Adaptive Interleaving for Bit-Interleaved Coded Modulation

Transcription

1 Aaptive Interleaving for Bit-Interleave Coe Moulation Clemens Stierstorfer an Robert F.H. Fischer Lehrstuhl für Informationsübertragung, Frierich Alexaner Universität Erlangen Nürnberg Cauerstraße 7/LIT, Erlangen, Germany, Abstract In this paper interleaver esign for bit-interleave coe moulation an systems with channel-state information at the transmitter is investigate. Base on the bit level capacities of an equivalent channel moel an avantageous interleaver esign is propose. Unerstaning the varying level capacities as the result of a faing process, suite bit metric arrangements in the ecoer can significantly increase the performance. Numerical results show the superiority of the assesse approach over conventional interleaving an even over rate an power loaing. 1 Introuction We consier block-wise transmission over channels with faing characteristic, e.g., flat faing raio channels or multicarrier transmission [3] over frequency-selective channels, with perfect knowlege of the channel-state at the transmitter. The focus of our work is on very high ata rate transmission which requires the application of large signal constellations. In orer to enhance the reliability of transmission the introuction of channel coing is essential. The concept of bit-interleave coe moulation (BICM) 1 [20], [4] is a well-known coing scheme tailore to faing scenarios. For the sake of low latency an low complexity, coewors shall be restricte to a single transmitte block an non-iterative ecoing shall be use. Usually, channel-state information (CSI) is exploite for aaptive moulation techniques, i.e., both, bit rate an power allocation are optimize accoring to some criterion. Several rate an power loaing algorithms have been propose for uncoe transmission, e.g., [5], [8]. Their plain combination with BICM is not rewaring [9] an avantages can be mostly observe for smaller average signal constellations, though. At worst, rate an power loaing can even egrae performance when larger signal constellations have to be use. Literature offers some first attempts to match loaing with BICM (e.g., [11]), but it still lacks a convincing approach. In this contribution we introuce a novel approach of exploiting CSI at the transmitter for BICM. In contrast to existing loaing algorithms which optimize the rate an power allocation for an aaptive moulation, our new metho oes not change the moulation. Instea, we recommen to take avantage of the CSI in the esign of the employe bit interleavers, i.e., we propose an aaptive interleaving scheme for BICM. 2 In [16] the significant impact of the bit level arrangement on the ecoing performance has been emonstrate. Consequently, so-calle intralevel-interleaving, i.e., the This work was supporte by Deutsche Forschungsgemeinschaft (DFG) uner grant HU 634/5 2 within the framework TakeOFDM. 1 In the context of this paper an in orer to keep the receiver s complexity low, we restrict ourselves to the non-iteratively ecoe variant of BICM. The term bit is use for binary igits in this context. To enote the binary information unit we employ information bit. 2 In [14] a similar approach, though restricte to symbol interleaving, has been presente. systematic combination of bit metrics originating from, on average, weaker an stronger bit levels in the ecoing, has been introuce. Here, we ientify the bit level capacities as an appropriate measure of evaluating the reliability of the bit metric use in the ecoer. Due to the transmitter s CSI we can etermine the exact bit level capacities at both, transmitter an receiver, an hence, can esign an accoring optimize arrangement of the bit metrics. We present numerical results for several settings that reveal the superiority of our novel approach over existing bit-interleaving strategies. Aaptive interleaving even outperforms the plain combination of rate an power loaing algorithms with BICM. Section 2 presents the channel an BICM system moels. In Section 3 the ecoing an the impact of the interleaver are analyze. Section 4 gives esign rules for aaptive interleavers, followe by numerical results in Section 5. Section 6 conclues the paper. 2 System Description 2.1 Bit-Interleave Coe Moulation an Faing Channel Block-wise coe transmission over a single-input/singleoutput faing channel is consiere. We use a rate-k/n convolutional encoer (ENC) to encoe a sequence of binary k-tuples q = (q (1),q (2),...,q (k) ) of source bits (K bits in total) into binary n-tuples c = (c (1),c(2),...,c(n) ) of N encoe bits. Here, the symbol rate of the source bits is enote by 1/T b, that of the encoe bits by 1/T c, an the iscrete inex of the tuples by, =1,..., ( = N n ). The sequence of encoe bits is then passe through a bit interleaver Π which also converts the stream of encoe bits into a sequence of m-tuples x =(x (1),x(2),...,x(m) ) with inex =1,...,D with D = N m. These tuples x are then mappe (M: x F m 2 a A) onto a block of D channel symbols a A C, rawn from the signal constellation A (M = A, m =log 2 (M), m N). An accoring transmitter is sketche in Fig. 1. After transmission over the faing channel, the receive signal at time reas y = h a + n, =1,...,D. (1)

2 q c x a Π M ENC k n m 1 x 1, x 2, x 3,... binary input channel 1 binary input channel 2 λ 1, λ 2, λ 3,... inex inex binary input channel m Fig. 1. Block iagram of the coe moulation transmitter. Fig. 2. Block iagram of serialize channel moel with m perioically selecte binary input channels. Here, h enotes the channel coefficient an n the aitive white Gaussian noise (AWGN). The variance of the channel symbols is given as σ 2 a = Ēs/T s (Ēs: average energy per symbol; 1/T s : symbol rate), that of the noise as σ 2 n = N 0 /T s (N 0 : one-sie noise power spectral ensity). The faing channel coefficients h are i.i.. complex Gaussian istribute with zero mean an unit variance (h CN(0, 1)). Thus, after a phase equalization at the receiver the channel coefficients are Rayleigh istribute, i.e., a Rayleigh faing channel is present. As this work focuses on interleaver esign base on bit level capacities rather than on breaking up statistical epenencies of correlate faing states, the channel coefficients are assume to be statistically inepenent. Furthermore, for the sake of simplicity we resort to M-ary amplitue shift keying (ASK) constellations (A = A ASK = {±1, ±3,...,±(M 1)}). The translation of the obtaine insights to M 2 -QAM constellations is immeiate, an extension to other signal constellations, e.g., phase shift keying, is straightforwar. 2.2 Equivalent Serial Channel Moel In the following we inclue the mapping M we employ the so-calle binary reflecte Gray mapping, cf. [15] into the channel moel. Accoring to [18], the combination of mapping an channel can be equivalently represente by a set of m parallel subchannels with binary inputs an continuous output. The m-tuple x (aka. binary label of a ), can be ientifie as the respective input; the receive signal y constitutes the continuous output. Apparently, the µ-th label bit x (µ) is transmitte over the µ-th subchannel (aka. µ-th bit level). Referring to [4] for a etaile escription of the computation of a lossless bit metric, we here use ( λ (µ),b = y a 2 ) σn/ h 2 2, (2) min a A (µ) b where A (µ) b enotes the subset of A with b {0, 1} as the µ- th label entry. Due to the employe M there is a bijective mapping of the receive value y onto an m-tuple of bit metrics Λ =(λ (1), λ(2),...,λ(m) ). The output of the µ-th level is represente by λ (µ) =[λ (µ),0,λ(µ),1 ]T, i.e., by a pair of metrics for two hypotheses: transmitte zero an transmitte one, respectively. Serializing both, input an output sequence by introucing the time inex η =1,...,N yiels a system with symbol rate 1/T c = m/t s, cf. Fig. 2. The input symbols are given as 3 x η = x ( 1)m+µ = x (µ), for the output symbols respective rules apply. The resulting channel exhibits faing characteristic ue to the h s an the subchannel selecte for transmission is change perioically with a perio of length m. We use these equivalent moels (tuples/serialize) when appropriate. 3 Variables referring to the serialize channel moel carry a tile. 2.3 Capacity Bit Level Capacity The capacity of the µ-th level of symbol a can be efine as the mutual information between the receive signal y an the binary input signal x (µ) (Y an X (µ) enote the respective ranom variables) C (µ) (E s,/n 0 )=I(Y ; X (µ) E s,/n 0 ). (3) Here, E s, = Ē s h 2 reflects the epenence of the receive energy on the channel-state h. We assume equally istribute input signals, flat power spectral ensities/no waterfilling an knowlege of the channel-state h at the receiver. Note: transmitter CSI woul have only little impact on the iniviual level capacities in (3), if waterfilling were applie [2]. For a fixe state h just a scale AWGN channel is present. The capacities cannot be etermine analytically, we have to resort to numerical computations. Results for an exemplary constellation are epicte in Fig. 3 (cf. also [9]). Due to the bijection between the receive signals y an the tuples of bit metrics Λ, the mutual information in (3) coul be equally compute between the bit metrics an the binary input symbols. Hence, the bit level capacity can be well unerstoo as a measure of reliability of the employe bit metric. C [information bit/symbol] log 10 (Ēs/N0) [B] C [information bit/symbol] log 10 (Ēs/N0) [B] Fig. 3. Exemplary subchannel capacities of equivalent channel moel for 16- ASK (m =4) over 10log 10 (Ēs/N 0). Binary reflecte Gray mapping. Left: AWGN channel (h =1). Right: Rayleigh faing channel (h CN(0, 1)) Parallel Decoing Capacity The ecoing of BICM realizes a parallel ecoing approach, cf. [18]. Contrary to joint ecoing of the outputs of m subchannels, any knowlege originating from other levels is iscare. As a result the parallel ecoing capacity is slightly inferior to that of joint ecoing 4 an etermine by the sum over the N level capacities of a block as given in (3). The 4 The employe binary reflecte Gray mapping minimizes this loss in capacity in the relevant Ē s/n 0 range, cf. [15].

3 capacity per symbol a of the entire scheme thus reas C(Ēs/N 0 ) = 1 D m C (µ) D (E s,/n 0 ) (4) C(Ēs/N 0 ) = 1 D =1 µ=1 N C η (E s, η/m /N 0 ). (5) η=1 Here, η/m = yiels the nearest integer greater than or equal to η/m which is. Since the scaling factor 1/D equals m 1/N, switching to the serialize channel moel (cf. Fig. 2) with time inex η (5) can be interprete as the computation of m times the ergoic capacity per binary symbol of a binary input channel with time-varying channel conitions, e.g., [6]. In aition to the faing states h, the changing bit level capacities form another source of faing in the system. 3 Interleaving an Decoing 3.1 Interleaver Description In the serialize moel the bit interleaver Π represents a bijective mapping of a sequence of encoe bits ( c 1, c 2,..., c N ) onto a sequence ( x 1, x 2,..., x N ) (inices acc. to Section 2.2) Π: {1, 2,...,N} {1, 2,...,N}. (6) Apparently, the interleaving can be simply escribe by relating the inices, i.e., x η = c Π(η), where Π is an arbitrary permutation of {1,...,N}. At the receiver the einterleaver is escribe by the inverse mapping Π 1 to (6) an operates on the inices η of the bit metrics. The pairs of einterleave () metrics are given as λ [ λ T η = η,0, λ η,1] = [ λπ 1 (η),0, λ T Π 1 (η),1] = λπ 1 (η). (7) 3.2 Decoer: The Viterbi Algorithm Here, we focus on the application of non-iteratively ecoe BICM an thus the employe ecoer uses the Viterbi algorithm [10]. The path metric in the Viterbi algorithm is obtaine from the einterleave bit metric λ Π 1 (η). Denoting the ecoer s path metric with λ VA, the total path metric for a hypothesis (č 1, č 1,...,č N ) on ( c 1, c 1,..., c N ) is given as N λ VA (č 1, č 2,...,č N )= λ Π 1 (η),č η. (8) η=1 The ecoer returns an estimate (ˆq 1, ˆq 2,...,ˆq K ) on the source sequence 5 ( q 1, q 2,..., q K ) base on the hypothesis (č 1, č 2,...,č N ) with minimal total path metric λ VA. Obviously, the metric for an entire coewor as given in (8) is not affecte by interleaving ue to the commutativity of summation. The same applies to the capacity given in (5). Clearly, interleaving can only shift the arrangement of the bit metrics (an the level capacities, respectively) within a transmitte block. 5 Here, the relation of sequence elements q κ, κ =1,...,K, to elements of the k-tuples introuce in Section 2.1 is given as q κ = q ( 1)k+γ = q (γ) with γ = 1,...,k. Respective rules apply for the estimates ˆq κ. Tile is roppe to avoi ouble accents. 3.3 Impact of Interleaving an State-of-the-Art However, the application of bit interleavers is crucial for the performance of BICM an its superiority over alternative coe moulation schemes (e.g., trellis coe moulation (TCM) [17]) in faing environments. The great impact of the interleaver on the performance of BICM results from the sliing winow characteristic when ecoing convolutional coes. Accoring to a rule of thumb, the Viterbi algorithm returns ecoing results on symbols after processing approximately five times the constraint length ν of the convolutional coe [10]. The purpose of the interleaver is to break up statistical epenencies between neighboring receive bits an to avoi aggregations of unreliable metrics within the ecoing winow of the Viterbi algorithm. Ieal interleavers as they are employe in the theoretical analysis of BICM in [4] woul completely remove statistical epenencies between any bits an provie an ieal arrangement of the bit metrics. A variety of interleavers have been investigate an propose so far. In the initial publication on BICM [20], three inepenent ranom bit interleavers were use for transmission with 8-PSK (phase shift keying). Caire et al. rejecte this approach in [4] an propose the application of a global ranom interleaver instea. Present attempts on the esign of implementable interleavers, like, e.g., simple block interleavers (sprea ajacently receive bits over the entire length of a block) or, more sophisticate, an s-ranom interleaver (introuce a minimum spacing), e.g., [7], [1], recognize the faing channel as the reason for more or less reliable bit metrics. The intention is to place bit metrics affecte by the same faing states as far apart as possible in orer to avoi the occurrence of clusters of unreliable bit metrics resulting from eep faes. 4 Aaptive Interleaving 4.1 Motivation Review: Intralevel-Interleaving In [16] we have shown that a sensible arrangement of the bit levels in the ecoing can significantly improve performance. The main iea can be sketche as a combination of bit metrics originating from stronger levels with those from weaker levels into a trellis segment to obtain similar average conitions within the relevant span of the Viterbi algorithm. Expressing the path metric of the ecoer as λ VA (č (1) 1, č(2) 1,...,č(n) )= n =1 υ=1 λ,(υ), (9),č (υ) i.e., employing tuple-notation, we can ientify trellis segments an the respective path metrics. The inner sum, combining n bit metrics, efines a segmental path metric λ VA. Consier for example 16-ASK with a coe of rate R =1/2 (accoring bit level capacities are epicte in Fig. 3): the metrics of levels 1 an 4 shoul be combine in a trellis segment, followe by metrics originating form levels 2 an 3 in the succeeing segment an so forth. Regaring the level capacities in Fig. 3, we can see that the resulting average sum capacities within the segments o not vary as much as for an

4 arrangement of levels 1 an 2 followe by 3 an 4. Intralevelinterleaving is base on presume average conitions of the bit levels as no CSI is available at the transmitter. In the following we introuce an enhance interleaver esign exploiting transmitter CSI in orer to combine unequally reliable bit metrics into single trellis segments. The knowlege of the bit level capacities at the transmitter allows for a more sophisticate combination of metrics than the intralevelinterleaving approach. To the best of our knowlege interleaver esign base on transmitter CSI has not yet been investigate B 14B 8B 8B 14B 4.2 Relevance of Bit Level Capacities Aaptive interleaving aims at an improve performance in terms of bit-error ratio (BER). To pursue this goal an optimize bit metric arrangement in the ecoer is implemente. In contrast to aaptive moulation techniques, an though the optimization is base on level capacities, the suggeste interleaver esign oes not change the resulting system capacity. The suggeste esign rather ensures an equalize reliability of the segmental path metrics λ VA within each shifte version of the sliing winow spanne by the Viterbi algorithm. A balance path metric over the entire coewor prevents the occurrence of weak segments in the ecoing that woul ominate the resulting bit-error ratio. In orer to assess the reliability of a bit metric we chose the level capacity of the respective subchannel as measure. The significance of the level capacities on the reliability of bit metrics originating from equal levels with ifferent faing states is obvious: the smaller the bit level capacity, the eeper the respective fae. For level capacities arising from ifferent bit levels, the relation is not so evient. The following example emphasizes the relevance of the bit level capacity as a measure of reliability of the employe bit metric. Example: Consier transmission using 16-ASK (m =4), a coe of rate R = 1/2 an a non-recursive, non-systematic encoer with 1024 states (cf. [19, Tab. 11.5]). Blocks of length D = 1024 are transmitte (K = 2048, N = 4096). The interleaver Π implements a sorting of the pairs of einterleave bit metrics accoring to their bit level capacities, i.e., Π is chosen such that C Π 1 (1) C Π 1 (2)... C Π 1 (N). (10) Here, CΠ 1 (η) is the capacity of the bit level employe for transmission of x Π 1 (η) (arguments have been roppe for the sake of brevity, i.e., Cη = C η (E s, η/m /N 0 ). The respective bit metric is λ Π 1 (η). In Fig. 4 the resulting BER over the block of K = 2048 source bits is shown for several signal-tonoise ratios. Apparently, there is a part of the coewor (κ > 1500), where we can achieve error-free ecoing for any of the simulate Ēb/N 0 =(ĒsR)/(mN 0 ). Then again, in another part of the coewor (κ <400), the BER oes not fall below 0.5 at all. Matching these parts with the arrangement of the bit level capacities emonstrates their tremenous impact on the BER an supports the significance of the chosen measure. To further emphasize the importance of the level capacity as a measure of reliability of bit metrics escening from ifferent levels, we present level-epenent BERs. I.e., we κ Fig. 4. BER over position κ within block. Rayleigh faing channel. Re: sorting wrt. bit level capacity, 10log 10 (Ēb/N 0 )=8, 10, 12, 14 [B]. Blue: ranom interleaving, 10log 10 (Ēb/N 0 )=8, 10, 12 [B]. Green: interleaver esign acc. to (11), 10log 10 (Ēb/N 0 )=8, 10, 12, 14 [B] log 10 (Ēs/N0) [B] C [information bit/symbol] Fig. 5. Level-epenent BERs for 16-ASK (m = 4). Rayleigh faing channel. Coe rate R = 1/2, 1024 encoer states. Left: BERs over 10log (Ēs/N 10 0) [B]. Right: BERs over resp. level capacity C (µ) (E s/n 0 ) as given on right-han sie of Fig. 3 (similar results for all levels). apply an interleaver that sorts the bit metrics accoring to their levels Π 1 (η)mo4=1, η = 1,...,1024, Π 1 (η)mo4=2, η = 1025,...,2048, Π 1 (η)mo4=3, η = 2049,...,3072, Π 1 (η)mo4=0, η = 3073,...,4096. (11) At the receiver BERs are etermine iniviually for m = 4 streams of length N/4 = 1024 (transitions between the streams are neglecte). Accoring numerical results are epicte in Fig. 5 an reveal strong istinctions. Levels with a superior capacity also succee in terms of the BER. To illustrate the relation of level capacity an BER, Fig. 5 shows the per-level BERs over the capacity of the employe bit level. Apparently, the level capacity an the resulting BER are irectly relate, as the level-epenent BERs show equal results when epicte over capacity Design of Aaptive Interleavers The suggeste aaptive interleaver esign for Π starts with a sorting of the N bit levels employe for transmission 6 This shows similarities to the so-calle information processing characteristic presente in [12].

5 accoring to their capacities C η (these can be obtaine very efficiently by a simple table lookup). We introuce an initial permutation Π that ensures an arrangement of the levels such that (10) hols. Base on this preliminary operation, we now propose attempts on bit metric combinations for common coe rates aiming at a minimization of the variance of the segmental sum capacity C VA = n C Π 1 (n υ+1). (12) υ=1 n =2: Consier a coe of rate R =1/2. Then, the bit metrics of two levels are combine into the path metric of the -th trellis segment λ VA (č 2 1, č 2 )= λ 2 1,č λ 2,č 2. (13) In orer to minimize the variance of the segmental sum capacities, we subsequently pair the remaining weakest an strongest of the N levels in a trellis segment (the sequence of sorte bit metrics is fole in the mile). Formally, this operation reas λ VA (č 2 1, č 2 )= λ Π 1 (),č λ Π 1 (N +1),č 2. (14) A respective permutation Π (or the accoring inverse) of the inices can be specifie base on the initial sorting Π as ( Π 1 = Π 1 (1), Π 1 (N), Π 1 (2), Π 1 (N 1),......, Π ) 1 (N/2), Π 1 (N/2+1). (15) Depening on the channel conitions, the resulting segmental capacities, resp. reliabilities, may still vary. Usually, neighboring segments exhibit similar properties ue to the initial sorting Π. In orer to prevent a clustering of weak an strong trellis segments, the final interleaving Π is generate from a ranom permutation of the segmental pairs of inices ( Π 1 (), Π 1 (N +1))in Π 1. n =3: Regaring coe rates k/3, i.e., R =1/3 an R = 2/3, three bit metrics are summe up for a segmental path metric λ VA (č 3 2, č 3 1, č 3 )= λ 3 2,č λ 3 1,č λ 3,č 3. (16) Here, we propose an approach similar to that of n =2. Again, our goal is to minimize the variance of the segmental sum capacities C VA. We start with the combination of the = N/3 weakest an strongest levels, so that we have pairs. These pairs are then sorte accoring to their temporal sum capacities an the remaining not yet assigne levels are then allocate to the pairs after the same metho. Finally, we again suggest to ranomly permute the receive triples to avoi clusters of weak segmental path metrics. Annotations: The above introuce methos for interleaver esign can easily be extene to arbitrary coe rates. Moreover, even puncture coes (e.g., [13]) can be comprehene into the presente approach by selecting weak levels for puncturing an/or by an appropriate arrangement of the bit metrics in the ecoer (punctures have zero capacity). 5 Numerical Examples In this section we present numerical examples to emonstrate the superiority of the suggeste aaptive interleaver esign. The BER of aaptive interleaving is compare to those of BICM with global ranom interleaving an BICM with rate an power loaing within a block (we use the algorithm of [8] tailore to uncoe transmission). Respective results are also given for the unprofitable arrangement of BICM with aaptive interleaving an rate an power loaing within a block. Parameters: We transmitte at least blocks of length D = 1024 symbols (following OFDM scenarios with 1024 carriers) rawn from M-ASK signal constellations. For all settings we employe the best known (wrt. free istance) convolutional coes [19, Tab. 11.5] of coe rate R =1/2 an a non-recursive, non-systematic encoer. Source sequences were zero-pae to ensure terminate trellises. Results an Discussion: In Fig. 6 bit-error ratios for 4- ASK, 16-ASK, an 64-ASK are epicte. Aaptive interleaving is compare to ranom interleaving (conventional approach to interleaving) an to BICM in combination with rate an power loaing acc. to [8]. 7 Furthermore, results for the latter in aition with aaptive interleaving are presente. Clearly, rate an power loaing enhances the performance for transmission with 4-ASK (Fig. 6, left). The receive gains are not overwhelming an even vanish for larger signal constellations, though (e.g., 16-ASK/64-ASK, Fig. 6, center/right, resp.). Exploiting the CSI available at the transmitter solely for the esign of the employe interleaver leas to significant gains that even grow with increasing constellation size. At BER = 10 5 aaptive interleaving outperforms ranom interleaving by 0.8B for 4-ASK, for 16-ASK gains of 1.2B can be achieve, an for 64-ASK a gap of more than 2B opens up. Apparently, the growing variance of the bit level capacities requires a sensible arrangement of the bit metrics in the ecoing an eserves specific attention. A simple concatenation of loaing an ranom interleaving cannot fulfill this requirement, an ue to the occurrence of signal constellations exceeing the average size M, the problem is even intensifie. Naturally, one coul anticipate avantages of aaptive interleaving in combination with rate (an power) loaing. However, the hope that aaptive interleaving might alleviate or even resolve the problem of very weak levels an compose a new promising aaptive moulation technique for BICM is isappointe. The results in Fig. 6 o not support this iea, joint aaptive interleaving an rate an power loaing cannot outperform plain aaptive interleaving. Fig. 7 exhibits the superiority of aaptive interleaving over ranom interleaving an BICM with rate an power loaing for an 8-ASK with R = 1/2 an several coe constraint lengths. Here, we can observe that a sensible application of transmitter CSI can significantly reuce the ecoer s complexity for a particular target BER. Again, the plain combination of rate an power loaing with BICM is not rewaring for larger constraint lengths ν. For shorter constraint 7 For rate an power loaing the mentione M-ASKs can be seen as average signal constellations (on average log 2 (M) bits per symbol). The actual M is of course carrier epenent.

6 M=4,R=1/2,ν=10 ranom int. aaptive int. ran. + loa. aap. + loa. M=16,R=1/2,ν=10 ranom int. aaptive int. ran. + loa. aap. + loa. M=64,R=1/2,ν=10 ranom int. aaptive int. ran. + loa. aap. + loa log 10 (Ēb/N 0) [B] log 10 (Ēb/N 0) [B] log 10 (Ēb/N 0) [B] Fig. 6. BERs for BICM with ifferent interleaving strategies an/or rate an power loaing over 10log 10 (Ēb/N 0 ) [B]. Coe rate R =1/2, 1024 encoer states, block length D = 1024, Rayleigh faing channel. Global ranom interleaving (blue), aaptive interleaving (re), rate an power loaing acc. to [8] (green), rate an power loaing acc. to [8] with aaptive interleaving (ark cyan). Left: 4-ASK (m =2). Center: 16-ASK (m =4). Right: 64-ASK (m =6). M =8,R =1/2 ν =10 ν =6 ν =2 ranom int. aaptive int. ran. +loa log 10 (Ēb/N 0) [B] Fig. 7. BERs for BICM over 10log 10 (Ēb/N 0 ) [B] for 8-ASK. Coe rate R =1/2, block length D = 1024, Rayleigh faing channel, 4, 64, 1024 encoer states. Global ranom interleaving (blue), aaptive interleaving (re), rate an power loaing acc. to [8] (green). lengths loaing may yiel some gains, e.g., up to 2 [B] at BER = for ν =2in Fig Conclusion We have introuce a novel metho of exploiting transmitter CSI for BICM by aapting the employe bit interleaver. Base on the bit level capacities of an equivalent channel moel the reliability of the bit metrics at the receiver can be evaluate. The interleaver is then esigne such that within the relevant working range of the Viterbi algorithm an optimize metric arrangement is present. Numerical results support the suggeste interleaver esign an show gains over both, conventional interleaving an BICM with rate an power loaing. Besies the communication of CSI to the transmitter, which coul be replace by passing the even simpler interleaver sequence, the aitional cost in complexity is low compare to non-aaptive interleaving. In relation to rate an power loaing complexity is almost negligible. References [1] A. S. Barbulescu an S. S. Pietrobon. Terminating the trellis of turbocoes in the same state. Electronics Letters, 31:22 23, Jan [2] E. Biglieri, J. Proakis, an S. Shamai. Faing channels: informationtheoretic an communications aspects. IEEE Trans. on Information Theory, 44(6): , Oct [3] J. A. C. Bingham. Multicarrier moulation for ata transmission: An iea whose time has come. IEEE Comm. Mag., pages 5 14, May [4] G. Caire, G. Taricco, an E. Biglieri. Bit-Interleave Coe Moulation. IEEE Trans. on Information Theory, 44(3): , [5] P. S. Chow, J. M. Cioffi, an J. A. C. Bingham. A practical iscrete multitone transceiver loaing algorithm for ata transmission over spectrally shape channels. IEEE Trans. on Communications, 43(234): , [6] T. M. Cover an J. A. Thomas. Elements of Information Theory. John Wiley & Sons, New York, NY, USA, [7] E. Dunscombe an F. C. Piper. Optimal interleaving scheme for convolutional coing. Electronics Letters, 25(22): , Oct [8] R. F. H. Fischer an J. B. Huber. A new loaing algorithm for iscrete multitone transmission. In Proc. IEEE Global Telecomm. Conference (GLOBECOM), volume 1, pages , Lonon, UK, Nov [9] R. F. H. Fischer an C. Stierstorfer. Comparison of coe esign requirements for single- an multicarrier transmission over frequency selective MIMO channels. In Proc. IEEE Intl. Symposium on Information Theory (ISIT), Aelaie, Australia, Sept [10] G. D. Forney Jr. The Viterbi algorithm. Proceeings of the IEEE, 61(3): , Mar [11] T. Giebel an H. Rohling. New aaptive moulation algorithms for BIC-OFDM systems. In Proc. of 10th Intl. OFDM Workshop, Hamburg, Germany, Aug [12] J. Huber an S. Huettinger. Information processing an combining in channel coing. In Proc. Intl. Symposium on Turbo Coes & Relate Topics, pages , Brest, France, Sept [13] J. B. Huber. Trelliscoierung. Springer Verlag, [14] S. W. Lei an V. K. N. Lau. Aaptive interleaving for OFDM in TDD systems. IEE Proc. Comm., 148(2):77 80, Apr [15] C. Stierstorfer an R. F. H. Fischer. (Gray) Mappings for Bit-Interleave Coe Moulation. In Proc. IEEE Vehicular Technology Conference Spring (VTC Spring), Dublin, Irlean, Apr [16] C. Stierstorfer an R. F. H. Fischer. Intralevel-interleaving for BICM in OFDM scenarios. In Proc. of 12th Intl. OFDM Workshop, Hamburg, Germany, Aug [17] G. Ungerböck. Channel coing with multilevel/phase signals. IEEE Trans. on Information Theory, 28(1):55 67, [18] U. Wachsmann, R. F. H. Fischer, an J. B. Huber. Multilevel Coes: Theoretical Concepts an Practical Design Rules. IEEE Trans. on Information Theory, 45(5): , July [19] S. B. Wicker. Error Control Systems for Digital Communications an Storage. Prentice Hall, Upper Sale River, NJ, USA, 1 eition, [20] E. Zehavi. 8-PSK Trellis Coes for a Rayleigh Channel. IEEE Trans. on Communications, 40(5): , 1992.