Discrete Adaptation Of Turbo Punctured Codes For ...

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Discrete Adaptation Of Turbo Punctured Codes For Hybrid-ARQ Kingsley Oteng-Amoako, Saeid Nooshabadi and Jinhong Yuan School of Electrical Engineering and Telecommunications University of New South Wales Sydney, NSW 2052, Australia

Abstract— The paper presents a process for assigning modulation and code rate in DS-CDMA for downlink throughput maximization. The system employed consists of a turbo encoder with PSK and QAM modulation with adaptation for slow-fading channels. The performance of the adaptation process is examined for 2-state, 4-state and 6-state sets of transmit parameters. The performance of the optimization process is verified through computer simulation. Index Terms - Hybrid-ARQ, AMC, adaptive, fading, diversity combining and turbo codes.

I. I NTRODUCTION Adaptive coding and adaptive modulation as subclasses of adaptive modulation and coding (AMC) are required in communication systems in order to achieve high-speed and high-spectrally efficient communications. Hybrid FEC/ARQ exists as an implementation solution for mobile systems due to the minimal additional implementation complexity required [1]. Turbo codes since their introduction in 1993, have been the focus of coding theoretic research as a FEC for next generation communications systems due to the near capacity performance of codewords [2] [3]. The performance of turbo codes has made it ideal for hybrid-ARQ. Next generation mobile systems, including W-CDMA and CDMA-2000 have adopted AMC as a means of providing high-speed transmissions [4]. In addition, the use of diversity combining in order to improve spectral efficiency in downlink transmission has been considered in high speed downlink packet access (HSDPA) and 1xEV-DV [5]. Diversity combining essentially collects the energy of information bits over multiple transmissions of a codeword, thereby minimizing the likelihood of error during decoding. There are two main categories of diversity combining, punctured coding such as incremental redundancy employing rate-compatible punctured turbo codes (RCPT) [6] [7] and repetition coding techniques such as metric-ratio combining or Chase combining [8] [9]. Given suitable channel state information (CSI), the transmitter is capable of optimizing transmit parameters in order to achieve high spectrally efficient communications. Previous research into AMC, has examined efficient systems in a wireless channel by adaptation of code rate and power level [10]. Further research has compared and contrasted the performance of adaptive power systems and adaptive rate systems [11].

Adaptation based on a fixed set of coding rates and a fixed set of power levels with discrete information cut-off was considered in [12]. An adaptation policy by a discrete code rate with continuous power levels was presented in [13]. The following work presents an adaptive strategy with consideration of DS-CDMA system parameters. The work extends previous research in [14]. The paper is organized as per the following. In section II, the system is presented. In section III, the problem description is presented along with a discrete quantization of the channel. In section IV, the proposed solution to the problem is presented. In section V, simulation results for 2-state, 4-state and 6-state discrete transmitter parameter adaptation are given. The paper concludes in sectionVII. II. S YSTEM M ODEL A simplified DS-CDMA system employing turbo hybridARQ is shown in figure 1. Information bits are initially encoded by a turbo encoder. In this paper, a binary turbo code of length n corresponding to k information bits are employed, such that the rate R is given by k/n . The key code is a rate 1/3 mothercode and punctured accordingly. The data is interleaved before mapping to a QPSK or M-QAM signal constellation. In DS-CDMA, the transmission channel is multi-user shared. The orthogonality of individual users in the forward link is achieved by spreading the information data through a user-specific pseudorandom sequence. In the system, channel code gain and spreading gain are simultaneously obtained. Pilot symbols for channel estimation are timemultiplexed at the beginning of each slot. The coded data sequence and pilot symbols are spread by a channelization code and long scrambling code of a spreading factor length, SF. The channel considered is a non frequency-selective flat fading channel. Coherent receiver reception is assumed in the analysis (i.e. the receivers perform channel estimation on receipt of codewords, such that the channel conditions can be assumed known for all decoding attempts). At the receiver, the time delay and fading coefficient gains of each resolved path are estimated based on the despread pilot symbols. Thus assuming QPSK modulation the received signals is expressed as Y = αX + N (1)

ACK/NAK feedback from RX

Fig. 1.

Signal Spreading

Signal pilot

S ignal constellation map

Interleaver

Puncturing Matrix

Buffer

Turbo Encoder

CRC encoder

Binary Encoder

DS-CDMA Block

Spreading sequence

Adaptive turbo encoder and DS-CDMA transmitter .

ACK/NAK feedback from RX

Rake com bining

Sequence despread

Signal dem odulation

Deinterleaver

T urbo decoder

CRC Decoder

Buffer

Channel estimate

DS-CDMA Block .

Fig. 2.

DS-CDMA receiver and turbo decoder

where α is the channel fade coefficient, X is the transmitted signals, N is the zero mean additive white Gaussian noise processes of variance σ 2 . The received data sequence is feed into the decoder to recover the transmitted signal. A. Channel Capacity Consideration It is well-established that capacity, for an AWGN channel given the constellation mi and code rate Ri is expressed as · ¸ Es Ci = max Bwlog2 1 + Ri .mi . bits/s/Hz (2) N0 (Ri ,mi ) where Es /N0 is the symbol energy to the single sided noise spectrum ratio and Bw is the system bandwidth. The central goal of this paper is to select a code rate and modulation index to maximize the spectral efficiency. III. P ROBLEM D ESCRIPTION In order to simplify the transmit parameter optimization, it is initially assumed that both the available set of rates and the available signal constellations are continuous in nature. Thus the joint codeword and constellation optimization problem can be formulated as two separate sub-problems: 1) the selection of signal constellation based on a BER constraint and channel state information; 2) determination of the optimal code rate such that ergodic capacity is achieved.

A. Channel State Quantization In choosing the signal constellation and code rate for the channel, the channel is quantized into multiple channel state intervals. A quantized channel state is characterized by a mean fading coefficient. In the paper, the set of all possible fading coefficients is divided into (κ + 1) groups, resulting in (κ + 1) channel quantization intervals. The resulting ith quantization interval, denoted Γi corresponds to a channel with an average fading coefficient αi , which is bounded by a possible range of real values, αi−1 ≤ Γi ≤ αi+1 . Thus Γi is a random valued integer of probability density function f (Γi ) and the cumulative density function F (Γi ). The channel is further assumed to be slow-fading such that αi can be estimated and assumed constant over the period of a transmitted codeword. B. Adaptation Parameters Given a channel state quantization interval, Γi , the optimal adaptation policy is to select a unique code rate Ri and the number of bits per signal constellation mi for an observed fading coefficient αi . The following set of vectors are employed to represent the set of parameters on each transmit, Γ = [Γ0 , Γ1 , ..., Γi ] R = [R0 , R1 , ..., Ri ] y = [y0 , y1 , ..., yi ]

(3)

The corresponding set of optimized transmit parameters of (κ + 1) quantization intervals is expressed as Γ(R, m) = ([R0 , m0 ], [R1 , m1 ], ..., [Ri , mi ])

(4)

thus it is considered a maximisation of the instantaneous transmit spectral efficiency subject to the available transmit parameters.

A. Spectrally Efficient Signal Constellation Selection based on Supportable Rate Since the exact error performance of turbo codes is difficult to find, a conditional pairwise error probability is usually employed for the approximation [15] [16]. However, as turbo codes offer close to Shannon capacity performance, the performance bound for a high-ordered signal constellation is employed [17]. · ¸ −1.5y Po ≤ 0.2exp (5) mi − 1 where Po is the target BER constraint of the system. Thus the upper bound of the signal constellation in order to achieve capacity is given as ! Ã 1.5y 2mi ≤ 1 − (6) log(Po /0.2) where r is the data rate, SF is the spreading factor of the CDMA, y is the signal-to-noise ratio (SNR) and Po is the target BER constraint. B. Maximum Supportable Rate based on an Analytic Union Bound The problem of finding an optimal codeword rate that achieves ergodic capacity is now addressed. Given the quantization interval, Γi , a unique code rate and signal constellation pair is assigned in order to achieve the capacity bound. The optimized parameters of the quantization interval is expressed as, (7)

The channel capacity Ci of a given channel interval can be shown to be a monotonically increasing function of Es /No subject to a constrained Ri and mi . Hence, for the ith quantization interval, the required Es /No in (2) to achieve capacity is expressed as Es ≥ f (Ci , Ri , mi ) No

Bandwidth

1.25 MHz

Codeword length

3072 bits

Spreading Factor,SF Spreading Code Sequence utilization factor Max. iteration of Turbo decoder

IV. O PTIMUM R ATE AND M ODULATION A DAPTATION

Γ(Ri , mi ) = max(Ri , mi )

TABLE I DS-CDMA SIMULATION PARAMETERS

(8)

where the C is the capacity of a channel based on an average power constraint P given as Z Γi P (Γ)f (Γ)d(Γ) ≤ P (9) Γi−1

Thus the code rates applied in the adaptation algorithm are based on an average power constraint. Given that in CDMA,

4 Walsh-Haddamard sequence 0.8 8 iterations

Channel estimation at Rake receiver

Common Pilot Symbols

Channel reliability estimation

Dedicated Pilot Symbols

Max no of retransmit attempts

4

Channel model

4-path Rayleigh channel

Modulation Scheme

Adaptive

Code Rate

Adaptive

a spread-spectrum QAM symbol spans r.m.Bw/Ri chips, the SNR per transmitted chip required for capacity transmission is given by [18] [19], Ec r.f (Ci , Ri , Mi ) ≥ No Ri .log2 Mi .Bw

(10)

where Ec is the energy per transmitted chip. For a given spreading factor SF , the required data rate to satisfy (2) is calculated as, r = Υ.Ri .log2 Mi .Bw.SF

(11)

where Υ is the channel utilisation factor. Rearranging (11) for Ri gives the codeword rate required for capacity transmission given the spreading factor, data rate and modulation index. Thus the required code rate is given as r Ri ≥ (12) log2 Mi .Υ.Bw V. C ONSIDERATIONS IN S YSTEM I MPLEMENTATION A. Adaptation Constraints In the following section, the considerations for practical implementation of the adaptive system assuming a turbo code in a CDMA system are briefly described. In an idealized system, modulation and code rate are selected from a continuous set of possible parameters. In a practical system, the code rates and signal constellation can only be selected from predetermined values bounded [1, 1/3] and [2, 2M ] respectively. Hence it is assumed that modulation and code rate are discretized. Thus, Discrete Rates: Ri ∈ [1/3, 1) Discrete Signal Constellation: mi ∈ [2, 2mi ]

(13)

B. Information Outage considerations The principle of an information outage probability details that a code rate exceeding a threshold value for given channel conditions will be unsuccessfully decoded [20] [21]. In a practical system, the turbo encoder is constrained to a minimum code rate 1/3. Thus the code rate of the turbo encoder is lower bounded by, R ≥ 1/3. In the adaptation algorithm if a

code rate below 1/3 is required, the transmitter side assigns R = 1/3 and M = 4 in order to minimize the BER.

3.5 AWGN Ergodic Capacity Pe = 1E−1 Pe = 1E−3 Pe = 10E−6

3

In adpating the transmit parametrs, the algorithm is summarised as follows: Step 1: The channel is quantized based on κ channel state boundaries, such that at time i the channel state is Γi . Step 2: For a given Γ and Po , assign a mi based on (6). Step 3: For a signal constellation mi and the CDMA downlink transmitter parameters , assign Ri to Γi based on (12). Step 4: If Ri < 1/3, set (mi = mi /2) and go back to step 3. If Ri ≤ 1/3 and m = 4, the codeword is expected to produce errors at the receiver and the Po requirement is not guaranteed. Step 5: If channel conditions change, reselect mi and Ri by going back to step 3.

2.5 Channel Efficiency (bps/Hz)

C. Summary of Adaptation Scheme

2

1.5

1

0.5

0

0

1

2

3

4

5 SNR(dB)

6

7

8

9

10

9

10

(a) R = (2/3, 1/3) and m = (QPSK, 16-QAM) 3.5 AWGN Ergodic Capacity Pe = 1E−1 Pe = 1E−3 Pe = 1E−6

VI. S IMULATION R ESULTS 3

VII. C ONCLUSION

Channel Efficiency (bps/Hz)

2.5

2

1.5

1

0.5

0

0

1

2

3

4

5 SNR(dB)

6

7

8

(b) R = (2/3, 1/2, 2/5, 1/3) and m = (QPSK, 8-PSK, 16-QAM, 64-QAM) 3.5 AWGN Ergodic Capacity Pe = 1E−1 Pe = 1E−3 Pe = 1E−6

3

2.5 Channel Efficiency (bps/Hz)

The simulation employs a rate 1/3 turbo encoder based on parallel recursive systematic convolutional (RSC) encoders of generator polynomials (G1 , G2 ) = (37, 23)8 . The block size employed for the codewords before puncturing is n1 = 3072. Given the maximum transmission time of a codeword as t and the Doppler spread frequency as fd , it is assumed that fd t ¿ 0.1 and thus the channel is considered slow-Rayleigh fading. The performance of the adaptive algorithm is examined for 2-state, 4-state and 6-state sets of transmitter parameters as shown in figures 3(a), 3(b) and 3(c) respectively. It is observed that as Eb /No increases the adaptation algorithm responds by selecting transmit parameters that enable spectral efficiency improvement. It is observed that by increasing the number parameters available for adaptation at the transmitter, better spectral efficiency across the entire Eb /No range is achieved. Thus the 6-state adaptation achieves higher spectral efficiency than the 4-state and 2-state adaptation algorithms. The spectral efficiency of the system is observed to increase as a lower Po is employed at the receiver. Thus a system with Po = 10−1 has better spectral characteristics than systems with Po = 10−3 and Po = 10−6 respectively.

2

1.5

1

In this paper, an adaptive algorithm is presented for the discrete optimization of the signal constellation and code rate based on a bit-error-rate constraint for DS-CDMA systems. The throughput performance of the scheme was evaluated based on RCPT and multilevel signalling. It is concluded that an adaptive algorithm approaches capacity as the number of available signal constellations and code rates at the transmitter are increased. Further, higher throughput is achieved in the system when a lower bit-error-constraint is applied during adaptation.

0.5

0

0

1

2

3

4

5 SNR(dB)

6

7

8

9

10

(c) R = (4/5, 3/4, 2/3, 1/2, 2/5, 1/3) and m = (QPSK, 8-PSK, 16-QAM, 64-QAM) Fig. 3. Spectral efficiency of 2, 4 and 6 parameter sets of (R, m) employed in adaptation of DS-CDMA: solid line indicates ergodic capacity.

TABLE II T RANSMIT PARAMETERS SETS FOR DS-CDMA A DAPTATION IN R AYLEIGH FADING C HANNELS

TABLE III 2-S TATE PARTITION A DAPTATION AT Po = 10−1 SNR range (dB)

Assigned parameters (m,R)

Partitions

Code Rate

Modulation

0.0 - 3

QPSK, 1/2

2-state

2/3,1/3

QPSK, 16-QAM

3.2 - 50

16QAM, 1/3

4-state

2/3,1/2,2/5,1/3

QPSK, 8-PSK, 16-QAM, 64-QAM

6-state

4/5, 3/4, 2/3, 1/2, 2/5, 1/3

QPSK, 8-PSK, 16-QAM, 64-QAM

TABLE IV 2-S TATE PARTITION A DAPTATION AT Po = 10−3 SNR range (dB)

R EFERENCES [1] S. Lin and J. Costello, Error Control Coding Fundamentals and Application. Englewood Cliffs, NJ: Prentice-Hall, 1983. [2] C. Berroux and A. Glavieux, “Near optimum error correcting coding and decoding: Turbo-codes,” IEEE Commun. Lett., vol. 1, pp. 77–79, May 1997. Boston: Kluwer Academic [3] B. Vucetic and J. Yuan, Turbo Codes. Publishers, 2000. [4] “Physical layer aspects of utra high speed downlink packet access,” White Paper, 3GPP, May 2000. [5] A. Ghosh, L. Jalloul, M. Cudak, and B. Classon, “Performance of coded high order modulation and hybrid-arq for next generation cellular cdma systems,” in Proc. IEEE Vehicular Technology Conference (VTCFall’00), Sept. 2000, pp. 500–505. [6] D. N. Rowitch and L. B. Milstein, “Rate compatible puncture turbo (rcpt) codes in hybrid fec/arq,” in Proc. IEEE International Conference on Comm. Theory (Globecomm’97), Nov. 1997, pp. 55–59. [7] A. S. Barbulescu and S. S. Pietrobon, “Rate compatible punctured turbo codes,” IEEE Trans. Commun., vol. 44, pp. 591–600, May 1996. [8] D. Chase, “Code combining - a maximum likelidhood decoding approach for combining an arbitrary number of noisy packets,” IEEE Trans. Commun., vol. 33, pp. 385–393, May 1985. [9] K. Oteng-Amoako, J. Yuan, and S. Nooshabadi, “Selective hybrid-arq turbo schemes with various combining methods in fading channels,” in Proc. IEEE of Wireless Optimization in Mobile and Ad-Hoc Networks (WiOpt’03), Sohpia-Antipolis, France, Mar. 2003, pp. 290–294. [10] A. J. Goldsmith and S. Chua, “Variable-rate variable-power mqam for fading channels,” IEEE Trans. Commun., vol. 47, pp. 844–855, June 1999. [11] ——, “Capacity of fading channels with channel state information,” IEEE Trans. Commun., vol. 43, pp. 1985–1992, Nov. 1997. [12] S. Lin and P. S. Yu, “A hybrid arq scheme with parity retransmission for error control of satellite channels,” IEEE Trans. Commun., vol. 30, pp. 1701–1719, July 1982. [13] P. Bender, P. Black, M. Grob, R. Padovani, N. Sindhushyana, and S. Viterbi, “Cdma/hdr: A bandwidth efficient high speed wireless data service for nomadic users,” IEEE Commun. Mag., vol. 38, pp. 70–77, June 1999. [14] K. Oteng-Amoako, J. Yuan, and S. Nooshabadi, “Adaptation of turbo punctured codes for hybrid-arq,” in Proc. IEEE Vehicular Technology Conference (VTC-Fall’03), Florida, USA, Oct. 2003, to be published. [15] S. Benedetto and G. Montorsi, “Average performance of parallel concatenated block codes,” Electronic Letters, vol. 31, pp. 156–158, Feb. 1995. [16] ——, “Performance evaluation of turbo-codes,” Electronic Letters, vol. 31, pp. 163–168, Feb. 1995. [17] G. J. Foschini and J. Salz, “Digital communications over fading radio channels,” Bell Systems Tech. Journal, pp. 429–456, Feb. 1983. [18] S. J. Lee, H. W. Lee, and D. K. Sung, “Capacities of single-code and multicode ds-cdma systems accomdating multiclass service,” IEEE Trans. Veh. Technol., vol. 48, pp. 376–384, Mar. 1999. [19] D. G. Jeong, I. Kim, and D. Kim, “Capacity analysis of spectrally overlaid narroband and wideband cdma systems for future mobile communication services,” IEICE Trans. Commun., vol. E82-B, pp. 1334– 1342, Aug. 1999. [20] L. H. Ozarow, S. Shamai, and A. Wyner, “Information theoretic considerations for cellular mobile radio,” IEEE Trans. Veh. Technol., vol. 43, pp. 359–378, May 1994. [21] R. Knopp and P. A. Humblet, “On coding for block fading channels,” IEEE Trans. Inform. Theory, vol. 46, pp. 189–205, Jan. 2000.

Assigned parameters (m,R)

0.0 - 24.8

QPSK, 1/2

25 - 50

16QAM, 1/3

TABLE V 2-S TATE PARTITION A DAPTATION AT Po = 10−6 SNR range (dB)

Assigned parameters (m,R)

0.0 - 50

QPSK, 1/3

TABLE VI 4-S TATE PARTITION A DAPTATION AT Po = 10−1 SNR range (dB)

Assigned parameters (m,R)

0.0 - 3.2

QPSK, 2/5

3.4 - 6.6

8PSK, 1/3

6.8 - 29

16QAM, 1/3

29.2 - 50

64QAM, 1/3

TABLE VII 4-S TATE PARTITION A DAPTATION AT Po = 10−3 SNR range (dB)

Assigned parameters (m,R)

0.0 - 24.8

QPSK, 1/2

25 - 50

8PSK, 1/3

4-S TATE

TABLE VIII PARTITION A DAPTATION AT Po = 10−6

SNR range (dB)

Assigned parameters (m,R)

0.0 - 50

QPSK, 1/3 TABLE IX

6-S TATE PARTITION A DAPTATION AT Po = 10−1 SNR range (dB)

Assigned parameters (m,R)

0.0 - 3.2

QPSK, 2/5

3.4 - 6.6

8PSK, 1/3

6.8 - 29

16QAM, 1/3

29.2 - 50

64QAM, 1/3

6-S TATE

TABLE X PARTITION A DAPTATION AT Po = 10−3

SNR range (dB)

Assigned parameters (m,R)

0.0 - 24.6

QPSK, 1/2

24.8 - 50

8PSK, 1/3

TABLE XI 6-S TATE PARTITION A DAPTATION AT Po = 10−6 SNR range (dB)

Assigned parameters (m,R)

0.0 - 50

QPSK, 2/5