K. Kusume, G. Dietl, W. Utschick, and G. Bauch, "Performance of Interleave Division Multiple Access Based on Minimum Mean Square Error Detection," in Proc. IEEE International Conference on Communications (ICC’07), pp. 2962-2966, (Glasgow, Scotland), June 2007.

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

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

Performance of Interleave Division Multiple Access Based on Minimum Mean Square Error Detection Katsutoshi Kusume∗ , Guido Dietl∗ , Wolfgang Utschick† , Gerhard Bauch∗ DoCoMo Euro-labs, Landsbergerstr. 312, 80687 Munich, Germany. Email: {kusume,dietl,bauch}@docomolab-euro.com † Munich University of Technology, Arcisstr. 21, 80290 Munich, Germany. Email: [email protected]

I. I NTRODUCTION Interleave division multiple access (IDMA) is a multiple access scheme which has similarities to code division multiple access (CDMA). Unlike CDMA, however, IDMA does not apply user-specific spreading sequences. Instead, a bandwidth expansion is fully exploited for a forward error correction coding that results in a very low rate code compared to CDMA systems. Interestingly, the principle of IDMA is in the direction of the statement by Viterbi in [1] that spreadspectrum multiple-access communication system approaches its ultimate potential only with the use of very low rate forward error control code with consequently large bandwidth expansion. Instead of user-specific spreading sequences for CDMA, user-distinct interleavers are the unique feature to distinguish users for IDMA. Its user separation relies on an iterative multiuser detection technique. A receiver comprises a multiuser detector (MUD) and a bank of user-independent a posteriori probability (APP) decoders which exchange soft information in an iterative fashion to mitigate multiple access interference (MAI) as well as intersymbol interference (ISI). IDMA recently attracted many research activities due to its good performance with reasonable low complexity, e.g. [2]– [4]. Its low complexity is typically realized by the MUD implementation that applies an approximation similar to the rake receiver for CDMA systems. So far, this type of the MUD implementation has been most frequently considered for IDMA in literature and, despite the simplicity, its excellent performance has been reported.

b (k )

s (nk )

k) c(n,m Convolutional encoder

Πk

Rep.

Symbol mapper

Transmitter yn

(m) k ) Le ( c(n,m

)

− (m) k ) La ( c(n,m

for K users Fig. 1.

)

(d)

Πk

−1

Πk

k) La ( c(n,m )

− (d)

k) Le ( c(n,m )

APP decoder

Abstract— Interleave division multiple access (IDMA) recently attracted many research activities because of its excellent performance despite its reasonable low complexity. The low complexity is usually realized by the multiuser detector that applies an approximation similar to the rake receiver for CDMA systems. So far, this type of detector has been most frequently considered in IDMA literature. In this paper we investigate the performance of IDMA based on linear minimum mean square error (MMSE) detection. The MMSE detector is more complex than the rakelike approximation. At the price of the complexity, however, it is shown that the MMSE detector brings several advantages over the rake-like approach such as the superior performance on channels with spectrally poor characteristics, effective iterative processing for lower SNR values, faster convergence and therefore shorter decoding delays, and better performance for short block length. We also confirm that the complexity can be drastically reduced by the low rank approximation of the MMSE filter by its multistage representation without compromising on the performance.

MUD



L( b (k))

Receiver System Model of IDMA.

In [5], [6], three different approaches have been compared: soft rake, maximal ratio combining (MRC), and joint Gaussian (JG). And the authors reported that the JG approach performs best, but it is most complex, and the soft rake approach has the least complexity and appears a good compromise between cost and performance. This soft rake approach is frequently applied in most IDMA literature in the past. In this paper we particularly focus on linear minimum mean square error (MMSE) detection which has been studied in the areas of iterative schemes for CDMA systems, equalization problems and so on, e.g. [7], [8]. Although MMSE detection has been proposed as a low complexity technique (alternative to the optimum APP detector), its direct form has a much higher complexity than the rake-like approach. Then, we wish to address the following questions in this paper: (1) does the increased complexity bring us any benefits which we do not get using the rake-like approach? (2) what is the impact on the number of iterations necessary to obtain reasonable performance that determines decoding delays? (3) can we reduce the complexity of MMSE filtering itself without compromising on the performance? The JG approach in [5], [6] is quite similar to the MMSE detection and recently their relation and efficiencies have been discussed in [9]. We take a different approach from [9] to reduce the complexity. We start with a general overview of the transmitter and the receiver structures of IDMA in Section II, before explaining the principle of iterative detection and decoding. Several algorithms at the MUD are presented in Section III. Computer simulations are provided in Section IV where we also discuss various consequences. Section V concludes this paper.

1-4244-0353-7/07/$25.00 ©2007 IEEE 2961

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

(k)

II. S YSTEM M ODEL Fig. 1 shows the transmitter and receiver structures of IDMA systems. At the transmitter, information bits b(k) of user k, k = 1, . . . , K, are encoded by the rate Rc convolutional code followed by the rate Rr simple repetition code. The (k) resulting code bits cn,m are interleaved by the interleaver Πk (k) and then, mapped to the complex symbols sn that are the elements of a QAM/PSK signal space constellation S with (k) cardinality |S| = 2M . Note that cn,m denotes the m-th bit of (k) the n-th transmit symbol sn which is also often called “chip” following the CDMA convention. The channel is modeled as the order L finite length impulse L (k) response filter =0 h δ[n − ] which has the normalized L (k) energy of =0 E[|h |2 ] = 1 where E[·] denotes expectation. Then, the received signal can be expressed as yn =

K  L 

(k) (k)

h sn− + ηn ,

(1)

k=1 =0

where ηn is a zero-mean complex Gaussian noise with a variance of N0 /2 per real dimension. Now, we consider a sliding window model for the detection of a symbol at time n by collecting (1) as follows: y = Hs + η,

(2)

where y = [yn , . . . , yn+L ]T , η = [ηn , . . . , ηn+L ]T , and we T T T defined the symbol vectors s = [sT n−L , . . . , sn , . . . , sn+L ] , (1) (K) T T sn = [sn , . . . , sn ] with (·) denoting transposition. By (1) (K) defining hT ], the channel matrix H of  = [h , . . . , h dimension (L + 1) × (2L + 1)K reads as  T  hL · · · hT 0   .. .. .. H = (3) . . . . hT L

···

hT 0

At the receiver, the MUD and the K user-independent APP decoders compute and exchange soft information as described below. At the beginning the decoders are inactive and the MUD computes the a posteriori log-likelihood ratio (L-values) which reads as: (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

(k)

P (cn,m = ci,m ) which are assumed to be uncorrelated due to the interleaver. Thus, we compute P (s(k) n = si ) =

where P (cn,m = ±1|y) is the conditional probability that the code bit was transmitted given the received sequence y. We + as the set of all constellation points si where its denote Sm − as the set of all constellation points si m-th bit is +1 and Sm where its m-th bits is −1. Our main interest in this paper is (k) how to compute P (y|sn = si ) in (4). Several approaches are described in Section III and the performance will be discussed (k) in IV. The a priori probability of the symbol P (sn = si ) is computed from the a priori probabilities of the code bits

P (c(k) n,m = ci,m ),

(5)

m=1 (k)

where P (cn,m = ci,m ) is computed from the L-value sent from the decoder: 1 (m) (k) (6) P (c(k) n,m = ci,m ) = (1 + ci,m tanh(La (cn,m )/2)), 2 (m)

(k)

and La (cn,m ) is initialized to 0 before the first iteration. (k) From the a posteriori L-values L(m) (cn,m ), the extrinsic (m) (k) information Le (cn,m ) is computed by a bit-wise subtraction (m) (k) of the a priori L-values La (cn,m ). The extrinsic L-values (d) (k) are sent to the decoder as the a priori L-values La (cn,m ) −1 after deinterleaving by Πk . The decoder computes improved a posteriori L-values (k) L(d) (cn,m ) about the code bits and L(b(k) ) about the infor(d) (k) mation bits from the a priori L-values La (cn,m ) taking into account the code constraints. At first, the repetition code is decoded by summing up every 1/Rr L-values [10]. Then, the convolutional code is decoded which can be based on the BCJR algorithm [11]. In this paper we use its lowcomplexity max-log approximation (Max-Log-MAP) which can be found, e.g. in [12]. The output L-values from the decoder of the convolutional code are repeated 1/Rr times due (d) (k) to the repetition code. The a priori L-values La (cn,m ) are (k) subtracted from the resulting a posteriori L-values L(d) (cn,m ) (d) (k) to get the extrinsic L-values Le (cn,m ) which are sent to the (m) (k) MUD as the a priori L-values La (cn,m ) after interleaving by Πk . In turn, the MUD computes and delivers new L(m) (k) values Le (cn,m ) based on the received sequence y and the (m) (k) a priori L-values La (cn,m ) from the decoder. The error performance can be improved by performing some iterations. Finally, taking the sign of the L-values L(b(k) ) gives the detected information bits. III. D IFFERENT S TRATEGIES OF M ULTIUSER D ETECTION This section presents different strategies to compute the (k) conditional probability P (y|sk = si ) in (4). It is computed in two steps. The first step is common for all strategies that is the soft interference cancellation:

(4)

m

M

˜ (k) = y − H(˜ y s − s˜(k) n eκ ),

(7)

˜ is defined similar to s, κ = LK + k, and eκ where s denotes the κ-th column of an identity matrix. The softsymbol estimates are computed from the a priori information:  (k) (k) (k) (k) s˜n = E[sn ] = si ∈S si P (sn = si ) where P (sn = si ) is computed according to (5). Note that the soft interference ˜ (k) = y, at the first iteration cancellation is inactive, i.e. y (m) (k) since La (cn,m ) is initialized 0 (cf. Eqns. 5, 6, and also  si ∈S si = 0 for a QAM/PSK constellation S). The second step of each approach is described in the following subsections.

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TABLE I (k) (k) L ANCZOS A LGORITHM C OMPUTING T n,si (D) AND gn,si (D). t0 = 0L+1 , c0,1 = 0 (k) (k) (k) t1 = rsi /rsi 2 , β1 = tH 1 Rn,si t1 , c1,1 = β1 (1) (1) (1) −1 gfirst = c1,1 , glast = gfirst for i = 2, . . . , D (k) v = Rn,si ti−1 − ci−1,i−1 ti−1 − ci−2,i−1 ti−2 (k) ci−1,i = v2 , ti = v/ci−1,i , ci,i = tH i Rn,si ti , −1 2 βi = ci,i − ci−1,i βi−1    (i−1)  (i−1) (i) (i−1) c2i−1,i glast + βi−1 eT gfirst = gfirst g 1 last 0 −ci−1,i   (i−1) (i) −1 g −c i−1,i last glast = βi 1 (k) (k) (k) (D) T n,si (D) = [t1 , . . . , tD ], gn,si (D) = rsi 2 gfirst

A. Rake-Like Approximation (Softrake) This approach has been used in most IDMA literature in the past and it is based on the following approximation: P (y|s(k) n = si ) ≈

L

(k)

P (˜ yn+ |s(k) n = si ),

(8)

=0

which resembles the rake combiner of CDMA systems, thus we call this approach “softrake” henceforth as in [5]. Since we can write from (2) and (7): (k)

(k)

T ˜) − (s(k) y˜n+ = h s(k) ˜(k) n + e+1 H((s − s n −s n )eκ ) + ηn+ ,

and assuming that the residual interference (the 2nd term) plus (k) (k) noise (the 3rd term) is white, the probability P (˜ yn+ |sn = si ) in (8) can be characterized by only its mean and variance. The mean is computed as (k)

(k)

n and (·)∗ denotes complex conjugation. The output zn,si is assumed to be Gaussian distributed, then we compute its mean and variance:

(k)

E[˜ yn+ |s(k) n = si ] = h si .

H

By defining the covariance operator Cov(x, y) = E[xy H ] − E[x]E[y H ] where (·)H denotes complex conjugate transpose, the variance computes as (k)

(k)

(k)

H T (k) 2 Cov(˜ yn+ ,˜ yn+ |s(k) n =si ) = e+1HC nH e+1−ρn |h | +N0 , (k)

(k)

(k)

(k)

(k)

where ρn = Cov(sn , sn ) = E[|sn |2 ] − |˜ sn |2 =  (k) (k) 2 2 = si ) − |˜ sn | , C n = Cov(s, s) = si ∈S |si | P (sn (1) (K) T T T diag([ρn−L , . . . , ρn , . . . , ρn+L ]) and ρT n = [ρn , . . . , ρn ] assuming uncorrelated symbols. Note that, in contrast to the mean, the variance does not depend on a particular symbol si (k) 2 (k) (k) (k) and we define σ = Cov(˜ yn+ ,˜ yn+ |sn = si ). With the computed mean and variance, we can rewrite (8) as:   (k) (k) L L 2  |˜ y −h s | 1 i n+  . (9) exp− P (y|s(k) n =si ) ≈ (k) 2 (k) 2  πσ σ  =0 =0   B. Time-Variant MMSE Detection (TV MMSE) In this approach, the linear MMSE filter is applied to the received signal after the soft interference cancellation in (7): H

(k) ˜ (k) , zn,s = w(k) n,si y i (k)

in order to mitigate the residual MAI and ISI. Note that zn,si is the output of the MMSE filter given that the symbol si is transmitted. Then, the conditional probability is approximated (k) using the output zn,si as follows (k) (k) P (y|s(k) n = si ) ≈ P (zn |sn = si ).

(10)

The MMSE weight vector is found as

(k) (k) (k) µ(k) n,si = E[zn |sn = si ] = w n,si Heκ si and 2

respectively. Finally, we rewrite (10) as:   (k) (k) 2 − µ | 1 |z n,s n,s i i P (y|s(k) exp − . (12) n = si ) ≈ (k) 2 (k) 2 πσn,si σn,si Due to the matrix inversion in (11), the MMSE filtering approach is rather complex. In the next subsections, we consider its approximated versions aiming at complexity reduction. We follow several techniques explored in [13] in the context of the iterative equalization problem that will be extended to the multiuser transmission in IDMA systems. C. Reduced-Rank Approximation of TV MMSE (TV MSWF) A multistage representation of the MMSE or Wiener filter (WF) based on orthogonal projections was introduced in [14]. The solution is called multistage WF (MSWF). This new multistage structure also provides its reduced-rank approximation that leads to the low-complexity implementation. The idea is to find the approximate solution of the MMSE weight vector in (11) in a lower dimensional subspace: (k) (k) w(k) n,si (D) = T n,si (D)g n,si (D),

(13)

(k)

(L+1)×D , and D < L + where g n,si (D) ∈ CD , T (k) n,si (D) ∈ C 1 denotes the reduced rank. In [15], [16] it was shown that the columns of T (k) n,si (D) are basis vectors of the D-dimensional Krylov subspace [17]:

−1

(k) H (k) 2 (k) (k) ˜ | |sn =si ] = R(k) w(k) n,si r si , (11) n,si = argmin E[|sn −w y

D−1 (k) r si }.

(k) (k) (k) (k) (k) K(D) (R(k) n,si ,r si ) = span{r si ,Rn,si r si , . . . ,Rn,si

w

where the correlation vector and∗ correlation matrix can be (k) (k) (k) computed as r n,si = E[˜ y (k) sn |sn = si ] = Heκ |si |2 = (k) (k) ˜ (k)H |sn = si ] = H(C n − r si and R(k) y (k) y n,si = E[˜ (k) H (ρn − |si |2 )eκ eT + N0 I, respectively. Note that the κ )H cross-correlation vector does not depend on the symbol index

H

(k) 2 (k) (k) (k) (k) 2 σn,s = E[|zn(k) − µ(k) n,si | |sn = si ] = w n,si r si − |µn,si | , i

With this fact and because of the Hermitian structure of the correlation matrix R(k) n,si , the computationally efficient iterative Lanczos algorithm [13], [16], [17] can be used to compute (k) T (k) n,si (D) and g n,si (D). The algorithm is summarized in Table I for readers’ convenience.

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10

10

0

10

−1

10

−2

4 users 5 paths fixed Porat channel Nb=128 10 iterations

0 −10 −20 −30 0

0.2 Fig. 2.

0.4 0.6 0.8 frequency Frequency response of Porat channel.

1

BER

magnitude in dB

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

D. Time-Invariant Approximation of MMSE (TI MMSE) The MMSE filter in (11) has to be computed for every symbol n = 1, . . . , N . Following the time invariant approach in [8] replaces the covariance matrix C n by its time average, (14)

thereby the matrix inversion in (11) is computed only once ¯ (k) ¯ ρ(k) − for user k by replacing R(k) n,si with Rsi = H(C − (¯  (k) N H ¯ |si |2 )eκ eT ¯(k) = 1/N n=1 ρn = eT κ )H +N0 I and ρ κ Ceκ . This results in a tremendous complexity reduction. Note that, if the signal space constellation S has multi-level magnitudes of the modulation alphabets, the solution needs to be computed for the different levels. IV. N UMERICAL R ESULTS This section presents several numerical results obtained from computer simulations. Throughout this paper, the rate Rc = 1/2 memory 2 standard [7, 5]8 convolutional code is used and the trellis is terminated with 2 additional termination bits. The convolutionally coded bits are further encoded by the rate Rr = 1/4 repetition code, interleaved by the randomly chosen user-distinct interleaver, mapped on QPSK symbols using Gray labeling, and then transmitted over the channel. In all scenarios, K = 4 users are synchronously transmitting. In the following the simulation results are shown for two different channels: a fixed and randomly chosen multipath channels. A. 5 Paths Fixed Porat Channel In this subsection, we investigate the performance of different MUD algorithms explained in Section III on the 5 paths (k) (k) complex-valued fixed channel, hT = [h0 , . . . , h4 ], ∀k, defined by Porat in [18]: hT=[0.49+j0.10, 0.36+j0.44, 0.24, 0.29−j0.32, 0.19+j0.39], which is normalized such that it has norm one. Fig. 2 clearly shows the poor spectral characteristics of the channel. Fig. 3 compares the performance of IDMA using different MUD algorithms after 10 iterations for the frame length of Nb = 128 information bits. Thus, the resulting interleaver length is (128 + 2) · 2 · 4 = 1040. The single user bound is also plotted as a reference curve. It can be observed that the performance of the TV MMSE approaches the single user bound for sufficiently high Eb /N0 -values. The performance of the softrake saturates for high Eb /N0 -values and the high error floor can be seen. Further iterations do not improve the

−3

10

−4

10

−5

10

−6

softrake TI MMSE TV MMSE single user bound

0

Fig. 3.

2

4

6 8 10 Eb/N0 in dB BER performance of IDMA with different MUD algorithms.

0.5

0.4

MUD K=4 users, QPSK 5 paths fixed Porat channel, Eb/N0=6 dB

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

N  ¯ = 1 C n, C N n=1

10

0.3

Softrake

MMSE

0.2

0.1

0

Decoder rate 1/2, [7,5]8 convolutional code with rate 1/4 repetition code 0

Fig. 4.

0.2

0.4 0.6 0.8 1 I ( c( k), L(d) ( c( k))) e EXIT curves of the decoder and MUD at Eb /N0 = 6 dB.

performance. The TI MMSE performs quite well with a slight degradation from the TV MMSE despite the large complexity reduction of the factor of N (= 520 symbols in this example) for the matrix inversions (cf. Eqns. 11 and 14). Note that no result is provided here for the TV MSWF as there is no advantage in terms of complexity reduction against the TV MMSE for the 5 paths channel. We also provide the analysis of the system using extrinsic information transfer (EXIT) chart [19] in Fig. 4. The EXIT chart shows the average mutual information (d) I(c(k) , Le (c(k) )) at the input of the MUD in the horizontal (m) axis and I(c(k) , Le (c(k) )) at the output of the MUD in the vertical axis. The EXIT curves for the MUD using either the MMSE or the softrake are computed at Eb /N0 = 6 dB. Given high mutual information from the decoder (cf. around upper-right area in Fig. 4), both algorithms perform similarly well because in this case the estimates of the transmitted code bits are reliable, and thus the common first step in (7), i.e. the soft interference cancellation, effectively eliminates the interference. With low to moderate values of the mutual

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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

10

0

10

−1

10

−2

0

0

10

10 itr=0

4 users 5 paths fixed Porat channel 10 iterations

itr=0

−1

−1

10

10

itr=1

10

−3

10

−4

10

−5

10

−6

−2

10 BER

BER

itr=1 −2

softrake, Nb=128 softrake, Nb=256 softrake, Nb=1024 softrake, Nb=4096 TV MMSE, Nb=128

−3

10

−4

10

−5

10

single user bound −6

10 single user bound

−3

itr=2

10

−4

4 users 30 paths random channel Nb=1024

10

−5

10

softrake itr=3 TV MMSE

single user bound

4 users 30 paths random channel Nb=1024 itr=3

−6

TV MMSE,rank=30 TV MSWF,rank=2

10

10

Fig. 5. BER performance of IDMA using softrake for different block lengths.

Fig. 6.

information, however, the MMSE clearly outperforms the softrake. The wider tunnel for the MMSE between the EXIT curve of the MUD and that of the decoder brings several advantages at the price of the increased complexity at the MUD. The advantages include: effective iterative processing for lower Eb /N0 -values; faster convergence and thus shorter delays due to the smaller number of iterations necessary; and also the smaller unfavorable effect of losing the inter-iteration gains for short block length. The last point about the interiteration gains versus block sizes is clarified in Fig. 5. It can be observed that larger block lengths result in significant performance improvement when using the softrake algorithm. The block length of Nb = 4096 is necessary for the softrake in order to have the comparable performance of the MMSE with Nb = 128 information bits.

MSWF. With rank 1 the performance degradation from the full-rank MMSE becomes apparent and the performance is similar to the softrake. We also evaluated the TI MMSE, however, the convergence behavior is poorer than the softrake.

0

2

4

6 Eb/N0 in dB

8

B. 30 Paths Random Channels In this subsection, the performance of different MUD algorithms in Section III is investigated on randomly generated multipath channels. The channel taps are generated from zeromean complex Gaussian distribution with a uniform power (k) delay profile, i.e. E[|h |2 ] = 1/(L + 1) = 1/30, ∀k, and constant over each transmission frame. Fig. 6 shows the performance of the softrake, TV MMSE, and rank 2 MSWF where the block length is chosen as Nb = 1024. On the left, the performance is compared over iterations using the softrake and the MMSE. As for the fixed channel, the faster convergence of the MMSE compared to the softrake can be observed. However, in contrast to the fixed channel, the performance of the softrake successfully converges to the single user bound after 3 iterations. Due to the severe frequency selectivity of the channel, the complexity reduction of the TV MMSE is of great interest. On the right hand side of Fig. 6, we compare the performance of the rank 2 MSWF with that of the full rank TV MMSE (rank 30). Despite the large complexity reduction, no performance degradation can be observed by the rank 2

0

2

4 6 Eb/N0 in dB

8

10

itr=2

0

2

4 6 Eb/N0 in dB

8

BER performance of softrake, TV MMSE, and rank 2 TV MSWF.

V. CONCLUSION We have investigated the performance of IDMA using the MMSE detector. The TV MMSE detector is more complex than the softrake which has been used in most IDMA literature so far. At the price of the complexity, however, the TV MMSE detector brings several advantages over the softrake such as the superior performance on channels with spectrally poor characteristics, effective iterative processing for lower SNR values, faster convergence and therefore the shorter decoding delays, and the smaller unfavorable effect of losing the interiteration gains for short block lengths. It was also shown that the high complexity of the TV MMSE detector for the severe ISI channels can be drastically reduced by the MSWF. Only rank 2 already results in the performance almost as good as the full rank solution while achieving the large complexity reduction. The TI MMSE is another scheme achieving the tremendous complexity reduction, however, it does not always lead to the excellent performance. ACKNOWLEDGMENT The authors thank anonymous reviewers for their valuable comments and for pointing out some related references which were missing in the first submission.

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R EFERENCES [1] A. J. Viterbi, “Very low rate convolutional codes for maximum theoretical performance of spread-spectrum multiple-access channels,” IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 641– 649, May 1990. [2] L. Ping, L. Liu, K. Y. Wu, and W. K. Leung, “Interleave-division multiple-access,” IEEE Trans. on Wireless Commun., vol. 5, no. 4, pp. 938–947, April 2006.

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

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