K. Kusume and G. Bauch, "A Simple Complexity Reduction Strategy for Interleave Division Multiple Access," in Proc. IEEE Vehicular Technology Conference (VTC2006-fall), (Montreal, Canada), September 2006.

©2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. (http://www.ieee.org/web/publications/rights/policies.html)

Katsutoshi Kusume http://kusume.googlepages.com/

A Simple Complexity Reduction Strategy for Interleave Division Multiple Access Katsutoshi Kusume and Gerhard Bauch DoCoMo Euro-Labs, Landsberger Strasse 312, D-80687 Munich, Germany. Email: {kusume,bauch}@docomolab-euro.com

Interleave Division Multiple Access (IDMA) is a recently proposed multiple access scheme which relies on an iterative multiuser detection and it has a close relation to CDMA [1], [2]. Unlike CDMA which uses user-specific spreading codes, IDMA exploits a full bandwidth expansion for coding that results in a very low rate code. IDMA, instead, uses userdistinct interleavers as a unique feature to distinguish users. Iterative multiuser detection techniques comprise multiuser detector (MUD) and a bank of user-independent a posteriori probability (APP) decoders. Both MUD and APP decoder are soft-in soft-out (SISO) blocks which exchange soft information. Multiple access interference (MAI) as well as intersymbol interference (ISI) is mitigated in an iterative manner. In [3] the performance of IDMA has been reported to be better than or at least as good as that of CDMA in various scenarios such as user-asynchronism, multipath channels, near-far effects, and highly user-loaded scenarios despite its simplicity comparing to the state-of-the-art iterative MUD technique for CDMA [4]. The reduction of complexity leads to a higher number of users that can be supported, e.g. in the uplink of cellular systems. The complexity of IDMA, however, may be still too high for some receivers, for instance, if we consider ad hoc wireless networks. The traditional medium access control (MAC) protocol sees the physical layer as a collision model (e.g. [5]) and therefore tries to avoid simultaneous transmissions (regarded as “collisions”). Recently, the potential of multiuser detection techniques in a distributed network is discussed, e.g. in [6]. Higher efficiency may be achieved if a certain amount of interference is allowed due to the multiuser detection. In such a network, on the other hand, not all receivers will probably afford the full complexity of MUD. Our proposed simple strategy aims at supporting

1-4244-0063-5/06/$20.00 ©2006 IEEE

s (nk )

k) c(n,m

Πk

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encoder

Symbol mapper

Transmitter (m)

yj

k) ) Le ( c(n,m

− (m) k ) La ( c(n,m

for K users

)

(d)

Πk

−1

Πk

k) ) La ( c(n,m

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k) ) Le ( c(n,m

APP decoder

I. I NTRODUCTION

Symbol mapper

encoder

IDMA b (k ) Convolutional

un(k )

s (nk )

k) CDMA c(n,m b (k ) Convolutional Πk

MUD

Abstract— Interleave Division Multiple Access (IDMA) is a multiple access scheme similar to CDMA and it relies on an iterative (“turbo”) multiuser detection and decoding technique. IDMA applies a very low rate code which is typically realized by a convolutional code followed by a simple repetition code. We propose to limit the decoding of the convolutional code at the receiver aiming at complexity reduction. Although the transmitted bits cannot be recovered without decoding the convolutional code, decoding only the repetition code already gives some improvements of soft information to the next (“turbo”) iteration. We show that such a simple scheme can be of advantage of IDMA against CDMA to achieve significant complexity reduction with graceful performance degradation. We also provide analyses to answer when it makes sense to apply the simple strategy.

L( b (k ))

Receiver

Fig. 1. System model of CDMA and IDMA. Basic receiver structure is common for both schemes.

a variety of receivers with different capabilities of handling interference. It allows to reduce the complexity significantly while graceful performance degradation can be realized. We also provide analyses in some scenarios where our simple strategy is found to be useful. II. S YSTEM M ODEL We consider CDMA and IDMA systems in Fig. 1. At the transmitter, information bits b(k) of user k, k = 1, . . . , K, are encoded by the rate Rc convolutional code. For CDMA, the coded bits are interleaved by the interleaver Πk , mapped on (k) the complex symbols sn which are elements of a QAM/PSK signal space constellation S where |S| = M , and then spread (k) (k) (k) by the spreading code un = [un,0 , . . . , un,Nu −1 ]T ∈ CNu T where (·) denotes transposition. For IDMA, the convolutionally coded bits are further encoded by the rate Rr simple repetition code. Then, the coded bits are interleaved by Πk (k) and mapped on the complex symbols sn . For convenience, (k) we denote by cn,m the coded bits before the interleaver for both CDMA and IDMA. A common linear equation system for both CDMA and IDMA is summarized as follows. The channel
νk is(k)modeled g δ[j − ] by the finite-length impulse response filter =0
νk (k) 2 with the normalized energy of E[|g | ] = 1. We =0  denote by τk and νk , respectively, a user-specific delay and a memory of multipath channel of user k, then the total delay of user k becomes τk + νk which is normalized by a chip duration. Then, it is convenient to define the delays:

Dc = maxk (τk +νk +1) in chips and Ds = (Dc −1)/Nu +1 in symbols. · rounds the argument to the nearest integer towards infinity. Note that the symbol delay Ds is equal to the chip delay Dc for IDMA since there is no spreading (1) (K) (Nu = 1). By denoting sn = [sn , . . . , sn ]T and the (1) (K) effective channel H n, = [hn, , . . . , hn, ] of dimension K, the received signal vector may be expressed as Nu ×
Ds y n = =0 H n−, sn− + η n where η n is a vector of zeromean complex Gaussian noise with a variance of N0 /2 per (k) real dimension. The effective channel hn, takes into account the channel and the spreading code, and therefore it can be (k)
determined from the discrete convolution f (k) = ak ui ∗ n

(k) (k) T T g (k) where g (k) = [0T τk , g0 , . . . , gνk , 0Dc −τk −νk −1 ] , (k)


(k) T

T and 0n denotes a zero vector un = [un , 0T Nu (Ds −1) ] of dimension n. The amplitude of user k is denoted by (k) ak ∈ R. Then, the effective channel is defined as hn, = (k) (k) [fn,Nu +1 , . . . , fn,(+1)Nu ]T ∈ CNu . Now, we consider a sliding window for the detection of a symbol at time n. By definT T T ing the symbol vector s = [sT n−Ds +1 , . . . , sn , . . . , sn+Ds −1 ] of dimension K(2Ds − 1) and the channel matrix   H n−Ds +1,Ds −1 · · · H n,0   .. .. .. H =  . . .

H n,Ds −1 · · · H n+Ds −1,0 of dimension Nu Ds × K(2Ds − 1), the received signal vector T T y = [y T n , . . . , y n+Ds −1 ] can be concisely expressed as y = T T Hs + η where η = [η n , . . . , η T n+Ds −1 ] . The MUDs of CDMA and IDMA compute the a posteriori log-likelihood ratio (L-values): (k)

L(m) (cn,m ) = log = log

P (c(k) n,m =+1|y) (k)

P (cn,m =−1|y)
(k) (k) + P (y|sn =si )P (sn =si ) s ∈Sm .
i (k) (k) − P (y|sn =si )P (sn =si ) s ∈S i

(1)

m

+ the set of all constellation points si where We denote by Sm − the set of all constellation its m-th bit is +1 and by Sm points si where its m-th bits is −1. The a priori probability (k) of the symbol P (sn = si ) is computed from the a priori (k) probabilities of the code bits P (cn,m = ci,m ) which are assumed to be uncorrelated due Thus, we Mto the interleaver. (k) (k) compute P (sn = si ) = m=1 P (cn,m = ci,m ) where (k) P (cn,m = ci,m ) is computed from the L-value sent from the (k) (m) (k) decoder: P (cn,m = ci,m ) = 12 (1 + ci,m tanh(La (cn,m )/2)) (m) (k) and La (cn,m ) is initialized to 0 before the first iteration. The (k) computation of P (y|sn = si ) depends on particular schemes and will be explained in the next subsections II-A and II-B. The decoder computes improved a posteriori L-values (k) L(d) (cn,m ) about the code bits taking into account the code constraints. The decoding of the repetition code is summing up every 1/Rr L-values [7]. The decoding of the convolutional code can be based on the BCJR algorithm [8], and in this paper we use its implementation in the logarithmic domain (Log-MAP). We also use its max-log approximation (MaxLog-MAP) which can be found, e.g. in [9].

A. CDMA In the following the iterative MUD technique for CDMA based on the instantaneous minimum mean square error (MMSE) filter with BPSK modulation in [4] is extended for higher order modulation like QAM/PSK constellations. There are two steps to compute the conditional probability (k) P (y|sn = si ). The first step is the soft interference cancellation: ˜ (k) = y − H(˜ y s − s˜(k) (2) n eκ ), T ˜T ˜T ˜n = ˜ = [˜ where s sT n−Ds +1 , . . . , s n, . . . ,s n+Ds −1 ] , s (1) (K) T [˜ sn , . . . , s˜n ] , κ = (Ds − 1)K + k, and eκ denotes the κ-th column of identity matrix. The soft-symbol estimates are (k) (k) computed from the a priori information: s˜n = E[sn ] =
(k) = si ). By defining a covariance operator si ∈S si P (sn Cov(x, y) = E[xy H ] − E[x]E[y H ], the auto-correlation of (k) (k) (k) (k) the symbol sn is computed as ρn = Cov(sn , sn ) =
(k) 2 (k) 2 (k) (k) 2 E[|sn | ] − |˜ sn | = = si ) − |˜ sn |2 si ∈S |si | P (sn where (·)H denotes Hermitian transpose. Assuming uncorrelated symbols, the covariance matrix can be written as T T C = Cov(s, s) = diag([ρT n−Ds +1 , . . . , ρn , . . . , ρn+Ds −1 ]) (1) (K) T and ρn = [ρn , . . . , ρn ]. In the second step, we apply the MMSE filtering to the received sequence after the soft interference cancellation: (k) (k) H (k) (k) ˜ where zn,si is the output of the MMSE filzn,si = wn,si y ter given the symbol si is transmitted. The MMSE weight vec(k) (k) (k) ˜ (k) |2 |sn = tor is found as wn,si = argminw E[|sn − wH y −1 (k) si ] = Rn,si r n,si where the correlation vector and the corre(k) ∗

(k)

(k)

lation matrix can be computed as r n,si = E[˜ y (k) sn |sn = (k) (k) (k)H (k) 2 ˜ y y |sn = si ] = si ] = Heκ |si | and Rn,si = E[˜ (k) H 2 T H(C−(ρn −|si | )eκ eκ )H +N0 I, respectively. The output (k) zn,si is approximated to be Gaussian distributed with the mean (k)

(k)

(k) H

(k)

µn,si = E[zn |sn = si ] = wn,si Heκ si and the variance (k) 2

(k)

(k)

(k) H (k)

(k)

(k)

σn,si = E[|zn −µn,si |2 |sn = si ] = wn,si r n,si −|µn,si |2 . Then, we finally compute the conditional probability as: (k)

P (y|sn = si )

(k)

(k)

≈ P (zn |sn = si )

(k) 2 |zn,s −µ(k) n,si | 1 i exp − . = (k) 2 (k) 2 πσn,si

σn,si

B. IDMA The iterative MUD for IDMA with BPSK modulation in [1]–[3] is extended for higher order modulation below. The first step is the soft interference cancellation as for CDMA in (2). Then, the conditional probability is approximated as: νk (k) (k) (k) P (y|sn = si ) ≈ (˜ y+τk +1 |sn = si ) =0 P

(k) (k)
νk |˜y
+τ −g
si |2 k +1 = α · exp − =0 , (k) 2 σ


νk (k) 2 where α = ). The approximation is to =0 1/(πσ compute the probability from the independent channel delay components, and the probability of each delay component is approximated to be Gaussian distributed with

(d)

0

+

Rep.

L(b(k ))

(k)

(k) 2

IDMA CDMA

−1

max−log MAP decoding of conv. code for strong user1&2

IDMA CDMA

−1

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for user 1 only

(d) k ) Le ( c(n,m ) Fig. 2. Decoder of user k for IDMA. Decoding of convolutional code can be avoided for complexity reduction.

the mean g

10

max−log MAP decoding of conv. code for user 1&2

10

BER of user1

decoder of convolutional code

Πk

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k) ) La ( c(n,m −1 Πk DeMux

10

single user bound

−3

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for strong user 1 only

IDMA CDMA

−2

10

−3

10

single user bound

(channel tap coefficient) and the vari(k)

(k)

(k)

= Cov(˜ y+τk +1 , y˜+τk +1 |sn ance σ (k) (k) 2 H eT HCH e +τk +1 − ρn |g | + N0 . +τk +1

−4

=

si )

=

−5

III. C OMPLEXITY R EDUCTION S TRATEGY FOR IDMA The complexity of the MUD for IDMA is relatively low as we saw in the previous section. The complexity of the decoder, on the other hand, can be quite high for a large number of users because of the K independent decoders. The decoding task for IDMA is two fold as shown in Fig. 2: decoding the repetition code and the convolutional code, where the former is far simpler than the latter. We propose to limit the exploitation of the decoding of convolutional code aiming at complexity reduction. If the convolutional code is not decoded, there will be still some improvements due to the decoding of the repetition code. In case of CDMA, however, no performance improvement can be obtained without decoding the convolutional code. In the following, we will show that our simple method is useful in the two different switching strategies. A. User-Wise Switching Strategy In ad hoc networks, not all network nodes are likely to afford the full complexity of the multiuser detection. Therefore, some form of complexity reduction should be considered. Here, we propose to decode the convolutional code for a limited number of users. Computer simulations are performed to evaluate our scheme. Nb = 128 information bits are encoded by the rate Rc = 1/2 memory 4 standard [31, 27]8 convolutional code where octal notation with the least significant bit on the left. The trellis is terminated with 4 additional termination bits. For CDMA the code bits are interleaved by a random interleaver, mapped on BPSK symbols, and spread by an Nu = 4 spreading code that is constructed from the OVSF code and the UMTS uplink long scrambling sequence specified in [10]. For IDMA the convolutionally coded bits are further encoded by a rate Rr = 1/4 repetition code, interleaved, and mapped on BPSK symbols. Both schemes have the same bandwidth-efficiency. Fig. 3 shows the BER performance of IDMA and CDMA on an AWGN channel where K = 4 users are asynchronous with τk = k − 1 user delays. Let us first look at the left figure where the performance is plotted for the equal-power user scenario. The convolutional code is decoded either for the first and the second users (solid lines) or only for the first user (dashed lines). The BER performance of user 1 is plotted. It

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Fig. 3. BER performance of IDMA and CDMA on AWGN channel after 6 iterations in equal power user scenario (left figure) and in near-far scenario where 2 users are 3 dB stronger than the other 2 users (right figure).

can be observed that IDMA performs better than CDMA due to the decoding of the repetition codes. The performance gap between IDMA and CDMA becomes larger by decreasing the number of users for which the convolutional code is decoded. The right figure in Fig. 3 shows the weak-user performance in the near-far scenario where 2 users are 3 dB stronger than the other 2 users. The convolutional code is decoded either for the two strong users (solid lines) or only for one strong user (dashed lines). In the former case we see that CDMA performs as good as IDMA in contrast to the previous equal-power user case. This is due to the fact that the strong users’ signals can be reliably detected without iteration, and thus can be subtracted from the weak user’s signal with low probability of error. IDMA, however, performs much better than CDMA when the complexity is further reduced (dashed lines), since IDMA can still improve detection of strong users by the decoding of the simple repetition code. We conclude that the proposed scheme achieves graceful performance degradation for IDMA while drastically reducing the complexity due to the decoding of the convolutional code. We observed the similar tendency for multipath channels. The results are omitted due to space limitation. We note that, if the convolutional code is always decoded for all users, the performance of IDMA and CDMA after some iterations is very similar and it approaches the single user bound [3]. B. Iteration-Wise Switching Strategy IDMA relies on the iterative multiuser detection technique. It is well known that the interleaver size must be large enough for the iterative processing to be effective over many iterations while it is always limited in practice. Fig. 4 shows the BER performance of IDMA on an AWGN channel for different sizes of interleaver. The coding parameters are the same as in Fig. 3. The code bits are QPSK modulated. K = 8 users are synchronous. At the receiver the convolutional code is decoded by max-log MAP algorithm. On the left figure the performance

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always with max−log MAP of convolutional code

Nb=128

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first 4 itrs. w/o max−log MAP of convolutional code

Nb=128 Nb=512

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single user bound

−7

Nb=1024 Nb=4096

10

2 4 6 0 2 4 6 Eb/N0 in dB Eb/N0 in dB Fig. 4. BER performance of IDMA for different sizes of interleaver after 14 iterations. K = 8 users are perfectly synchronous on AWGN channel.

is plotted when the convolutional code is always decoded for all users. It can be seen that the performance improves as the frame size gets larger. It converges to the single user bound at Eb /N0 = 6 dB for Nb = 4096. Plotted on the right is the performance when only the repetition code is decoded in the first 4 iterations, then the convolutional code is also decoded in the rest of iterations in addition to the repetition code. Surprisingly, the performance already converges to the single user bound at Eb /N0 = 6 dB for Nb = 1024. We analyze the system using extrinsic information transfer (EXIT) chart [11]. The EXIT chart shows the average mutual information between the transmitted code bits and the input Lvalues, which are obtained from the other SISO block, versus the average mutual information between the transmitted code bits and the extrinsic output L-values, which are sent to the other SISO block. In our system, the horizontal axis is the (d) mutual information I(c, Le (c)) at the input of the MUD, which is the extrinsic information sent from the decoder. The (m) vertical axis is the mutual information I(c, Le (c)) at the output of the MUD, which is sent to the decoder as the input. Curves for the relation between input and output mutual information are plotted for both the MUD and the decoder. The trajectory between the two curves starting from the MUD without a priori information illustrates the performance improvements by iterations. The average mutual information between code bits c and L-values L(c) can be computed by numerical evaluation of [11]  +∞
I(c, L(c)) = c=+1,−1 −∞ P (L(c)|c)P (c) 2P (L(c)|c) × log2 P (L(c)|c=+1)+P (L(c)|c=−1) dL(c). For the EXIT chart computation, it is assumed that the (m) (k) (d) (k) input L-values Le (cn,m ) and Le (cn,m ) are statistically independent and Gaussian distributed. Fig. 5 shows the EXIT charts corresponding to Fig. 4 at Eb /N0 = 6 dB. In Fig. 5(a) the trajectory is plotted for Nb = 4096 where the convolutional code is always decoded by the max-log MAP decoder. The trajectory follows the prediction

MUD, Eb/N0=6 dB

see Fig. (c)

0 0

I ( c (k) , L(m) ( c (k))) e

−1

(b) Nb=1024

1/2 conv. code with 1/4 rep. code I(c

(k)

1/4 rep. code 0 1 0 0.145

, L(d) ( c (k))) e

0.48 (c) zoom of Fig. (b) always with max−log MAP of conv. code

0.44 0.97

I ( c (k) , L(d) ( c (k))) e

1

(d) zoom of Fig. (b)

first 4 itrs. w/o max−log MAP of conv. code I ( c (k) , L(d) ( c (k))) e

see Fig. (d)

I ( c (k) , L(m) ( c (k))) e

10

0.5 (a) Nb=4096

I ( c (k) , L(m) ( c (k))) e

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crossing point I ( c (k) , L(d) ( c (k))) e

0.41

Fig. 5. EXIT charts of Fig. 4 at Eb /N0 = 6 dB. (a) Trajectory for Nb = 4096 where convolutional code is always decoded by max-log MAP decoder. (b)-(d) Trajectories for Nb = 1024 are plotted when convolutional code is (1) always decoded (solid line) (2) after 4 iterations (dashed line).

of EXIT curves well. Trajectories for Nb = 1024 are plotted in Fig. 5 (b)-(d) for two cases: (1) convolutional code is always decoded by the max-log MAP decoder (solid line), and (2) the decoding of the convolutional code starts after the first 4 iterations (dashed line). We observe that the trajectories do not follow the prediction of EXIT curves after some iterations due to the limited interleaver size. Although, in the latter case (2), the trajectory stacks at the crossing point of the EXIT curve of the rate 1/4 repetition code and that of the MUD (cf. Fig. 5(d)), it further goes through the tunnel by decoding the convolutional code as well as the repetition code. Then, the (d) trajectory finally reaches the error free point I(c, Le (c)) = 1 (cf. Fig. 5(c)) while in the former case (1) it does not. It should be also pointed out that, in the lower part of the EXIT charts in Fig. 5(b), the improvement is similar with/without decoding the convolutional code because the improvement is mainly due to the decoding of the repetition code in such a region where the a priori information still has a low reliability. Therefore, it makes sense to decode only the repetition code in initial few iterations. That apparently leads to the reduction of the complexity. We observed that the number of initial iterations with the ‘repetition-code-only decoding’ does not influence the final performance as long as it is taken large enough. So far, we always used the max-log approximation for the decoding of the convolutional code because of its low complexity. That is important for practical systems. We are now interested in the degradation due to the max-log approximation. In order to solely observe the degradation of the decoding of the convolutional code, repetition code is excluded from the following simulation. The information bits are encoded by the rate 1/4 memory 4 standard [25, 35, 33, 37]8 convolutional code, interleaved, and then mapped on QPSK symbols. K = 4 users are perfectly synchronous on an AWGN

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0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Eb/N0 in dB Eb/N0 in dB Fig. 6. BER performance of IDMA for different sizes of interleaver after many iterations up to 30 until no improvement can be obtained.

1

1 I( c (k), L (m) ( c (k))) e

I( c (k), L (m) ( c (k))) e

log MAP decoding Nb=128 MUD Eb/N0=6dB

I( c (k), L (d) ( c (k))) e

1

log MAP decoding Nb=1024 MUD Eb/N0=6dB

0 0 Fig. 7.

rate 1/4 conv. code I( c (k), L (d) ( c (k))) e

0 0 1 I( c (k), L (m) ( c (k))) e

I( c (k), L (m) ( c (k))) e

0 0 1

rate 1/4 conv. code

1

max−log MAP decoding Nb=128

0 0

MUD Eb/N0=6dB

rate 1/4 conv. code I( c (k), L (d) ( c (k))) e

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max−log MAP decoding Nb=1024 MUD Eb/N0=6dB

rate 1/4 conv. code I( c (k), L (d) ( c (k))) e

1

EXIT charts corresponding to Fig. 6 at Eb /N0 = 6 dB.

channel. Fig. 6 shows the BER performance for different sizes of interleaver after many iterations up to 30 iterations until no improvement can be observed anymore. The results are plotted without max-log approximation (log MAP, left figure) and with max-log approximation (max-log MAP, right figure). We observe the significant degradation due to the approximation in such a severe MAI scenario. The respective EXIT charts at Eb /N0 = 6 dB are illustrated in Fig. 7. It can be clearly seen that the trajectories in case of using the max-log MAP decoding are not as good as those in case of using the log MAP decoding. Let us recall the performance improvement for the ‘repetition-code-only decoding’ in initial few iterations when the low rate code is realized by the convolutional code followed by the repetition code. By doing so, at least in the

initial few iterations, the iterative processing is not suffered from the degradation due to the max-log approximation. When we start decoding also the convolutional code with the maxlog approximation, the a priori information has been already improved by the MUD and the decoding of the repetition code (cf. the crossing point in Fig. 5 (b)(d)). Thus, we finally end up with the performance better than the case of always decoding the convolutional code. IV. C ONCLUSION We proposed a simple complexity reduction strategy for IDMA. IDMA typically realizes a very low rate code by a covolutional code followed by a simple repetition code to flexibly support a number of users. Considering that the decoding task consists of the decoding of the repetition code and that of the convolutional code, we proposed to decode the computationally intensive, yet powerful, convolutional code in a restricted manner aiming at the complexity reduction. One strategy is to exploit the decoding of the convolutional code for a limited number of users. This significantly reduces the overall complexity at the receiver while the graceful performance degradation is realized. Another strategy is to start the decoding of the convolutional code after initial few iterations. That makes sense since the improvements mainly come from the decoding of the repetition code in the initial few iterations. Furthermore, the performance may even improve for a highly user-loaded system with a short block length requiring many iterations when the convolutional code is decoded with the low-complexity max-log approximation. R EFERENCES [1] L. Ping, L. Liu, K. Y. Wu, and W. K. Leung, “Interleave-division multiple-access,” submitted to IEEE Transaction on Wireless Communications. [2] H. Schoeneich and P. A. Hoeher, “Adaptive interleave-division multiple access - a potential air interface for 4G bearer services and wireless LANs,” in Proc. 1st IEEE and IFIP Int. Conf. on Wireless and Optical Communications and Networks (WOCN ’2004), June 2004, pp. 179–182. [3] K. Kusume and G. Bauch, “CDMA and IDMA: Iterative multiuser detections for near-far asynchronous communications,” in Proc. IEEE Int. Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 2005), September 2005. [4] X. Wang and H. V. Poor, “Iterative (Turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Transactions on Communications, vol. 47, no. 7, pp. 1046–1061, July 1999. [5] IEEE Std 802.11-1997, “Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications,” June 1997. [6] L. Tong, V. Naware, and P. Venkitasubramaniam, “Signal processing in random access,” IEEE Signal Processing Magazine, vol. 21, no. 5, pp. 29–39, September 2004. [7] D. Divsalar and F. Pollara, “Hybrid concatenated codes and iterative decoding,” California Institute of Technology, Pasadena, California, Tech. Rep. TDA Progress Report 42-130, 1997. [8] L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Transactions on Information Theory, vol. 20, no. 2, pp. 284–287, March 1974. [9] P. Robertson, P. Hoeher, and E. Villebrun, “Optimal and sub-optimal maximum a posteriori algorithms suitable for turbo decoding,” European Trans. on Telecommun. (ETT), vol. 8, no. 2, pp. 119–125, March 1997. [10] 3G TS 25.213, “3rd generation partnership project; technical specification group radio access network; spreading and modulation (FDD) (release 4),” June 2002. [11] S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Transactions on Communications, vol. 49, no. 10, pp. 1727–1737, October 2001.