EFFECT OF OUTER BLOCK INTERLEAVING IN TURBO CODES PERFORMANCE OVER RAYLEIGH FADING CHANNELS FOR 3GPP Costas Chaikalis, Felip Riera-Palou, James M Noras University of Bradford, Dept. of Electronics & Telecomms, BD7 1DP, Bradford, UK,
[email protected]
Abstract - Outer block interleaving improves the performance of turbo codes in correlated Rayleigh fading channels. The longer the outer interleaver, the better is the performance, with the penalty of more delay. Power could be saved by choosing the optimum interleaver for different operating environments. In this paper the four possible outer block interleaver lengths specified for 3GPP are examined for correlated Rayleigh fading channels with different normalized fade rates fdTS. SOVA and log-MAP algorithms are used in the turbo decoder, with a turbo interleaver length of 5114 bits. Our results show that choosing a TTI of 40 msec instead of 80 msec does not make a very large difference in performance, while the highest performance gain occurs for a TTI of 20 msec. We discuss the selection of the optimum interleaver length for the same bit-rate, but different scenarios. Keywords - Turbo codes, iterative decoding, outer block interleaving, correlated Rayleigh fading channel, WCDMA (UMTS) I. INTRODUCTION During the past few years, turbo codes have attracted considerable attention because of the large coding gains they can achieve in an additive white Gaussian noise (AWGN) channel [1]. For wireless communication systems, turbo codes have also been shown to provide impressive coding gains in fading channels [2], [3], [4]. In correlated Rayleigh fading channels performance can be greatly improved if outer block interleaving is used [2], [3], [4]. Outer block interleaving is required because turbo encoding may not be sufficient to cope with the errors induced in a correlated fading channel, which tend to produce burst errors. Turbo codes are more effective with random errors, so the outer block interleaver is needed to break up the burst errors of the correlated fading channel. Furthermore, according to [2] perfect interleaving over a long period for correlated Rayleigh fading can approximate the performance of the uncorrelated Rayleigh fading channel. Turbo codes have been adopted as a channel coding scheme in a number of mobile systems, one being 3GPP (third generation partnership project) for high data rates. This paper considers the different outer block interleaver lengths specified in 3GPP, and proposes interleaver lengths which
0-7803-7589-0/02/$17.00 ©2002 IEEE
are optimum in terms of performance and complexity for correlated Rayleigh fading channels. II. DATA TRANSFER IN 3GPP The way that the information is transferred over the radio interface from the MAC (Medium Access Control) sub-layer of layer 2 to the physical layer defines a transport channel [5], [6]. The characteristics of a transport channel are determined by its TF (transport format) or TF set, specifying the physical layer processing to be applied to the particular transport channel. Thus, data exchange between the MAC and the physical layer is defined in terms of transport block sets, defined as the number of input bits in the turbo encoder. On a transport channel, one transport block set can be transmitted every TTI (time transmission interval). A transport block set consists of one or several transport blocks, and a TTI is defined as the maximum allowed time to transmit a transport block set. In other words, TF is a format offered by the physical layer to MAC (and vice versa) for the delivery of a transport block set during a TTI on a particular transport channel. The TF consists of two parts: dynamic and semi-static. Attributes of the dynamic part are: •
Transport block size
•
Transport block set size (number of bits in a transport block set)
Attributes of the semi-static part are: •
TTI
•
Type of channel coding and rate
•
Static rate matching (specifies the amount of rate matching to apply relatively to other parallel transport channels)
Each transport channel is assigned a TF set [5], [6]. A TF set contains several different dynamic parameters defining different TFs, but the semi-static parameters are the same. A mobile terminal may use several parallel transport channels simultaneously, each having its own TF set. For example one transport channel can be used for control signalling, another for a speech service and another for a video service. These transport channels are multiplexed onto the same physical channel. The combination of TFs used at a given
PIMRC 2002
time on parallel transport channels is called TFC (transport format combination). It consists of one TF per transport channel. The set of allowed TFC is called a TFC set. Given the TFC set, the MAC sub-layer can select between TFC, depending on the priorities mapped onto the corresponding transport channels. For example, a real-time service will have a higher priority than a non-real-time service. A field in each frame at the physical layer called TFCI (transport format combination indicator) points to the TFC used in this particular frame within the TFC set. Detecting the TFCI bits, the physical layer on the receiver can decode and transfer the information on the appropriate transport channels.
B. Channel The encoded bits are transmitted over the communications channel as shown in figure 1. With appropriate sampling, the discrete representation of this channel is rk=akyk+nk where k is an integer symbol index (k=3i), yk is a BPSK symbol amplitude and nk is a AWGN component with zero mean and power spectral density No/2. The variable ak is a fading amplitude that may vary from code bit to code bit. For the correlated Rayleigh fading channel model ak is modeled with a Rayleigh pdf, p(ak)=2akexp(-ak2) for ak>0 using Jake’s model as in [8]. C. Decoder
III. SYSTEM MODEL The system model that is used for the simulations is shown in figure 1. The 3GPP standard parameters are used [7]. The information bits ui are grouped into frames whose length must be ≥40 and ≤5114. Our simulations use frames of 5114 bits. The output bits of the turbo encoder are then block interleaved. According to the 3GPP standard the frame duration is 10, 20, 40 or 80 msec, which means that the outer block interleaver has 1, 2, 4 or 8 columns respectively [7]. It is obvious that in the case of 10 msec there is no outer interleaving. As was mentioned before, the frame duration is also called TTI and corresponds to the maximum allowed time to transmit the bits of the frame. After block interleaving, the bits are modulated using a Binary Phase Shift Keying (BPSK) modulator.
A simplified diagram of the turbo decoder [1], [2], [3] that neglects the details of interleaving and deinterleaving is presented in figure 2. Turbo decoding is performed iteratively, with each soft input-soft output (SISO) decoder using information from the previous step. The two main candidate algorithms used in the SISO decoder are SOVA (soft output Viterbi algorithm) and log-MAP (log maximum a posteriori algorithm). Log-MAP gives better performance than SOVA, but SOVA is less complex, resulting in lower latency [9]. Eight decoder iterations are used. It must be mentioned that the simulations use a scaling factor s=0.7 in both algorithms in order to scale the extrinsic information in the turbo decoder. Our simulations show that this improves the performance compared to the standard algorithms (s=1) with minimal effort [10].
The receiver has exact estimates of the fading amplitudes (perfect channel estimation is assumed). Furthermore, the received signal is not quantized (floating point arithmetic is used). Then the symbols rk are BPSK demodulated, block deinterleaved and then turbo decoded. The output of the turbo decoder is an estimate ui´ of the information bit ui.
s
p1
ui
Turbo encoder
Block interleaver
BPSK modulator
x xs
yk
z1
SISO DEC 1
Lex1
s
Lex2 z2 xp2
SISO DEC 2
u´
ak nk Turbo decoder
ui´
Block deinterleaver
BPSK demodulator
xi
rk Fig. 1. System model
A. Encoder The turbo encoder [1], [2], [3], [7] is made up of two ½ rate Recursive Systematic Convolutional (RSC) encoders, each with constraint length K=4 and octal polynomials 13 (feedback) and 15 (redundancy). The two encoders are concatenated in parallel and separated by an interleaver whose parameters are specified in [7]. The rate of the encoder is assumed to be 1/3. No tailing scheme is applied.
Fig. 2. Decoder diagram Using Λ i from (6) for log-MAP or (9) for SOVA the extrinsic information Lexi is calculated. After interleaving, this provides a priori information in the other SISO decoder: Λ 4 ⋅ αi ⋅ E s s Lex i = i − yi − zi ⋅ s No 2
(1)
where α i is the fading amplitude for symbol i and Es/No is the signal to noise ratio.
IV. TURBO DECODING ALGORITHMS
For SOVA, equation:
A. Log-MAP algorithm For a code with rate 1/3 the branch metrics are calculated as follows: For DEC 1: D (s i , s i +1 ) = x si ( z i + y si ) + x ip1 ⋅ y ip1 For DEC 2: D (s i , s i +1 ) = x si ( z i + y si ) + x ip 2 ⋅ y ip 2
(2)
where xs and xp1, xp2 are the systematic and the parity outputs of the turbo encoder respectively for the state transition si to si+1. The symbols ys and yp1, yp2 are received symbols, and zi is a priori information for symbol index i from the previous decoder. Applying the Jacobian logarithm to MAP results in log-MAP [2], [3], [9]:
(
max* (m, n ) = ln e m + e n
)
(
= max (m, n ) + ln 1 + e
− m−n
)
(3)
Here, m and n are real numbers. The forward state metric a(si) for state si and symbol i is calculated as follows: a (s i ) = max* (a (s i −1 ) + D (s i −1 , s i ) ) s i −1 ∈ Α
(4)
where A is the set of states si-1 connected to state si. The backward state metric b(si) is: b(s i ) = max* (b(s i +1 ) + D(s i , s i +1 )) s i +1∈B
Λ i is calculated according to the following
Λ i = (2 m i − 1)⋅ ρ i
(9)
where mi is the estimated bit sequence (hard decision) computed by tracing Γ (si) back in the trellis the survivor path, as in the Viterbi algorithm. For each node i along the surviving path, the competing path that was pruned at that node is traced back to the point where it initially diverged from the surviving path. The difference between the two paths metrics ∆ (si) is used to update the reliability ρ i of the bits that differ along the two paths (if the same decision is made along both paths for any particular bit, then the reliability is not reduced and therefore not updated). V. SIMULATION RESULTS In the simulations a carrier frequency of 2 GHz is assumed, while an uncorrelated Rayleigh channel is used for comparison purposes. Two input bit-rates are considered for the calculation of the normalized fade rate fdTS: 28.8 and 128 kbps according to [12]. A. Normalized fade rate fdTS=0.000019
(5)
where B is the set of states si+1 connected to state si. The soft output Λ i for symbol i is: Λ i = max* (a ( s i ) + D ( s i , s i + 1 ) + b ( s i + 1 ) ) − S1
max* (a ( s i ) + D ( s i , s i + 1 ) + b ( s i + 1 ) )
(6)
S0
where S1 and S0 are the sets of all state transitions associated with a bit 1 and 0 respectively. B. SOVA algorithm The branch metric calculation in SOVA is exactly the same as that for log-MAP in (2). For SOVA the state metric Γ (si) for the state transition si to si+1 is [2], [3], [11]: Γ (s i ) =
max (Γ (s i −1 ) + D (s i −1 , s i ) ) s i −1 ∈ Α
(7)
where A is the set of states si-1 connected to state si. The difference ∆ (si) between the two state metrics that are compared is: ∆ ( s i ) = max
s i −1 ∈ Α
min
s i −1 ∈ Α
(∆ ( s i − 1 ) + D ( s i − 1 , s i ) ) −
(∆ ( s i − 1 ) + D ( s i − 1 , s i ) )
(8)
Fig. 3. Performance of 3GPP turbo code over correlated Rayleigh fading with fdTS=0.000019 using SOVA and logMAP decoding algorithms for different outer block interleaver lengths, frame length 5114 bits, s=0.7 and 8 iterations In figure 3 the performance of our system for normalized fade rate fdTS=0.000019 for the four possible outer interleaver lengths is stated. A Doppler frequency fd=7.407 Hz (corresponding to a mobile speed of 4 km/h and an indoor or low range outdoor operating environment) and an
input bit-rate of 128 kbps (equivalent to a symbol rate of 384 Kbaud) are used. It can be observed that, either for SOVA or log-MAP, for a decrease of the TTI from 20 to 10 msec there is a power penalty of 1 dB at a BER of 5*10-3. For a decrease of the TTI from 80 to 40 msec and from 40 to 20 msec there is no performance gain at the same BER. B. Normalized fade rate fdTS=0.00024 For figure 4 the normalised fade rate is fdTS=0.00024. Other parameters used are a Doppler frequency fd=92.592 Hz (corresponding to a mobile speed of 50 km/h and an urban or suburban outdoor operating environment) and an input bit-rate of 128 kbps. Either for SOVA or log-MAP, for a decrease of the TTI from 80 to 40 msec, from 40 to 20 msec, and from 20 to 10 msec there are power penalties of 0 dB, 1.2 dB and 9 dB respectively at a BER of 10-3.
Fig. 5. Performance of 3GPP turbo code over correlated Rayleigh fading with fdTS=0.0012 using SOVA and logMAP decoding algorithms for different outer block interleaver lengths, frame length 5114 bits, s=0.7 and 8 iterations D. Normalized fade rate fdTS=0.0053
Fig. 4. Performance of 3GPP turbo code over correlated Rayleigh fading with fdTS=0.00024 using SOVA and logMAP decoding algorithms for different outer block interleaver lengths, frame length 5114 bits, s=0.7 and 8 iterations C. Normalized fade rate fdTS=0.0012 In figure 5 a normalized fade rate of fdTS=0.0012 is considered. A Doppler frequency fd=462.962 Hz (for a mobile speed of 250 km/h and a rural outdoor operating environment) and an input bit-rate of 128 kbps are used. With log-MAP, for a decrease of the TTI from 80 to 40 msec, from 40 to 20 msec, and from 20 to 10 msec there are power penalties of 0.35 dB, 2.7 dB and 6 dB respectively at a BER of 10-3. For SOVA the power penalties are 0.5 dB, 2.5 dB and 6 dB at the same BER.
Fig. 6. Performance of 3GPP turbo code over correlated Rayleigh fading with fdTS=0.0053 using SOVA and logMAP decoding algorithms for different outer block interleaver lengths, frame length 5114 bits, s=0.7 and 8 iterations For figure 6 fdTS=0.0053. The Doppler frequency is fd=462.962 Hz and the input bit-rate is 28.8 kbps (a symbol rate of 86.4 Kbaud). For log-MAP, for a decrease of the TTI
from 80 to 40 msec, from 40 to 20 msec, and from 20 to 10 msec there are power penalties of 0.8 dB, 1.8 dB and 2.8 dB respectively at a BER of 10-3. For TTI=80 msec the performance approaches the ideal case of the uncorrelated Rayleigh channel (1 dB difference). For SOVA, for a decrease of the TTI from 80 to 40 msec, from 40 to 20 msec, and from 20 to 10 msec there are power penalties of 0.35 dB, 1.7 dB and 2.8 dB respectively at the same BER. In this case the performance is 1.5 dB away from the uncorrelated Rayleigh channel. Therefore, as in [3] and [4], the performance improves as fdTS increases. Furthermore for a constant bit-rate and considering performance and complexity as parameters, an outer block interleaver with 1 column is recommended for figure 3, 2 columns for figure 4, while for figure 5 an interleaver with 4 columns is optimum. VI. CONCLUSIONS This paper shows how the outer interleaver length affects the performance of turbo codes for correlated Rayleigh fading channels in the 3GPP standard. Our simulations show that for both SOVA and log-MAP turbo decoding algorithms and for four normalised fade rates, we have the highest performance gain for a TTI of 20 msec. For TTI=40 msec the performance improves, but not as much as for 20 msec. Another useful observation is that choosing a TTI of 40 msec instead of one of 80 msec does not make a very large difference in performance. Finally, power could be saved if the optimum outer block interleaver length is chosen. Therefore, as a compromise between performance and complexity and for a constant bitrate of 128 kbps TTI=10 msec is recommended for indoor or low range outdoor operating environment. For an urban or suburban outdoor environment TTI=20 msec is optimum, while for a rural outdoor operating environment TTI=40 msec is recommended. REFERENCES C. Berrou, A. Glaviex and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes”, in Proceedings of IEEE ICC, Geneva, Switzerland, pp. 1064-1070, 1993 [2] J. P. Woodard and L. Hanzo, “Comparative study of turbo decoding techniques: An overview”, IEEE Trans. on Vehicular Technology, vol. 49, No. 6, pp. 2208-2233, November 2000 [3] M. Valenti, “Iterative detection and decoding for wireless communications”, PhD thesis, Virginia Polytechnic Institute and State University, July 1999 [4] E. Hall and S. Wilson, “Design and analysis of turbo codes on Rayleigh fading channels”, IEEE Journal on Selected Areas in Communications, vol. 16, No. 2, pp. 160-174, February 1998 [1]
H. Holma and A. Toskala, WCDMA for UMTS, Radio Access for Third Generation Mobile Communications, J.Wiley, Chichester, 2000 [6] M. Haardt, A. Klein, R. Koehn, S. Oestreich, M. Purat, V. Sommer and T. Ulrich, “The TD-CDMA Based UTRA TDD Mode”, IEEE Journal On Selected Areas In Communications, vol. 18, No. 8, pp. 1375-1384, August 2000 [7] 3GPP TS 25.212 V5.0.0, “Multiplexing and channel coding (FDD)”, Release 5, March 2002 [8] M. Patzold, U. Killat, F. Laue and Y. Li, “On the statistical properties of deterministic simulation models for mobile fading channels”, IEEE Trans. on Vehicular Technology, vol. 47, No. 1, pp. 254-269, February 1998 [9] P. Robertson, E. Villebrun and P. Hoher, “A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain”, in Proceedings of IEEE ICC, Seattle, USA, pp. 1009-1013, 1995 [10] C. Chaikalis, J. M. Noras and F. Riera-Palou, “Improving the reconfigurable SOVA/log-MAP turbo decoder for 3GPP”, in Proceedings of CSNDSP, Stafford, UK, July 2002 [11] J. Hagenauer and P. Hoher, “A Viterbi algorithm with soft outputs and its applications”, in Proceedings of IEEE GLOBECOM, Dallas, USA, pp. 1680-1686, 1989 [12] 3GPP TR 25.944 V4.1.0, “Channel coding and multiplexing examples”, Release 4, June 2001 [5]
