Large-Scale Grant-Free Sparse Chaos Code Multiple Access Scheme

5 downloads 0 Views 499KB Size Report
Nagoya Institute of Technology. Gokiso-cho ... code multiple access (GF-SCCMA) scheme exploiting the principle of chaos ... In the fifth-generation mobile communications system (5G), not only in the .... Next, the extrinsic LLR is obtained by subtracting the priori LLR from ..... Ericsson, 3GPP RAN1-NR#1, Jan. 2017.
Large-Scale Grant-Free Sparse Chaos Code Multiple Access Scheme for 5G IoT Eiji Okamoto

and

Naoto Horiike

Graduate School of Engineering, Nagoya Institute of Technology Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan. [email protected], [email protected]

Abstract—In the fifth-generation mobile communications system (5G), wireless connections among numerous Internet of things (IoT) devices will be accommodated in the massive machine-type communications (mMTC) scenario. To realize such massive connectivity, non-orthogonal multiple access (NOMA) technologies have been proposed for 5G. As one of the NOMA schemes, we have proposed a grant-free sparse chaos code multiple access (GF-SCCMA) scheme exploiting the principle of chaos communications for mMTC. It realizes both physical layer security and large-capacity transmission. However, in conventional studies, a message-passing algorithm (MPA) was used in the receiver, which required relatively high calculation complexity, and the maximum number of users in GF-SCCMA was limited to approximately 10. Therefore, we propose an application of the Gaussian belief propagation (GaBP) algorithm for user signal detection to realize a large-scale transmission of more than 50 users with low calculation complexity. The improved transmission performances are shown through numerical simulations, by comparison with a conventional grantfree low-density signature scheme. Keywords—5G; non-orthogonal multiple access scheme; chaos; physical layer security; Gaussian belief propagation; turbo code.

I. INTRODUCTION In the fifth-generation mobile communications system (5G), not only in the enhanced mobile broadband (eMBB) scenario, which provides large-capacity wireless communication in a similar manner as fourth generation (4G), but also the massive machine-type communications (mMTC) scenario, which accommodates wireless connections among numerous Internet of things (IoT) terminals, will be newly developed [1,2]. As technology to aid in realizing mMTC, non-orthogonal multiple access (NOMA) schemes have been proposed previously [3-6]. In NOMA, more than two users are non-orthogonally superposed at one wireless resource, such as the subcarrier, and both superposed signals are correctly decoded in the receiver when the signal waveform and decoding scheme are carefully designed. Consequently, the system capacity can be increased more than in orthogonal multiple-access schemes. Furthermore, in the mMTC uplink transmission, a grant-free access, in which the advanced control signaling between an IoT terminal and base station (BS) is simplified as much as possible, is desirable for energy saving in IoT devices. To meet these requirements,

Tetsuya Yamamoto Core Element Technology Development Center, Panasonic Corporation Saedo-cho, Tsuzuki-ku, Yokohama, Kanagawa 224-8539, Japan. [email protected]

Fig. 1. Secure 5G IoT uplink transmission by GF-SCCMA. low-density signature (LDS) [3] and sparse code multiple access (SCMA) [4] have been proposed. We have proposed a grant-free sparse chaos code multipleaccess (GF-SCCMA) scheme that has physical layer security in terms of computational security [7]. This is a secure NOMA scheme in which the codebook (transmission signal waveform) of each user is generated by the chaos equation, and only a legitimate user pair sharing a chaos common key can decode the received signal, as shown in Fig. 1. In addition, by creating a codebook that has a random Gaussian distribution, the error rate performance at the receiver is improved compared to conventional schemes. Unlike SCMA, an advanced and careful codebook design is not required in GF-SCCMA; thus, numberless codebooks can be created, which is suitable for grant-free massive IoT transmissions. In a conventional study [7], a message-passing algorithm (MPA) is used for user signal detection in the receiver, in which the log likelihood ratio (LLR) is recursively calculated, and an overloaded transmission of more than 100% (e.g., 150% of six user transmissions using four samples) can be realized. However, because an MPA is a quasi-maximum likelihood sequence estimation (MLSE) scheme that enables high performance in detection, the decoding complexity is an exponential to the number of users, such as MJ for the modulation index M and the number of users J, and approximately 10 user transmissions was maximum. Here, for a massive multiuser multiple-input multiple-output (MIMO) transmission, the Gaussian belief propagation (GaBP) algorithm using LLR is adopted as a low-complexity and highperformance user signal detection [8-11]. Utilizing this property, in this study, we propose an application of GaBP to GF-SCCMA, and achieve a large-

978-1-5386-6358-5/18/$31.00 ©2018 IEEE

u1 data

uJ data

u1 data

transmitter Turbo encoder

π

SCCMA mapping

Turbo encoder

π

SCCMA mapping

channel

IFFT

guard interval insertion

channel

LLR calculation

soft canceller

receiver Turbo decoder

+

uJ data

IFFT

guard interval insertion

Turbo decoder

+

π-1 π

π-1 π

AWGN + -

+ -

e n i b m o c

- extrinsic value

FFT

+ LLR calculation

soft canceller

guard interval deletion

channel estimation

- extrinsic value + GaBP demapper

Fig. 2. System model of proposed uplink GF-SCCMA. scaled (such as hundreds) and secure IoT uplink transmission in 5G. Subsequently, by comparing the performance to conventional GF-LDS, we clarify the effectiveness of the proposed scheme. In the following, the proposed GF-SCCMA system using the GaBP is described in section II, numerical results are shown in section III, and conclusions are drawn in Section IV. II. LARGE-SCALED GF-SCCMA SYSTEM Fig. 2 shows the proposed turbo-coded GF-SCCMA system. J users or IoT terminals transmit data in an uplink grant-free manner. Here, we assumed that the frame timing among users and the BS are synchronized even in the grant-free transmission [12]. The bits transmitted by each user are turboencoded, interleaved, and modulated by the SCCMA mapper. The mapped signals are called the codebook. Subsequently, the codebooks are non-orthogonally superposed to the subcarriers, transformed into the time domain with an inverse fast Fourier transform (IFFT), and transmitted by an orthogonal frequencydivision multiplexing (OFDM) scheme. In the receiver BS, the received signals are transformed into the frequency domain with a fast Fourier transform (FFT), and each set of the user data is demodulated by a GaBP-based SCCMA demapper. In the GaBP demapper, parallel interference cancellation (PIC) and LLR calculations are recursively conducted, and the a posteriori LLR is obtained. Subsequently, after de-interleaving, the output LLR is transferred to the turbo decoder, and the outer iterative decoding is conducted between the SCCMA demapper and the turbo decoder. Finally, the bit decision is made by the output LLR at the turbo decoder. Here, we assumed that the codebook of the SCCMA is shared between the transmitter and receiver. In particular, the initial chaos value and the nonzero sample location in the codebooks are known to the BS. To conduct this process, the indices of the initial chaos value and the nonzero sample location are transmitted by advanced preambles such as the sounding reference signals (SRSs) or demodulation reference signals (DMRSs) [13, 14], as well as the conventional grant-free schemes. Here, key sharing is required between the BS and users, but unnecessary among users . Thus, the security among users is ensured. The number of antennas is assumed to be one both for the BS and for each terminal. A. Transmitter structure User (1 ≤ ≤ ) conducts turbo coding and interleaving,

divides the sequence into log2 M bits according to the modulation index M, and modulates them with an SCCMA mapper. Subsequently, each user’s modulated signal is transmitted simultaneously. Let = ( ,⋯, ( ∈ ) ), {0,1} ( = 1, ⋯ , log ) be the transmit bits of user j before SCCMA mapping. The corresponding codebook is assumed to be = ( , ⋯ , ) , xij ∈ ℂ, where K is the number of transmit samples. In GF-SCCMA, b j is mapped to Nj-dimensional ( N j < K ) nonzero complex samples c j by = ( ,⋯, ) = ( ), (1) where g j is the multi-dimensional chaotic constellation function [7]. Subsequently, the codebook x j is obtained by x j = V j c j = V j g j (b j ), (2) K×N

where V j ∈ B j is the binary mapping matrix that determines the locations of the nonzero samples within the set of K total samples. Thus, the log2 M bits are mapped to K-sample codebooks consisting of Nj nonzero samples. When Nj is small, the codebooks for the M-ary bit sequence become sparse. In addition, V j limits the interference caused by the nonorthogonal superposition at the receiver, and the detection performance is improved. In a grant-type LDS and SCMA, Nj and V j are pre-designed and fixed to suppress the inter-user interference. While in GF-SCCMA, Nj and V j can be determined by each transmit user to realize grant-free transmission, and no harmonization among users is conducted. In the system shown in Fig. 2, each sample xkj of x j is allocated to a subcarrier of the OFDM. As it is with both LDS and SCMA, overloaded transmission, J > K , is available for the GF-SCCMA scheme, which is more frequency-effective than either orthogonal frequency multiple access (OFDMA) or the single-carrier frequency division multiple access (SCFDMA). The nonzero SCCMA samples have a quasi-Gaussian distribution generated by the chaos equation. A detailed description of the multi-dimensional chaotic constellation function of SCCMA [7] is omitted owing to space limitation. Fig. 3 shows a snapshot of the SCCMA codebooks x j , where = 2, and the average powers = 48, = 32, = 4, and of all codebooks are normalized to one. As shown, the distribution of the codebook samples is quasi-Gaussian. B. User signal detection using GaBP in the receiver When J users transmit SCCMA codebooks in the uplink, 1.2

Q

0.8 0.4

-1.2

-0.8

0 -0.4 0 -0.4

I 0.4

0.8

1.2

-0.8 -1.2

Fig. 3. Snapshot of SCCMA codebooks.

the received signal at the BS is given by J

y=



α k , j,m = −

( )

(3)

diag h j x j + n,

j =1

= ( ,⋯, ) is the received signal, = (ℎ , ⋯ , ℎ ) is the channel vector between user j and the BS, and = ( , ⋯ , ) is the zero-mean complex Gaussian noise.

where

When the transmit codebook vector for all users is described as = ( , ⋯ , ) , the BS tries to estimate the transmit vector from y as ˆ = arg max p(X y ) X (4) X

The calculation complexity increases exponentially according to J with the maximum a posteriori (MAP) criterion; in a largescale system, the calculation complexity becomes diverged. Therefore, we conduct the approximate calculation of (4) using the GaBP. First, focusing on one nonzero sample out of Nj samples at user j, PIC is conducted using a replica subtraction generated by the a priori LLR of other users, which is all zero at the first iteration. Next, the symbol LLR is calculated for the target interference-cancelled sample of user j. Subsequently, combining Nj symbol LLRs, the a posteriori LLR of user j is obtained. This operation is conducted for all J users. Next, the extrinsic LLR is obtained by subtracting the priori LLR from the a posteriori LLR, and it is fed back to the PIC operation as the a priori LLR. This iterative calculation is conducted several times, and finally, the a posterior symbol LLR is obtained as the output of the GaBP. Subsequently, it is transformed into the a posteriori bit LLR, and transferred to the latter turbo decoder. When we focus on the k-th received nonzero sample ( 1 ≤ k ≤ K ) of user j, other user interferences are cancelled in parallel from y k by PIC as follows: ykj = yk −

h

~ j ∈ξ k \ j

ˆ ~ ~x kj k j

(5)

Here, = ∈ (1, … , )| ≠ 0 is the nonzero superposed user group at the k-th sample. When F is defined as a factor graph matrix [4] that connects a nonzero sample position and corresponding users as

(

)

= ( , ⋯ , ), f j = diag V j VTj ,

(6)

user j transmits a nonzero sample at k when (F ) jk = 1 , and corresponds to the k-th row of F . xˆk ~j is the k-th replica signal of user j, given by xˆk ~j = tanh βk , ~j ,m − βk, ~j , m xk ~j , m

[

1

Here, β k , ~j , m is the m-th (1 ≤

2



]

1

(7)

) a priori symbol LLR of

~ user j at the k-th received sample, and xk ~j ,m is the k-th ~ sample of the m-th codebook at user j . At the first iteration,

these a priori symbol LLRs are zero. m1 and m2 are the first and second decoding candidates, respectively, which are given by m1 = arg max β k , ~j , m , m2 = arg max β k , ~j , m (8) m

m \ m1

Next, the a posteriori symbol LLR at the k-th sample of user j is calculated by

σ k2, j =

1 2σ k2, j

ykj − hkj xkj , m

 h (1− tanh [β 2

~ j ∈ξk \ j

2

~ kj

~ k , j ,m1

2

(9)

])

− βk , ~j ,m xk ~j ,m 2

1

2

(10)

These calculations of (9) and (10) are conducted for all k and j. Subsequently, the a posteriori symbol LLR β j, m for user j is obtained by combining α k , j , m as β j,m =

α

(11)

k , j,m

k

For the iterative calculation in the GaBP, a damping operation can prevent the generation of outlier LLR [15-17], and the damped extrinsic symbol LLR is used for the i-th iteration: βk(i,)j,m = η β j,m −αk , j,m + (1−η )βk(i, −j,1m) (12)

(

)

Here, η is the damping factor and set to 0.5 in this study. The () , ,

is used as the a priori symbol LLR in (7). After iterating the PIC and LLR calculations of α k , j , m and βk , j , m , the decoded

ˆ of user j is finally determined by symbol m mˆ = arg max β j , m

(13)

m

ˆ is transformed to the corresponding To obtain the bit LLR, m bit sequence, and its signs are multiplied by the amplitude factor , which are given by = max , , = max , , = − (14) ∖

The obtained bit LLR is used as the a posteriori bit LLR of user j. Using the GaBP algorithm, the low-complexity user signal detection for large J and K can be conducted. The maximum calculation order of a posteriori symbol LLR for a user under grant-free transmission is O { + } in GaBP, while that of ( ) . Then, for a large J, only GaBP becomes MPA is O a practical algorithm. The output bit LLR of the GaBP detector in Fig. 2 is transferred to the outer turbo decoder after it is converted to the a priori LLR and de-interleaved. The output extrinsic LLR of the turbo decoder is transformed into the symbol LLR and handed to the GaBP detector. After iterating this outer turbo loop, the decoded bit is obtained by the a posteriori bit LLR of the turbo decoder. III. NUMERICAL RESULTS We evaluated the performance of the proposed scheme by link-level numerical simulations and compared it with the conventional GF-LDS, where the same random factor graph matrix F is used as GF-SCCMA. Table 1 shows the basic simulation conditions. The number of maximum users J and the number of samples K are 64 and 32, respectively, that is, 200% overloaded at the maximum. Here, the extension to more than 100 users with larger K is straightforward. The channel is assumed to be the pass-loss, shadowing, and quasi-static multipath fading channel in a single non-sectorized hexagonal cell. The iteration number of the GaBP is fixed to 15, and the number of nonzero samples Nj is the same for all users. We assumed that the mapping matrix V j is randomly generated by

Table 1. Basic simulation parameters. access

Modulation No. of samples No. of users (layers) at maximum No. of weights (row, column) in F at the maximum Transmission No. of subcarriers No. of data blocks No. of guard interval Cell layout User location Channel Channel estimation Constellation function Multi-user detection algorithm No. of detection iteration Outer channel coding Channel decoding Error detection Outer decoding iteration

1.E+00

Conventional GF-LDS

Proposed GF-SCCMA Chaos-based QPSK, M = 4 codebook, M = 4 K = 32

J = 64 (J, K)

15 fixed Rate 1/2 punctured turbo code, code length = 1024 BCJR MAP decoding with 8 iterations CRC-16 in turbo code 1

Block error rate

1.E-01 M = 4, K = 32, J_A = 48 8 path fading channel avg. SNR at cell edge = 16 dB GaBP 15 iteration turbo coded

GF-LDS GF-SCCMA

1.E-03 0

5

10 15 20 No. of nonzero samples N_j

GF-SCCMA, J_A = 32 GF-LDS, J_A = 32

1.E-02

GF-SCCMA, J_A = 40 GF-LDS, J_A = 40

Multi-carrier (OFDM) 16384 16384 subcarriers = 32 samples x 512 blocks 8 samples Non-sectorized hexagonal single cell model Randomly distributed Path loss exp. = 3.5, Standard deviation of shadowing loss = 7 dB, 1-dB decaying 8-path i.i.d. quasi-static Rayleigh fading perfect 2 ( − 1)⁄( ), None j = 1,..,J Gaussian belief propagation with damping

1.E+00

1.E-02

1.E-01

Bit error rate

Multiple scheme

25

30

Fig. 4. BLER performance comparison versus the number of nonzero samples Nj. each user every time, and F is informed to the BS every time via any preambles. The turbo codeword was allocated in the frequency direction for one OFDM frame. The number of outer turbo iterations between the GaBP detector and the MAP decoder of the turbo code was one. Here, the turbo codeword includes CRC-16 binary bits, and the normalized throughput based on a CRC check was calculated. The throughput became one when one sample was transmitted by one subcarrier, i.e., the throughput became one for error-free orthogonal multiple access schemes.

1.E-03

M = 4, K = 32, J_A = 32, 40 8 path fading channel GaBP 15 iteration turbo-coded

1.E-04 0

5

10 15 Avg. SNR at cell edge per user in dB

20

Fig. 5. Bit-error-rate performance versus average SNR at cell edge where the number of transmitting user is 32 and 40. Fig. 4 shows the block error rate (BLER) versus the number of nonzero samples Nj where the number of transmitting users is = 48, and the average SNR at the cell edge is 16 dB. As shown, in GF-LDS, the best performance is obtained at Nj = 4 and the BLER is rapidly degraded in other configurations. In contrast, in GF-SCCMA, good performance is widely obtained in large Nj regions, in which many low-amplitude nonzero samples are transmitted, as in code division multiple access (CDMA). That many nonzero samples are better in GFSCCMA could be because the codebook of GF-SCCMA are composed of random Gaussian signals unlike QPSK of LDS; further, a more pronounced spreading diversity effect is obtained when using many nonzero samples in (11) of the GaBP. When the lowest BLER is compared in the figure, GFSCCMA has a slightly better performance. This is because the output LLR of the GaBP satisfies the consistency condition better [18] in the proposed scheme owing to the Gaussian codebook, which improves the outer turbo code performance. This CDMA-like transmission can suppress a large-peak waveform in the transmitter and is effective for the energy saving of IoT terminals. Fig. 5 shows the bit error rate versus the average SNR at the cell edge where Nj = 4 for LDS and 20 for SCCMA, obtained from the result of Fig. 4, and the number of users is = 32 and 40. As shown, SCCMA has the better performance at high SNR regions. Therefore, the proposed scheme is superior to LDS at high SNR areas even in an overloaded transmission. Fig. 6 shows the BLER and normalized throughput versus the number of transmitting users where the average SNR at the cell edge is 16 dB. The performance is similar to previous results in that the proposed scheme has a slightly better performance. However, when it is compared in the normalized throughput in Fig. 6(b), both are almost the same and no clear difference was found. Subsequently, we evaluated the security ability of GFSCCMA by calculating the BLER versus the similarity of the common key. The result is shown in Fig. 7, where the horizontal axis is the squared Euclidean distance from the initial key signal at the transmitter, i.e., the larger value in the horizontal axis means the closer key at the receiver of the eavesdropper. Here, the floating-point operation is assumed. It

realizes an energy-efficient, secure, and large-scaled IoT communication in the 5G mMTC scenario.

1.E+00 GF-LDS, N_j = 4 GF-SCCMA, N_j = 20 1.E-01

IV. CONCLUSIONS

Block error rate

M = 4, K = 32 8 path fading channel avg. SNR at cell edge = 16 dB GaBP 15 iteration turbo coded

1.E-02

We proposed a large-scale GF-SCCMA using lowcomplexity GaBP-based user signal detection. The nonorthogonal quasi-Gaussian codebooks were constructed based on chaos signals, and the common key encryption was created at the physical layer. Subsequently, both transmission performance improvement and physical layer security were obtained. Because the proposed scheme does not require a twoway authentication process or upper layer encryption operation, GF-SCCMA is suitable for energy-efficient, grant-free, and secure massive IoT communication in 5G. In future studies, an EXIT chart analysis [18] of GFSCCMA with an outer turbo code will be considered, and a better coding configuration will be created according to the EXIT chart analysis.

1.E-03

1.E-04 0

10

20 30 40 No. of transmit users J_A

50

60

(a) 2.0 M = 4, K = 32 8 path fading channel avg. SNR at cell edge = 16 dB GaBP 15 iteration turbo coded

Normalized system throughput

1.8 1.6 1.4

REFERENCES [1]

1.2 1.0

[2]

0.8

[3]

0.6 GF-LDS, N_j = 4

0.4

[4]

GF-SCCMA, N_j = 20

0.2

[5]

0.0 0

10

20 30 40 No. of transmit users J_A

50

60

[6]

(b)

Fig. 6. Performance comparison versus the number of transmitting users; (a) BLER, (b) normalized throughput.

[7]

1.E+00

[8]

Block error rate of eavesdropper

Block error rate

Block error rate of legitimate user

[9]

1.E-01

[10] M = 4, K = 32, J_A = 48 8 path fading channel avg. SNR at cell edge = 16 dB GaBP 15 iteration turbo coded

1.E-02

[11]

[12]

1.E-03 20

25 30 35 squared error distance of initial chaos signal 10^{-x}

40

Fig. 7. BLER changes versus squared error distance of initial chaos signal. is shown that the BLER is almost one until the key approached an error magnitude of 10-33, and the physical-layer common key encryption was achieved unless the copied key was exactly the same as the original. Consequently, we confirmed that the proposed GF-SCCMA with the outer turbo code has better transmission performance than the conventional GF-LDS, and a physical layer security. It

[13] [14] [15] [16] [17] [18]

ITU-R, Recommendation M.2083 : IMT Vision - "Framework and overall objectives of the future development of IMT for 2020 and beyond,” Sept. 2015. 5GMF White Paper, “5G Mobile Communications Systems for 2020 and beyond, ” ver. 1.0.1, July 2016. R. Hoshyar, F. P. Wathan, and R. Tafazolli, "Novel Low-Density Signature for Synchronous CDMA Systems Over AWGN Channel," IEEE Trans. Signal Processing, Vol. 56, No. 4, pp. 1616-1626, Apr. 2008. H. Nikopour and H. Baligh, “Sparse code multiple access,” Proc. IEEE Int’l Symp. Personal Indoor and Mobile Radio Communications (PIMRC), pp. 332-336, Sept. 2013. C. Yan, Z. Yuan, W. Li, and Y. Yuan, “Non-Orthogonal Multiple Access Schemes for 5G,” ZTE Communications, vol. 14, no. 4, pp. 1116, Oct. 2016. K. Higuchi and A. Benjebbour, “Non-orthogonal Multiple Access (NOMA) with Successive Interference Cancellation for Future Radio Access,” IEICE Trans. on Commun., vol. E98-B, no.3m pp. 403-414, Mar. 2015. E. Okamoto, N. Horiike, and T. Yamamoto, "Sparse Chaos Code Multiple Access Scheme Achieving Larger Capacity and Physical Layer Security," Proc. International Symposium on Wireless Personal Multimedia Communications (WPMC 2017), pp. 1-7, Dec. 2017. A. Chockalingam, “Low-Complexity Algorithms for Large-MIMO Detection,” Proc. International Symposium on Communications, Control and Signal Processing (ISCCSP), pp.1-6, Mar. 2010. A. Chockalingam and B.S. Rajan, “Large MIMO Systems,” Cambridge University Press, 2014. D. Pham, K.R. Pattipati, P.K. Willett, and J. Luo, “A Generalized Probabilistic Data Association Detector for Multiple Antenna Systems,” IEEE Commun. Lett., vol.8, no.4, pp. 205-207, Apr. 2004. W. Fukuda, T. Abiko, T. Nishimura, T. Ohgane, Y. Ogawa, Y. Ohwatari, and Y. Kishiyama, “Low-Complexity Detection Based on Belief Propagation in a Massive MIMO System,” Proc. IEEE Vehicular Technology Conference (VTC 2013-Spring), pp.1-5, June 2013. C. Bockelmann et al., "Massive Machine-Type Communications in 5G: Physical and MAC-Layer Solutions," in IEEE Communications Magazine, vol. 54, no. 9, pp. 59-65, Sept. 2016. R1-1609446, “Reference Signal Design for UL Grant-Free Transmission,” Huawei, HiSilicon, 3GPP RAN1#86-BIS, Oct. 2016. R1-1700691, “On Reference Signal Design for Grant-free Access,” Ericsson, 3GPP RAN1-NR#1, Jan. 2017. M. Pretti, "A Message-Passing Algorithm with Damping," Journal of Statistical Mechanics: Theory and Experiment, vol. 2005, no. 11, p. P11008, Nov. 2005. P. Som, T. Datta, A. Chockalingam, and B. S. Rajan, “Improved LargeMIMO Detection based on Damped Belief Propagation,” in Proc. ITW 2010, pp. 1-5, Jan. 2010. T. Takahashi, S. Ibi and S. Sampei, "On Normalization of Matched Filter Belief in GaBP for Large MIMO Detection," Proc. IEEE Vehicular Technology Conference (VTC-Fall2016), pp. 1-6, Sept. 2016. J. Hagenauer, “The Exit Chart - Introduction to Extrinsic Information Transfer in Iterative Processing," Proc. 12th European Signal Processing Conference, pp. 1541-1548, 2004.