achieve a data transmission with high speed and reliability [5]. The simplest STBC scheme, named Alamouti, is a space-time code where the system equips with 2 transmitting antennas and can provide fully launch diversity gain [6]. 3 Information Hiding Capacity Based on Channel Coding in the Multiple Antenna System 3.1 The Theory of Hiding Capacity Based on Channel Coding in Single Channel Communication System Considering the correction ability of channel coding, we must make sure that the overall effect of embedded information and channel noise is no more than the range of correction ability. Thus, we can receive source information without distortion and extract secret information correctly at receiver[7],[8]. The basic theory of hiding capacity is the following: Error produced by channel is plus by capacity of encoding secret information. Subtracts error derived from secret should be equal or lower than information error correction ability of channel coding. Block code as an example, the derivation is as follows[9]: Supposing that, C 0 ：source data streams；
(n1，k1，t1 ) ：channel coding scheme of source information; C = (c1，c2 ...c N ) ：encoded carrier data of C0 ； m0 = (m01，m0 2...m0 M 0 ) ：secret data stream； (n2，k 2，t 2 ) ：error correction coding method of secret information； m = (m1，m2 ...mM ) ：encoded secret information；
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Liquan Chen and/Miao Lu / Procedia Engineering (2011) 1848 – 1853 Author name Procedia Engineering 00 (2011)15 000–000
3
N is the number of blocks; M means the length of encoded secret information; Pe represents the BER of channel; M0 means the length of secret information. Then: N ⋅ n1 ⋅ Pe + M − M ⋅ Pe ≤ N ⋅ t1 (1) N ⋅ t1 − N ⋅ n1 ⋅ Pe M≤ 1 − Pe N ⋅ t1 − N ⋅ n1 ⋅ Pe ⎡ C0 ⎤ t1 − n1 ⋅ Pe M max = (2) =⎢ ⎥ 1 − Pe ⎣ k1 ⎦ 1 − Pe (3) k M 0 max = M max × 2 (4) n2 ⎡ C ⎤ t − n ⋅ Pe k 2 M 0 max = ⎢ 0 ⎥ ⋅ 1 1 ⋅ n2 ⎣ k1 ⎦ 1 − Pe The result of M 0 max is the upper limit of information hiding capacity based on channel coding.
(5)
3.2 Information Hiding Structure in Multiple Antennas Alamouti Channel Coding System Considering the multi-antenna system based on Alamouti coding scheme, the implementation of information hiding is shown in Figure1. Firstly, the system takes LDPC-encoded data as the carrier for secret information, conducts the process of error correction coding for secret information, and hides the secret information into the carrier according to the embedding algorithm. Next, the operation of modulation and space-time coding on the hiding carrier are completed. Finally, the receiver gets the original secret information with error correction decode after space-time decodes and demodulation at receiver.
Fig. 1. The information hiding structure in multi- antenna Alamouti channel coding system
3.3 Analysis of Information Hiding Capacity in the Multiple Antennas System The basic theory here is the same as those described in section 3.1. Assumption 1： BPSK modulation is assumed to be used in Alamouti space-time coding scheme. It’s assumed that channels between antennas are Quasi-static flat Raleigh fading channels whose decay coefficient remains
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LiquanLiquan Chen and Miao ProcediaEngineering Engineering00 15(2011) (2011)000–000 1848 – 1853 Chen ，et Lu al/ /Procedia
4
the same in an interval of a frame. The decay coefficients are complex Gaussian random variables whose mean and variance of each dimension are 0 and ½, respectively. Noise signals are also a complex Gaussian random variables whose mean and variance are 0 and N 0 /2, respectively. Total launch powers are Es, which are not related to the transmitting antennas and are distributed to each transmitting antenna equally; Channel information is known to the receiver; Receive correlation is only concerned. Assumption 2： { x1，x2 } ：a pair of modulated independent signals;
{r1，r2 } ：receiving signals in two time buttress;
The derivation is as follows. The ruling signal is gotten with a principle named MRC [10]: ~
(6)
*
x1 = h1 ⋅ r1 + h2 ⋅ r2
(
2
= h1 + h2 (7) ~
2
)⋅ x + h 1
*
x2 = h2 ⋅ r1 − h1 ⋅ r2
(
2
= h1 + h2
(9)
*
2
* 1
⋅ n1 + h2 ⋅ n2
*
⋅ n1 − h1 ⋅ n2
*
*
)⋅ x + h 1
2
(8) *
So, receiving SNR is defined as： S~ E 2 2 2 x γ o = 1 = h1 + h2 ⋅ s = h1 + h2 N~ N0
(
)
(
2
)⋅ γ
s
x1
(10) According to formula (6-10), SNR at receiver is proportional to the SNR at transmitter if the channel is determined. Therefore, the research of SNR at receiver can be simplified to that at transmitter. According to literature [11] and [12], the transmission BER of BPSK modulation signal in multiantenna system is equivalent to that: 2 2 ⎛ ⎞ P2b = Q⎜ h1 + h2 ⋅ 2γ s ⎟ ⎝ ⎠ (11) Where: ⎛ x ⎞ E 1 ⎟⎟，γ s = s Q(x ) = ⋅ erfc⎜⎜ (12) 2 N0 ⎝ 2⎠
(
)
So, according to the formula(1)-(5), the maximum capacity of hiding information is that: ⎛ E ⎞ 2 2 t1 − n1 ⋅ Q⎜ h1 + h2 ⋅ 2 ⋅ s ⎟ ⎜ N 0 ⎟⎠ k 2 ⎡C ⎤ k ⎝ M 0 max = M max ⋅ 2 = ⎢ 0 ⎥ ⋅ ⋅ , n2 n2 ⎛ E s ⎞⎟ 2 2 ⎣ k1 ⎦ ⎜ 1− Q h1 + h2 ⋅ 2 ⋅ ⎜ N 0 ⎟⎠ ⎝ (13) n1 in formula(13) is the length of the block in channel coding. According to formula (13), the information hiding capacity in multi-antenna system is related to the channel coding scheme, channel decline coefficient, and the launch SNR.
(
(
)
)
1852
Liquan Chen and/Miao Lu / Procedia Engineering (2011) 1848 – 1853 Author name Procedia Engineering 00 (2011)15 000–000
4. Numerical Calculations and Validation The parameters of numerical calculation are set next, assuming that each dimension of channel decay coefficient is a complex Gaussian random variable. The mean and variance are 0 and ½, respectively. Each dimension of noise signal is also a Gaussian variable whose mean and variance are 0 and ½, respectively. Transmitting power Es is normalized to 1. The length of code stream is 2400 bits. We use (400, 12, 24) regular LDPC codes and BPSK modulation, while the power of modulation signal is normalized to 1. The results are shown in Table 1and Table 2. Table 1. The comparison of information hiding capacity in single antenna system and multiple antennas system Hiding capacity
Embedded rate
Single antenna 1*1
38.95 bit
1.6%
Multiple antennas 2*1
52.52 bit
2.2%
According to Table 1, the scheme of two transmitting antennas with space-time code can improve the hiding capacity to some extent in comparison to that of one transmitting antenna under the same conditions. Table 2. The relationship between information hiding capacity and launch power in multiple antennas system
Launch power/w
Hiding capacity
1
52.52 bit
2
66.81 bit
4
68.74 bit 69.84 bit
6
Table 2 shows that increasing launch power can help improve hiding capacity when the number of antennas is fixed. However, when the launch power reaches a certain value, the increase of capacity is not obvious. The above phenomenon is related to Alamouti scheme whose spatial multiple gains are not obvious compared to diversity gain. 5 conclusions This paper puts forward an information hiding scheme in multi-antenna channel coding system with Alamouti coding method and gives the derivation and analysis of information hiding capacity. Along with the development of MIMO technology, the information hiding technology in encoded channel based on MIMO system will certainly obtain a widespread application and development. References [1] W. Chang, W. Liu. Overview of Information Hiding Technology. China Science and Technology Information, 2010, 26(3). [2] R. G. Gallager. Low-density parity check codes [J]. IRE Trans. on Information Theory, 1962, IT-8: 21-28. [3] D. J. C. MacKay and R. M. Neal. Near Shannon limit performance of low-density parity-check codes [J]. Electronics Letter, 19 96, 32(18): 1645-1646. [4] I. E. Telatar. Capacity of Multi-antenna Gaussian Channels. European Trans on Telecom, 1999, 10(6): 1-29. [5] Tarokh V, Seshadri N, CalderbankAR. Space-time codes for high data rate wireless communication: Performance criterion and code construction [J].IEEE Trans. Inform. Theory, 1998, 44: 744-765. [6] Alamouti S M A simple transmitter diversity scheme for wireless communications[J].IEEE, JSAC, 1998, 16(10): 1451-1458. [7] Weixiang Wang, Yujun Liu, Wenxiong Li. The Implementation of Channel Coding Information Hiding Based on LDPC Codes
5
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LiquanLiquan Chen and Lu Procedia / ProcediaEngineering Engineering0015(2011) (2011)000–000 1848 – 1853 ChenMiao ，et al/
. Journal of Information Engineering University, Mar. 2006, 3(7). [8] W. X. Wang, Y. J. Liu. The Research of Information Hiding Technology Based on Channel Coding. Television Technology, 2 006, 3. [9] Xuehu Yan. The Information Hiding Capacity Model Based on Error Correction Code. Computer Engineering, 2010, 36(3). [10] Dingfa Gong, Xuerong Qian, Yanming Chen. The Performance Research of Alamouti Space-time Coding Scheme. Journal of Chongqing University of Posts and Telecommunications (Nature Science Edition). 2008, 2(20). [11] Prokis J G. Digital Communication [M]. Fourth Version. Beijing: Electronic Industry Press, 2003. [12] Simon M. K, Alouini M. S. Digital Communication Over Fading Channel: A unified Approach to Performance Analysis [M]. New York: Wiley, 2000.
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