This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
On the Interaction Between Channel Coding and Hierarchical Modulation Seyed Mohammad Sajad Sadough
Pierre Duhamel
Faculty of Electrical and Computer Engineering Shahid Beheshti University 1983963113, Tehran, Iran Email: s
[email protected]
Laboratoire des Signaux et Syst`emes (L2S) CNRS, Universit´e Paris-Sud 11, Sup´elec 91192 Gif-sur-Yvette cedex, France Email:
[email protected]
Abstract—1 Classical systems using hierarchical modulation (such as DVB-SH) involve a “high-priority” (HP) and a “lowpriority” (LP) bit stream that are separately and independently encoded before being mapped on non-uniformly spaced constellation points, leading to different levels of error protection. However, an inherent drawback of this scheme is the severe performance degradation of the less protected LP stream. In this paper, we propose a concatenated encoding scheme that mixes the two streams in order to make the encoding of the LP stream dependent on the well protected HP stream. Consequently, at the receiver side, the reliable information on HP bits provided by the HP decoder is naturally involved in the decoding process of the LP stream and acts as “soft pilots”. We have exploited this feature inside a soft decoding mechanism in order to improve the LP decoding performance while keeping the HP decoding performance unchanged. Numerical results presented in the case of the DVB-SH standard show that the proposed system outperforms the classical approach in terms of LP bit error rate without a considerable increase in the receiver complexity.
I. I NTRODUCTION The key challenge faced by the future generation of wireless systems is to provide broadband access with high data rates and different quality of services for each user, even with very hostile link qualities. For reaching this goal, hierarchical modulation (HM) [1], [2], [3], [4] has been included in various standards, such as DVB-T [5] and very recently in the DVBSH standard proposal for mobile digital TV transmission [6]. The basic idea behind HM consists of the partitioning the video stream into two parts: the coarse or “high-priority” (HP) information and the refinement or “low-priority” (LP) information. After channel encoding, the HP and the LP information are de-multiplexed into a single stream and mapped on nonuniformly spaced constellation points creating different levels of error protection. The HP information is to be received correctly by each user even in a very bad channel environment, while the LP information is mostly destinated to users whose channels have better qualities and higher signal-to-noise ratios (SNR). The basic transmission scheme proposed in [6] for HM consists of two separate turbo encoders that encode independently each of the two streams. Although this approach 1 This work has been supported by Alcatel-Lucent Bell Labs in the context of the UMTV (unlimited mobile television) project.
protects well the HP information, it imposes a severe penalty on the performance of the LP stream so that the LP turbo decoder may require a considerable higher SNR in order to achieve the same bit error rate (BER) as that of the HP stream. In this paper, we propose a new transceiver which processes and receives both HP and LP information with the objective of improving the BER performance of the less protected LP stream. We consider a soft-input soft-output (SISO) channel decoder at the receiver. At the transmitter, we propose to mix the two streams in order to make the encoding of the LP bits dependent on the HP bits, even if the initial uncoded streams remain independent. This induced artificial dependency is well exploited in the LP turbo decoder since the soft information on HP bits (which is hopefully reliable due to HM) can help the LP decoder by playing the role of soft pilot information. We refer to this solution as the concatenated coding strategy throughout the paper. The organization of this paper is as follows. Section II presents the DVB-SH system model and the principle of hierarchical modulation. It also describes the basic transmission scheme proposed in [6]. In Section III, we present the improved transciever design that we propose in this work. More precisely, we describe the concatenated transmitter architecture and the associated concatenated receiver. Simulation results are presented in Section IV comparing the performance obtained with the disjoint and the concatenated recivers. Finally, Section V concludes the paper. II. DVB-SH SYSTEM ARCHITECTURE WITH H IERARCHICAL M ODULATION Figure 1 depicts the functional block diagram of the transmitter proposed in [6] for HM. As shown, the HP and LP streams are independently encoded by their respective turbo encoder module. The two encoded streams are then interleaved, combined and sent on non-uniformly spaced hierarchical 16-QAM signal points (we call it 16-HQAM). Figure 2 depicts the 16-HQAM mapping with parameter α a/b. When α = 1, one gets a standard 16-QAM modulation (also called uniform HM), with a specific mapping. However, when α is large, the four points in each quadrant form a “cloud”. The HP information is carried by the clouds, while inside each cloud, the mini QPSK constellations provide the LP
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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 IEEE ICC 2009 proceedings
Fig. 1.
Block diagram of the disjoint transmission scheme for hierarchical modulation.
information. Obviously, for a given average signal power, increasing the value of α increases the HP protection, but at the price of lower noise immunity for the LP information.
0010 0000 0011 0001 HP LP
Fig. 2. Non-uniform hierarchical 16-QAM constellation with parameter α a/b.
III. D ESIGN OF I MPROVED H IERARCHICAL T RANSCEIVERS Since the HP and the LP information are encoded separately in the scheme presented above (see Fig. 1), they can be decoded separately by two different turbo decoders. We refer to this approach as the disjoint encoding/decoding scheme. In what follows, we propose a new transmission/reception scheme in which the two turbo decoders can be used to aid each other by exchanging soft probabilistic information, with the aim of improving the LP decoding performance. A. Concatenated HP/LP Transmission The block diagram of the proposed transmitter is depicted in Fig. 3. As shown, the HP data stream is encoded by a turbo encoder with rate Rhp , interleaved and finally mapped to the two MSBs of the 16-HQAM constellation. Notice that the encoding process of the HP stream is similar to that adopted in the disjoint transmitter of Fig. 1. However, the encoding of the LP data stream differs from the disjoint scheme in that the LP and the HP data stream are mixed together before going through the second turbo encoder with rate Rlp . The mixing operation can be performed by any permutation function. Here, the mixing operation is implemented by a pseudo-random bitwise interleaver. Note that the systematic part in the output of the second turbo
lp ) contains the HP information stream encoder (denoted by b bhp due to the mixing operation. Since the HP information has already been transmitted inside the HP encoded stream of the first turbo encoder, direct transmission of the second encoded sequence leads to a loss of the spectral efficiency. To prevent this, we remove the HP stream from the systematic part of the second turbo code output. The output sequence is thus made from the parity part of the second encoder output (denoted by vlp ) and the uncoded LP stream blp . The resulting encoded sequence clp is then interleaved and mapped to the two LSBs of the 16-HQAM constellation. Finally, The hierarchical symbols are passed through an orthogonal frequency-division multiplexing (OFDM) [7] modulator and sent over the broadcast channel. Since each 16-HQAM symbol is formed by an equal number of HP and LP bits, the coded sequences chp and clp must be of equal length. To satisfy this requirement, according to the proposed transmission scheme of Fig. 3, one must choose the transmitter parameters so as they satisfy: −1 −1 = Llp + (Llp + Lhp ) (Rlp − 1), Lhp Rhp
(1)
where Lhp and Llp denotes the length of one uncoded HP and one uncoded LP packet, respectively. B. Proposed Receiver Structure We consider an OFDM system with N subcarriers through a frequency-selective multipath fading channel. At the receiver, after removing the cyclic prefix (CP) and performing a fast Fourier transform (FFT), the received signal at the k-th subcarrier can be written as [7]: yk = hk . sk + zk ,
k = 1, . . . , N,
(2)
where hk is the channel frequency coefficient, sk is the complex hierarchical symbol, zk is assumed to be zeromean circularly symmetric complex Gaussian with distribution z ∼ Nc (0, σ 2 ). As shown in Fig. 4, the receiver mainly consists in the combination of two sub-blocks that exchange soft information with each other. The first subblock, referred to as a soft demapper, produces soft information in the form of “extrinsic probabilities” from the input symbols and sends it to the second subblock which is a SISO turbo decoder [8]. Each subblock can take advantage of the quantities provided by the other subblock as a priori information. As traditionally done in turbo methods for improving the convergence properties, the
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
Fig. 3.
Block diagram of the proposed concatenated transmission scheme for hierarchical modulation.
D
Fig. 4.
Block diagram of the proposed concatenated reception scheme for hierarchical modulation.
quantities that are propagated between the decoding subblocks are the extrinsic probabilities, rather than the a posteriori probabilities (APP) [9]. Let dlk be the l-th (l = 1, ..., 4) coded and interleaved bit corresponding to the constellation symbol sk . We denote by γ(dlk ) and λ(dlk ) the extrinsic probability for the bit dlk at the demapper and the decoder output, respectively. Moreover, the extrinsic probability provided by each subblock takes the place of the a priori probability for the other subblock. In this way, having some a priori probabilities λ(d1k ), ..., λ(d4k ) provided by the two turbo decoders, the demapper extrinsic probability γ(dlk ) are given by [10], [11]: γ(dlk ) ∝
djk ∈{0,1},j=l
1
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4
2
e− σ2 |yk −hk .sk (dk ,...,dk )|
4 j=1,j=l
λ(djk ).
(3) By successive application of equation (3), the soft demapper can calculate the vector of extrinsic probabilities γ(d) corresponding to the compound sequence d. The resulting vector is divided into the vectors γ(dlp ) and γ(dhp ) corresponding to the sequences dlp and dhp , respectively. Each of the extrinsic vectors γ(dlp ) and γ(dhp ) is then de-interleaved as appropriate for the turbo decoding operation. As shown in Fig. 4, the turbo decoder subblock produces two type of outputs: the extrinsic and the APP. Let us first focus on the decoding of the HP stream. The HP decoder uses the demapper extrinsic vectors γ(bhp ) and γ(vhp ) to
calculate the decoder extrinsic vectors λ(bhp ) and λ(vhp ) corresponding respectively to the systematic and parity part of the encoded sequence chp . These extrinsic vectors are fed back2 to the demodulator and used as a priori information inside (3). As well, the HP turbo decoder provides the vector APP(bhp ) on the HP information, from which by thresholding hp . one can retrieve the decoded sequence b Actually, due to the introduced mixing procedure at the transmitter, the systematic HP sequence bhp is redundant information in the sense that it is also present in the LP encoded sequence. Hence, the extrinsic vector λ(bhp ) can be exploited as additional a priori information for improving the LP turbo decoder performance. To this end, we construct the hp ) (we call it the soft pilot vector) by mixing vector p1→2 (b the extrinsic vector λ(bhp ) with the vector [0.5, . . . , 0.5] of length Llp . The second mixing vector translates the fact that at the HP decoder, we do not have any a priori information on the uncoded LP stream. hp ) We now describe how the soft pilot vector p1→2 (b derived from the HP decoder can be exploited for improving the decoding performance of the LP stream. Since the input to the LP turbo encoder is a mixed version of the two streams (see Fig. 3), our first step consists of deriving the mixed extrinsic lp ) from the demapper extrinsic vectors γ(bhp ) and vector γ(b γ(blp ), as shown in Fig. 4. Hence the LP decoder, as explained 2 Due to space limitation, the feedback connection from the turbo decoders to the demapper is not represented in Fig. 4.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
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in the case of the HP decoder, includes the use of the a lp ) and γ(vlp )) coming priori information (i.e., the vectors γ(b from the demapper subblock. Let us denote by ˜bi a given bit lp and give the the expression of the inside the mixed vector b extrinsic probability for ˜bi , denoted by λ(˜bi ). We have [12]:
simulations, each uncoded LP and HP packet has a length of Lhp = 1000 bits and Llp = 2000 bits, respectively. The choice of Llp = 2 Lhp is in agreement with practical assumptions where the data rate of the HP stream is usually smaller than the data rate of the LP stream [4]. For LP and HP channel encoding, we consider a parallel turbo encoder with a common recursive systematic convolutional (RSC) constituent code with rate 1/3 and constraint length 4, defined in octal form by (15, 13, 17)8 . Different puncturing patterns defined in [6] enables us to have different coding rates for the LP and the HP encoders. In the concatenated scheme, we set Rhp = 1/5 and Rlp = 1/2, which satisfies the constraint (1). Moreover, in the disjoint scheme we set Rhp = 1/5 and Rlp = 2/5. Our setting ensures a fair comparison of the two competitive schemes since we have: i) equality between the length of the uncoded LP and HP sequences, ii) equality between the length of the HP and LP encoded sequences, and thus the same number of channel uses among the two schemes. The interleaving and the mixing sequences are pseudo-random and operate over their entire input sequence length. The number of turbo decoding iterations is set to 8. Figure 5 shows the system behavior of hierarchical modulation for HP and LP streams in the case of the disjoint receiver. For comparison, we have also reported the BER obtained with a non-hierarchical 16-QAM modulation. As can be seen, hierarchical modulation creates two level of error protection. Compared with non-hierarchical modulation, the HP stream is highly protected (almost a gain of 10 dB in Eb /N0 for α = 1) while the LP stream BER is slightly degraded compared to its non-hierarchical variant. Moreover, the robustness of the HP stream can be increased even further
λ(˜bi ) =
APP(˜bi ) , p1→2 (˜bi ) . γ(˜bi )
lp , for all ˜bi ∈ b
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where the APP on the bit ˜bi , APP(˜bi ), is provided by the LP turbo decoder. As is clear from the last equation, the LP decoder disposes of an additional a priori information (i.e., the soft pilot probability p1→2 (˜bi )) provided by the HP decoder, thanks to the mixing procedure implemented at the transmitter. Note that in the case of the disjoint decoding scheme, where there is not any exchange of information between the two turbo decoders, p1→2 (˜b)i is equal to 0.5 in (4). Moreover, by de lp ), the LP decoder can provide mixing the extrinsic vector λ(b an additional a priori information (denoted by p2→1 (bhp )) for the HP decoder on the sequence bhp that can be used in a framework similar to (4). Finally, the overall decoding process consists in alternating between the HP and the LP decoders and computing (after hp and a given number of iterations), the information bits b blp from the a posteriori probability vectors APP(bhp ) and lp ), respectively. APP(b IV. S IMULATION R ESULTS In this section, we provide numerical results to evaluate the performance improvement provided by the concatenated scheme in the presence of hierarchical modulation, in comparison with the classical disjoint receiver. Throughout the
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
V. C ONCLUSION Hierarchical modulation enables the transmission of two independent data streams on a single frequency channel, with different reception qualities. It was shown that the enhanced protection offered by hierarchical modulation for the HP stream is at the price of lower noise immunity for the LP stream. In this paper, we proposed a transceiver design that exploits the inherent reliability of HP bits (provided by hierarchical modulation), to improve the LP detection performance. Our numerical results indicated that disjoint (separate) encoding/decoding of the two streams is suboptimal in terms of LP BER, especially for large values of α. They also confirmed the adequacy of the proposed concatenated transceiver in reducing the SNR required to achieve a certain BER. The amount of performance improvement was shown to be more important when the HP stream is better protected (i.e., for large values of α). The performance improvement brought by the concatenated decoder was obtained with almost no additional complexity compared to the disjoint reception scheme.
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by increasing the parameter α at the expense of the robustness of the LP stream. However, as depicted in Fig. 5, the main drawback of the disjoint scheme is that when α increases, the LP stream requires a considerably larger SNR in order to achieve the same BER as that of the HP stream. We now compare the LP stream BER performance of the concatenated and the disjoint reception schemes. To keep the decoding complexity comparable to that of the disjoint scheme, the concatenated decoder is implemented by performing only one pass of soft pilot information exchange between the HP and the LP turbo decoders. Figure 6 shows that for α = 1 (the least robust mode for the HP stream), the improvement in terms of required Eb /N0 in order to attain a given BER for the LP stream is about 0.6 dB, compared to the disjoint receiver, while the non-hierarchical 16-QAM modulation would be 1.6 dB better. Note that the improvement becomes more significant when increasing the modulation parameter α. We observe that the Eb /N0 necessary to obtain a BER of 10−4 , is reduced by about 0.8 dB (for α = 2) and 1.5 dB (for α = 4), if the concatenated receiver is used instead of the disjoint receiver. In other words, when the HP stream is better protected (i.e., for large values of α), the LP decoder benefits more from the soft pilot vector for improving the LP BER performance. Finally, Fig. 7 illustrates the LP stream BER performance of the disjoint and concatenated receivers versus the number of turbo decoder iterations, at fixed values of Eb /N0 . This allows us to evaluate the number of decoding iterations necessary to achieve a certain BER. We notice that the concatenated decoder requires 6 iterations in order to achieve a BER of 10−4 at Eb /N0 =14.5 dB, while the disjoint decoder attains this BER with almost 8 iterations at Eb /N0 =16 dB.
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