multilevel rs/convolutional concatenated coded qam for hybrid iboc-am broadcasting

IEEE TRANSACTIONS ON BROADCASTING, VOL. 46, NO. 1, MARCH 2000 49

Multilevel RS/Convolutional Concatenated CodedQAM for Hybrid IBOC-AM Broadcasting

Sae-Young Chung and Hui-Ling Lou

Abstract—Bandwidth efficient modulation schemesusing Reed-Solomon (RS) codes are proposed for HybridIn-Band-On-Channel (IBOC) systems that broadcast digital audiosignals simultaneously with analog Amplitude Modulation (AM)programs in the AM band. Since both the power and bandwidthallocated for digital audio transmission are limited in this appli-cation, the system cannot afford to add enough redundancy forerror control using conventional concatenated coding schemes. Weshow that by using multilevel RS and convolutional concatenatedcoded Quadrature Amplitude Modulation (QAM), an efficientmodulation schemes can be obtained for applications such asIBOC-AM broadcasting.

Index Terms—Multilevel codes, concatenated codes, ReedSolomon codes, quadrature amplitude modulation, amplitudemodulation, audio broadcasting, in-band-on-channel systems.

I. INTRODUCTION

H YBRID IBOC systems [1], [2] are used in the AM band[1], [3] to broadcast digital audio signals simultaneously

with analog AM programs. In these systems, RS codes are usedfor error protection of the digital information. RS codes are non-binary codes that are widely used because of their good distanceproperties and efficient decoding algorithms [4]. RS codes havea wide range of code rates and can correct burst errors that areprevalent in the AM channels in the presence of interference. ARS decoder also provides an error flag that indicates the relia-bility of the decoded frame. Such a flag is essential for the errormitigation or concealment algorithms that sophisticated sourcedecoders provide.

Multilevel coding combined with multistage decoding firstproposed by Imai and Hirakawa [5] uses several block codes toconstruct a good coding scheme for band width limited chan-nels. Sayegh [6] used block codes at each level and showed thatit is possible to achieve coding gain of about 3–7 dB with simpleblock codes such as repetition codes and Bose-Chaudhuri Hoc-quenghem (BCH) codes. Husni and Sweeney [7] showed that byusing RS codes as component codes for multilevel coding com-bined with -ary Phase Shift Keying (MPSK) modulation, wecan get coding gain of about 1 dB compared to the nonmulti-level schemes.

This paper explores efficient ways of applying RS codesto -QAM for IBOC systems by using multilevel RS codedQAM—a joint RS coding and modulation scheme that appliesa different RS code of appropriate rate to each bit of the-bitQAM symbol. We found that, for example, for a code rate of0.8, by using multilevel RS coded QAM, one can get a coding

Manuscript received March 3, 1999; revised March 8, 2000.Publisher Item Identifier S 0018-9316(00)04320-1.

TABLE IREED SOLOMON CODES OF RATE 0.8. n

DENOTES THELENGTH OFCODE, k THE NUMBER OF INFORMATION SYMBOLS

AND t THE ERRORCORRECTINGCAPABILITY .

Fig. 1. Mapping rule for 32-QAM, RSGF(2 ) symbols.

Fig. 2. Encoder for two-level RS coded QAM.

Fig. 3. Encoder for multilevel RS coded QAM.

gain of about 4 dB when the Bit-Error-Rate (BER) is . Toextend the idea further, we found that by using a concatenatedcoding scheme for the critical levels in the multilevel codingscheme, an additional 0.8 dB of coding gain can be obtained.This multilevel concatenated RS/convolutional coded QAMscheme falls into the general structure of the multilevel partitioncodes described in [8].

In the following sections, we will first describe the conven-tional nonpartitioned mapping scheme in Section II-A. After

0018–9316/00$10.00 © 2000 IEEE

50 IEEE TRANSACTIONS ON BROADCASTING, VOL. 46, NO. 1, MARCH 2000

Fig. 4. Decoder for multilevel RS coded QAM.

that, a two-level RS coded modulation scheme is given in Sec-tion II-B, a general multilevel RS coded modulation scheme isgiven in Section II-C and the multilevel concatenated RS andconvolutional coded QAM scheme is given in Section II-D. Wewill also compare the performances of these different schemesin Section III.

II. RS CODED QAM SCHEMES

A. Non-Partitioned Mapping of RS Symbols to QAM Symbols

To map a RS coded symbol into a QAM constellation point,the current techniques use RS codes based on if themodulation is -QAM [9]. Thus, each -bit RS symbol canmap directly into an -bit QAM symbol. However, this limitsthe choice of RS codes one can apply and thus may affect theerror-correction capability. For example, if a 32-QAM system isused, a perfect matched RS code will be based on 1. Fora given coding rate of 0.8, a RS code of can be applied tomatch the alphabet size. Since longer block codes are desired formore powerful error protection, one may want to use aRS code based on because it can correct twice as manyrandom errors as the code [3]. However, this will resultin a mismatch between the 6-bit RS symbols and the 5-bit QAMsymbols. One way to match the modem symbols to the RS codealphabet is to take every 6 modem symbols and map them onto 5RS symbols. With this scheme, shown in Fig. 1, one can see that

of the modem symbols will only affect one RS symbol andof the modem symbols will affect at most two RS symbols.

An alternate method is to map the least significant bits of the32-QAM symbols onto one RS-coded symbol so that when thenoise is low only the least significant bits may be affected, whichwill affect only one RS symbol. However, when the noise levelis high, one QAM symbol error may cause multiple errors.

B. Two-Level RS Coded QAM

The motivation behind using a two-level RS coded QAMscheme is that the least significant bits in QAM symbols aremore likely to be corrupted by noise. Thus, for a given amountof redundancy, it may be a good idea to protect only those bitsrather than to use RS codes for all bits. In this system, an

1Two 32-QAM symbols can also be matched perfectly to one symbol of aRS code based onGF(2 ). However, the decoding complexity will be muchhigher.

RS code over is used in place of the convolutional coderin TCM as shown in Fig. 2, where . Sincethe RS symbol size isbits, the total number of information bitsis and the total number of encoded bits is.

Input bits are divided into two groups—one uncoded and theother RS coded. Let denote the number of the uncoded bitsper two dimensions and letdenotes the number of bits per twodimensions that will be RS coded, thus bits are beingtransmitted. Since the RS encoder takesbits, we assumeis divisible by and is divisible by , the number ofcoded bits per two dimensions. The uncoded bits and the codedbits are mapped to QAM symbols by Ungerboeck’smapping byset partitioning[10]. The -QAM signal constellation is par-titioned into two subsets, with each subset having pointsand the partitioning is done in a way that the minimum Eu-clidean distance between points in each subset is maximized.We can do this partitioning iteratively so that aftersteps, wehave single point subsets. At theth step, we have sub-sets, where each subset has points. We use coded bitsas an index for the subsets and use the remaininguncodedbits to choose a point within the subset specified by thecodedbits. The decoder first decodes a sequence of subsets of length

by using hard decision. After that, this-bit sequence oflength is corrected by the RS decoder and this corrected bitsare used to generate a corrected sequence of subsets. At the nextstage of decoding, the remaining sequence of the-bit symbolsis decoded by choosing a point in each subset that is closest tothe received point at each time. If the RS decoder cannot correctthe errors because there are too many errors, it will not attemptto correct them. Thus, error propagation due to incorrect errorcorrections to the next stage of decoding is unlikely since theerror flag of a RS decoder is very reliable.

C. Multilevel RS Coded QAM

The multilevel RS coded QAM scheme is a generalization ofthe two-level RS coded QAM scheme described in the previoussection. In multilevel RS coded QAM, we construct an encoderwith different RS coders with different rates combined witha -QAM constellation as shown in Fig. 3, where low rate RScodes are used for lower levels more error protection is needed.

Let be the set of information symbol sizesfor the -level RS encoders, with being the informationsymbol size for the lowest level and being that of the

CHUNG AND LOU: HYBRID IBOC-AM BROADCASTING 51

Fig. 5. Set partitioning for 32 QAM.

highest level. The RS codes for each level are defined overand let be the number of output symbols of each

RS encoder. The rate of this encoder is , whereis the total number of information symbols. Since

there are bits produced by the encoder, -QAM is usedtimes to transmit the coded sequence and at each time,

bits are mapped into an -bit QAM symbol by mapping byset-partitioning. For example, 32-QAM symbols are partitionedas shown in Fig. 5. The lowest bit is first used to choose oneof the two subsets of the 32-QAM points, then the rest of thebits , and are used subsequently to select the ap-propriate subsets from their parent sets.

Decoding is performed similarly as in the two-level RS codedQAM. First, the lowest level is decoded and the corrected se-quence is used to decode the next level. This is performed itera-tively as shown in Fig. 4. At each level, hard decision is used onwhich most RS decoders are based. First, the sequence of bitsfor the lowest level is decoded by hard decision. This sequenceis then corrected by the RS decoder at the lowest level. Then thiscorrected sequence of bits is used to decide the next sequenceof bits for the next lowest level. This is equivalent to selectingone of the two 8-point subsets of the 16-point parent subset thatwas determined in the previous iteration. The output of this stepis the sequence of the bits as shown in Fig. 5. This sequence


Fig. 6. Encoder for multilevel concatenated RS coded QAM using convolutional codes (C/C).

is then corrected by the RS decoder at the second lowest level.This procedure is repeated until all levels are decoded. Finally,the output bit stream is reformatted to form the decoded mes-sage.

Since a RS decoder can detect uncorrectable errors with highprobability, error propagation due to incorrect error correctionsfrom the lower levels to the higher levels is unlikely as describedin the previous section for the two-level case.

D. Multilevel Concatenated RS/Convolutional Coded QAM

Since hard decisions are used in the multilevel RS codedQAM scheme, it is possible to get more coding gain by usingsoft decision decoding. Soft decision decoding for RS codes,however, is too complex to implement. One alternative is to useconcatenated coding scheme using a RS code as an outer codeand a convolutional code as an inner code, since soft decisiondecoding (Viterbi algorithm) is available for the inner code. In-stead of concatenating a RS code and a convolutional code, wepropose applying the concatenated scheme to each level of amultilevel coding scheme as in Fig. 6. We will show that, toachieve good coding gain, the concatenated coding scheme maybe necessary only for the lower levels in a multilevel codingscheme. These codes also fall into the general structure of themultilevel partition codes described in [8].

Similar to the multilevel RS coded QAM, we assumeis the set of information symbol sizes

for the RS encoders from the lowest to the highest levels,where the RS codes are defined over . We also let

be the set of numbers of output symbols ofeach RS encoder. Further, let be the setof rates of the convolutional encoders for the-levels, with

as the rate for the lowest level and as the rate for thethe highest. In addition, let be the number of output bits ofeach convolutional encoder such that is equal to ,where is the number of output bits of the RS encoder at the-th level. The rate of this overall encoder is , where

is the total number of information symbols.Since there are bits produced by the encoder, -QAMis used times to transmit the coded sequence where coded

-bit symbols are mapped into the QAM symbols viamappingby set-partitioning.

Decoding is performed similarly as in the multilevel RScoded QAM scheme except that soft decisions can be exploited

in this case because we can use the Viterbi algorithm to decodethe convolutional coded bits [11].

III. SIMULATION OF PERFORMANCE

After discussing the four different multilevel coding schemesin the previous sections, we compared the performance of thefour schemes by simulations. This section discusses the perfor-mance of the four schemes using a 32-QAM constellation and anoverall channel coding rate of . The Shannon limit infor this case is about 5.74 dB. The BER result using each schemeis compared to the uncoded case where Gray coded 16-QAM isused. Simulation results are shown in Figs. 7, 8, 9, 13, for thefour coding schemes.

A. Non-Partitioned Mapping of RS Symbols to QAM Symbols

Figure 7 shows the results for the nonpartitioned RS coded32-QAM scheme described in Section 2.1. A RS codeover RS code over , and RScode over are used. Even though symbol sizes are notmatched for the and codes, simulation resultsonly confirm that longer block codes are generally better, sug-gesting the mismatch between RS code and QAM alphabets isnot a major problem. Coding gain for the code is abouta 1–2 dB at BER – .

B. Two-Level RS Coded QAM

When we use a two-level RS coded QAM scheme describedin Section II-B, we obtain better coding gains than that of thenonpartitioned schemes. A RS code over , a

RS code over , and a RS code overare used for this simulation. Among the 5 QAM bits,

three bits are uncoded and the other two bits are RS coded. Thus,the overall coding rate is . Except for the case, weobserve additional 1.25–1.75 dB coding gain as compared tothat of the nonpartitioned case at BER as shown in Fig.8. code performs poorly mainly because it is short butalso because the 5-bit RS symbols are not matched to the 2-bitsymbol size of the coded QAM bits. When the RScode is used, the coding gain is about 3.5 dB at BER .

C. Multilevel RS Coded QAM

Figure 9 shows the simulation results for the multilevel RScoded 32-QAM scheme (Section II-C) when RS codes over

and RS codes over are used. For the


Fig. 7. Simulation results for nonpartitioned RS coded QAM.

Fig. 8. Simulation results for two-level RS coded QAM.

case, the two highest levels are uncoded and the remaining threelevels (from the middle level to the lowest level) are protectedby a RS code, a RS code, and a RScode, respectively. For the case, two highest levels are

also uncoded and the remaining three levels (from the middlelevel to the lowest level) are protected by a RS code, aRS code, and a RS code, respectively. Thesecode rates are chosen through simulations to minimize BER.


Fig. 9. Simulation results for multilevel RS coded QAM.

Fig. 10. Probability of correctable frame for multilevel RS coded QAM.

When RS codes over are used, we get about 4 dB codinggain at .

Figures 10, 11, 12 show the frame error rates for thecase, where the-th frame has information bits and

. Figure 10 shows theprobability of successfully corrected error frames, which occurswhen the decoded frame of symbols (or bits) is the same asthe input frame of symbols (or bits) and the RS decoder flag


Fig. 11. Probability of uncorrectable frame for multilevel RS coded QAM.

indicates that all errors are corrected. There are five curves thatcorrespond to each level of the multilevel coding scheme.isthe -th frame, where and is the lowest level.This graph shows that for each level, most errors are correctedwhen the SNR is higher than 11.2 dB. When the SNR is lessthan 9 dB, almost all frames contain errors. It can be also seenthat all five curves are almost on top of each other. Thus, theperformance of the chosen code rates for the different levelsare balanced. Figure 11 shows the probability of uncorrectableerror frames. That is, the decoded frame is different from theinput frame and the decoder correctly decides that the frame isuncorrectable. This figure is consistent with Fig. 10 except thatthe probabilities of the uncorrected error frames for levels 2, 3and 4 are almost zero for all values of SNR. This is because therates are so high—0.98 for level 2 and uncoded for levels 3 and4—that error flags are either unreliable or unavailable. Figure 12shows the probability of undetected error frames. That is, theframe contains errors but the RS decoder indicates there is nouncorrectable error (i.e. the error flag of the decoder indicatesno error). As for the uncorrectable error case, it can be seenthat the two lowest level RS decoders are performing very wellproducing no undetected error frames. However, the RS decoderat level 2 is not good at detecting errors, which is due to the highrate of the code. Levels 3 and 4 have no error flags. For theselevels, the “undetected error” is the case when there are errorsin the frame and “successfully corrected error” is the case whenthere is no error.

D. Multilevel Concatenated RS Coded QAM

Figure 13 shows the performance of the correspondingmultilevel concatenated coding scheme where RS codes are

used as outer codes and convolutional codes are used as innercodes (Section II-D). A simple rate- convolutional codewith four states is used for the lowest level. Since the ratesof the concatenated codes for the other four levels are higherthan 0.5, it is not possible to use a rate- convolutionalcode for those levels. Therefore, for these levels RS codesare used without any convolutional codes. We compare threedifferent schemes using codes over different finite fields. Thefirst scheme uses RS codes over and the parametersof the RS codes are and for the lowest twolevels. The highest three levels are not protected and remainuncoded. The second scheme uses RS codes over andthe parameters (from middle to the lowest level) are

, and , respectively. The higher two levels areuncoded in this scheme. The third scheme uses RS codes over

and parameters (from middle to the lowest level) are, and , respectively. The highest

two levels are also uncoded as in the second case. We observethat there is about a 4.8 dB coding gain at withthe third scheme, which is about 0.8 dB better than that ofthe multilevel RS coded QAM scheme in Section II-C. Thedifference in the performance between the second and the thirdschemes suggests that the code rates for different levels shouldbe optimized for better performance. As in the multilevel RScase without concatenation, the rates for the third scheme arechosen through simulations to minimize BER. To determinethe appropriate constraint length for the convolutional code,we ran simulations using four different constraint lengths (orequivalently, different number of states). Figure 14 shows theperformances of using 4, 16, 64, and 256-state convolutionalcodes. From this figure, we can see that there is no noticeable


Fig. 12. Probability of undetected error for multilevel RS coded QAM.

Fig. 13. Simulation results for multilevel concatenated RS coded QAM using a rate-1=2 4-state convolutional code for the lowest level.

difference among the four curves. Thus, from a complexitypoint of view, a simple 4-state convolutional code should beused.

Figure 15 shows the probability of successfully correctedframe for each level. This is similar to the multilevel caseexcept that the graphs are shifted to the left because the


Fig. 14. Performance of using a rate-1=2 convolutional code with different constraint lengths for the multilevel concatenated RS coded QAM scheme.

Fig. 15. Probability of correctable frame for multilevel concatenated RS coded QAM.

performance is better for this scheme. The probabilities forlevel 0 and level 1 are not similar in this case, suggesting thatthe performance of the two levels are not balanced. Figure 16

shows the probability of uncorrectable frames for each leveland Fig. 17 shows the probability of undetected error framesfor each level.


Fig. 16. Probability of uncorrectable frame for multilevel concatenated RS coded QAM.

Fig. 17. Probability of undetected error for multilevel concatenated RS coded QAM.


IV. A PPLICATION ADVANTAGES OFUSING MULTILEVEL CODED

QAM

From the previous section, we can see the performance gainof using multilevel coded QAM schemes. These schemes havethe added advantage of being able to carry coded bits from asource coder with variable number of bits per frame throughdifferent levels of the multilevel coding schemes. Furthermore,if different levels in a multilevel coding scheme carry differentsource coded bit frames, each QAM symbol can carry bits fromdifferent source coded bit frames. Thus, time diversity is alsoachieved using this scheme. The trade-off here is that additionaldelay can occur since different source coded bit frames are mul-tiplexed before transmission. However, for broadcasting sys-tems, such as Hybrid IBOC-AM systems, real-time delay of afew seconds is tolerable. In addition, unequal error protectionof the source coded bits can easily be achieved since each levelin the multilevel coding scheme can potentially use a differentchannel protection rate.

V. CONCLUSION

Simulation results for RS coded modulation schemes showthat coding gain of 3–4 dB can be obtained by using multi-level RS coded QAM combined with multistage decoding andextra coding gain is possible by exploiting multilevel concate-nated coding schemes. Without multilevel coding, we can onlyachieve 1–2 dB coding gain when we map RS coded bits di-rectly to a QAM symbol. Multilevel RS coding can achieve anadditional coding gain of about 2–3 dB by using the same RSencoders and decoders with the same symbol size but with dif-ferent code rates. In applications where RS codes are requiredfor error protection but when there is not enough redundancy forerror protection schemes such as concatenated RS with TCM,these multilevel schemes can be useful, because we can get extracoding gain compared to the nonpartitioned RS coded modula-tion schemes and we can have all the benefits of the RS codessuch as error flag and burst error correction capabilities wherea reliable error flag is essential for the error mitigation or con-cealment algorithms that sophisticated source decoders provideand good burst error correction capability is required for IBOCsystems in the AM band.

REFERENCES

[1] C.-E. Sundberg, D. Sinha, H. Lou, P. Kroon, and B.-H. Juang, “Tech-nology advances enabling “in-band on-channel” digital sound broad-casting systems,” inInternational Conference on Broadcast Asia, Sin-gapore, June 1998.

[2] B. W. Kroeger, “Compatibility of FM hybrid in-band-on-channel(IBOC) system for digital audio broadcasting,”IEEE Transactions onBroadcasting, vol. 43, no. 4, pp. 421–430, 1998.

[3] H. Lou, D. Sinha, and C.-E. W. Sundberg, “Multi-Stream Transmis-sion for Hybrid IBOC-AM with Embedded/Multi-Descriptive AudioCoding,”, Lucent Technologies Bell Labs Technical Memorandum,Aug. 1998.

[4] R. E. Blahut,Principles and Practice of Information Theory. MenloPark, CA: Addison-Wesley, 1987.

[5] H. Imai and S. Hirakawa, “A new multi-level coding method using error-correcting codes,”IEEE Trans. on Information Theory, vol. 23, no. 3, pp.371–377, 1977.

[6] S. I. Sayegh, “A class of optimum block codes in signal space,”IEEETrans. on Communications, vol. COM-23, no. 10, 1986.

[7] E. Husni and P. Sweeney, “Robust Reed-Solomon coded MPSK modu-lation,” in 6th IMA International Conference Proceedings, Cirencester,UK, Dec. 1997.

[8] G. J. Pottie and D. P. Taylor, “Multilevel codes based on partitioning,”IEEE Trans. on Information Theory, vol. 35, pp. 87–98, Jan. 1989.

[9] P. Corbo and J.-C. Belfiore, “Reed-Solomon coded QAM modulation ona Rayleigh fading channel,” inPIRMC’92 International Symposium onPersonal Indoor and Mobile Radio Communications Proceedings, 1992.

[10] G. Ungerboeck, “Trellis-coded modulation with redundant signal sets:Parts I and II,”IEEE Communications Magazine, vol. 25, Feb. 1987.

[11] G. D. Forney Jr., “The Viterbi algorithm,”Proceedings of the IEEE, vol.61, pp. 268–278, Mar. 1973.

Sae-Young Chungwas born in Seoul, Korea in1967. He received the B.S. (summa cum laude)and the M.S. degrees in electrical engineering fromSeoul National University, Seoul, Korea, in 1990and 1992, respectively. Since 1995, he has beenworking toward the Ph.D. degree in the Departmentof Electrical Engineering and Computer Scienceat the Massachusetts Institute of Technology,Cambridge, MA. His research interests are in jointsource-channel coding and channel coding theory, inparticular low-density parity-check codes and turbo

codes.

Hui-Ling Lou received her B.S. degree in electricalengineering from the University of Texas at Austinin 1986. She received the M.S. and Ph.D. degreesin electrical engineering from Stanford University in1988 and 1992 respectively.

She consulted for Amati Communications Corp.,in Palo Alto, CA in 1992, developing a reconfig-urable trellis codec chip for an Asymmetric DigitalSubscriber Line (ADSL) system. Since 1993, she hasbeen a Member of Technical staff at the Multimediacommunications Laboratories at Bell Laboratories,

Lucent Technologies, in Murray Hill, New Jersey, where she was involved inthe design of system, algorithm and architecture of wireless systems.

Her current research interest is in forward error correction and joint sourceand channel coding algorithm design for transmission of multimedia signalsover wireless networks. She is also interested in finding efficient mapping ofalgorithms onto VLSI architectures.

multilevel rs/convolutional concatenated coded qam for hybrid iboc-am broadcasting

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