reed–solomon decoding algorithms for digital audio broadcasting in the am band

IEEE TRANSACTIONS ON BROADCASTING, VOL. 47, NO. 2, JUNE 2001 115

Reed–Solomon Decoding Algorithms for DigitalAudio Broadcasting in the AM Band

J. Nicholas Laneman, Student Member, IEEEand Carl-Erik W. Sundberg, Fellow, IEEE

Abstract—Digital audio broadcasting (DAB) systems for theAM band are being developed to provide higher-quality radiobroadcasts, broader coverage, and data services. Transmission istypically done by means of multistreaming with QAM/OFDM inthe high bits/sec/Hz regime, in which Reed–Solomon codes, eitheralone or in concatenation with inner trellis coded modulation(TCM), are natural choices for error control. For the AM DABapplication, Reed–Solomon codes with suboptimal decodersof the bounded-distance type offer error correction importantfor bringing down the error probability, but also offers errordetection important for generating block detected-error flags foruse in the error concealment, or error mitigation, algorithm in theaudio decoder. For multistream systems, the block detected-errorflags can also be used to select the component streams retainedby the audio decoder. In this paper, we evaluate the performanceof Reed–Solomon codes in terms of both detected (flag) andundetected error rates for DAB applications. We provide sim-ulation results for a variety of decoding algorithms, includinghard-decision decoding (HDD), successive-erasure decoding(SED), and fixed-erasure decoding (FED), and discuss the channelenvironments in which each of these algorithms may be appro-priate. Among other results, for example, we address the issue ofmatching the blocklength of the Reed–Solomon code to the audiodecoder with its variable frame structure. From our simulationresults for HDD, we conclude that the increased error correctioncapability of longer Reed–Solomon codes more than compensatesfor the mismatch in terms of error mitigation in the audio decoder.We also observe that SED provides only small improvements foruniform interference channels, while FED offers considerableimprovements for some partial-band interference channels. Wedescribe an appealing two-mode adaptive configuration usingHDD and FED for mitigating partial-band interference caused bysome second-adjacent AM broadcasts.

Index Terms—Bounded-distance decoding, digital audio broad-casting (DAB), error mitigation, generalized minimum-distancedecoding, joint source-channel coding, Reed–Solomon codes.

I. INTRODUCTION

A NALOG and digital Hybrid In Band on Channel(HIBOC), as well as all-digital In Band on Channel

(IBOC), Digital Audio Broadcasting (DAB) systems for theAM frequency band are currently being proposed and developedas a migration path from legacy analog AM radio broadcasts

Manuscript received September 19, 2000.J. N. Laneman was with the Multimedia Communications Research Labora-

tory, Bell Labs, Lucent Technologies, Murray Hill, NJ 07974 USA and is nowwith the Research Laboratory of Electronics, Massachusetts Institute of Tech-nology, Cambridge, MA 02139 USA.

C.-E. W. Sundberg was with the Multimedia Communications Research Lab-oratory, Bell Labs, Lucent Technologies, Murray Hill, NJ 07974 USA and isnow with the Media Signal Processing Research Department, Agere Systems,Murray Hill, NJ 07974 USA.

Publisher Item Identifier S 0018-9316(01)08404-9.

[1], [2]. The digital portions of these systems provide higherquality audio, broader coverage, and broadcast data servicesusing existing licensed frequencies by combining sophisticatedaudio compression algorithms with robust channel coding andtransmission techniques.

The Perceptual Audio Coder (PAC) [4]–[9] represents oneof the audio coders proposed for HIBOC and IBOC AMsystems. PAC encoding uses a perceptually-based bit allocationscheme for vector quantization, followed by lossless Huffmancoding, to produce variable sized frames, with the frame lengthstatistics varying as a function of the average audio coder rate[4]–[6]. When operating over noisy channels, PAC can reducethe impact of frames lost due to channel errors by employingerror concealment (or error mitigation) techniques. As a simpleexample of error concealment, a lost frame can be filled inby interpolating between its surrounding frames. In additionto audio-based error-detection mechanisms, it is useful forthe channel decoding subsystem to provide a flag indicatingblock detected errors for triggering the error concealmentalgorithms [4]. Generally speaking, long blocklength channelerror-detection codes can lead to multiple audio frames beinglost for a given uncorrectable channel error, while short block-length channel error-detection codes can allow more framesto pass to the audio decoder with undetected errors—both ofthese scenarios lead to reduced audio quality. Matching thechannel error-detection blocklength to the audio coder framestatistics for a given rate thus becomes an important problem infine-tuning the performance of the overall system.

Because AM DAB systems operate in very bandwidth lim-ited settings, audio coding rates in the range of 16–64 kb/secalong with multilevel modulation of e.g., M-QAM type, havebeen suggested. In this regime, natural channel coding optionsinclude trellis-coded modulation (TCM) and multi-level coding(MLC) [3], possibly in concatenation with outer Reed–Solomon(RS) codes [2]. For low-complexity implementations, RS alonemay be used, while, for improved power efficiency, inner TCMor MLC may be added [2]. In either case, the error-detectioncapabilities of RS codes decoded with bounded-distance-typedecoders can be exploited to providing a flag mechanism forerror concealment in the audio decoder.

Motivated by a need to effectively match the RS channelcode to the audio coder framelength for improved audio quality,this paper studies the performance of several Reed–Solomondecoding algorithms in terms of probability of flagging,or flag rate, as well as probability of undetected errors, orundetected error rate, for different blocklengths and coderates. Shortened codes are used to obtain codes of appropriaterate. The emphasis here is on low-complexity schemes for

0018–9316/01$10.00 © 2001 IEEE

116 IEEE TRANSACTIONS ON BROADCASTING, VOL. 47, NO. 2, JUNE 2001

daytime transmission, for which multistream audio coders withorthogonal frequency division multiplex (OFDM) modulationhave been proposed [2]. We model the channel in this situationwith additive receiver thermal noise and, in some cases, partialband interference from first and second adjacent broadcastingstations. This interference may only occur in certain locations(certain transmitters in certain markets) and/or certain areasof the total coverage area for a given transmitter. Dramaticchanges in channel conditions call for modified transmissionmodes for nighttime transmission. Specifically, skywave inter-ference corrupts the reception, and for this case singlestreamtransmission at a lower audio coder rate is envisioned [2].Detailed analysis of the nighttime transmission modes isbeyond the scope of this paper.

We point out that similar HIBOC and all-digital IBOCdevelopments are ongoing for transmission in the FM band[10]. More severe channel distortions such as multipath fadingas well as substantially more available bandwidth mandatedifferent audio coding rates and channel coding configurationsfor the HIBOC FM case. In particular, several system proposalsemploy an inner convolutional code and an outer high-ratecyclic redundancy check (CRC) code. For these systems, theouter code is employed only for the purpose of error-detection.More generally, certain digital cellular systems have employedsimilar coding configurations.

An outline of this paper is as follows. Section II describes ourmodel for the characteristics of the AM band channel and thecoding and modulation methods considered for daytime trans-mission. Section III summarizes three bounded-distance-typedecoding algorithms, including hard-decision decoding (HDD),successive-erasure decoding (SED), and fixed-erasure decoding(FED), and provides simulation results of their performance inseveral channel scenarios. Finally, Section IV discusses the re-sults and offers some concluding remarks.

II. SYSTEM MODEL

The AM-band radio channel is currently not as well-modeledas the FM band channel. AM-band transmissions appear tobe subject to mild fading, and significant distortions occurwhen mobiles travel near powerlines or through underpasses.Additionally, daytime and nighttime transmission environmentsdiffer dramatically due to strong nighttime skywave reflections,causing inter- and intra-channel interference. In this paper, wemodel the AM band channel as an additive white Gaussiannoise channel with slowly-varying signal-to-noise ratio (SNR),a reasonable model for daytime transmission in the absenceof underpasses and powerlines. We also consider potentialinterference from first and second adjacent AM broadcasts, thatlead to, e.g., partial band interference at the band edges.

Fig. 1 illustrates example spectra of daytime transmissionsystems for multistream HIBOC AM as proposed in [2]; the al-location with kHz can carry a higher data rate providedthere is room for the wider bandwidth, and the allocation with

kHz may be required for more crowded markets. Byusing “multistream transmission”—audio encoding performedusing multidescriptive and embedded techniques in conjunctionwith transmission in several separate frequency bands via, e.g.,

Fig. 1. Example multistream HIBOC AM system with three streams and asystem bandwidth of2B kHz, whereB = 10 kHz orB = 15 kHz dependingupon the available transmission bandwidth.

Fig. 2. Diagram illustrating second-adjacent interference between twostations.

Fig. 3. Multistream system transmitter block diagram.

OFDM—the effects of noise in highly-variable partial bandinterference channels can easily be mitigated. Such partialband interference might arise, e.g., because the host analog AMsignal is transmitted simultaneously with a digital stream, andsecond adjacent interference from other analog broadcasts mostlikely distorts the highest and/or lowest frequency componentsin the digital transmission, as depicted in Fig. 2. There areseveral other configurations that may be of interest for practicalHIBOC AM systems; see [2] for details. We consider only theallocations shown in Fig. 1 for the purposes of evaluation ofReed–Solomon code performance.

Figs. 3 and 4 show conceptual block diagrams for the trans-mitter and receiver, respectively, of a multistream HIBOC AMsystem [2]. Multistream DAB systems partition the frequencyband into several subbands for transmission, e.g., by suitablygrouping together subcarriers in an OFDM modulation scheme.The audio coder may combine embedded and/or multidescrip-tive techniques, and different streams of the audio bitstream arechanneled over certain of the subbands. Fig. 3 shows an ex-ample in which the audio information is partitioned into three

LANEMAN AND SUNDBERG: REED–SOLOMON DECODING ALGORITHMS FOR DIGITAL AUDIO BROADCASTING IN THE AM BAND 117

Fig. 4. Multistream system receiver block diagram. The OFDM demodulatoralso contains synchronization, training, equalization, timing, etc.

streams, with the “core” information transmitted in the middlesubband and multidescriptive versions of the “enhancement”on the sidebands [2]. Because the broadcasting environment isvarying with location but using only one standard transmissionformat, the main motivation for the multistream approach isflexible and adaptive interference management. The locationswith very strong partial band interference lead to cases wherecertain parts of the frequency band is muted [1], [2]. A sin-glestream system with one audio bitstream and one transmissionband may on the other hand be completely overwhelmed by thesame partial band interference. In Fig. 3, FEC 1 to FEC 3 indi-cate in the general case a concatenated RS and TCM encoder;the decoders consist of a TCM and a RS decoder. In the gen-eral case there are also interleavers and deinterleavers present,although we do not consider interleaving in this paper. Whilethe concept of multistreaming is important for the design of aviable AM (and FM) HIBOC system, the results presented inthis paper apply to both singlestream and multistream systems,as we consider a single RS code that performs the functions oferror-correction and error-detection for error concealment.

The narrowband channel environment and audio coderbit-demand for high-quality daytime transmission requireeither uncoded 16-QAM or rate trellis coded32-QAM signaling [2]. Outer Reed–Solomon codes [4] aregood candidates for providing additional channel robustnessvia error-correction as well as a flag mechanism for errorconcealment in the audio decoder via error-detection. UsingReed–Solomon codes defined over GF(), i.e., having 8 bitsper symbol, we may map two, 4-bit modulation symbols into asingle Reed–Solomon code symbol. We focus on the case ofuncoded 16-QAM, the performance of which is shown in Fig. 5for reference, with the understanding that trellis coded32-QAM should improve coverage at the cost of additionalcomplexity. For 32-QAM without inner TCM, Reed–Solomoncodes defined over GF( ) would be suitable candidate codes.

The channel and audio coder bit-rates in proposed systemsallow for Reed–Solomon codes with rates of and

, for example. For codes defined over GF(), themaximum blocklength is symbols, or 2040 bits.Codes with smaller blocklength can be obtained via shortening,i.e., encoding and decoding the full blocklength code with agiven number of symbols fixed at zero. To achieve rate ap-proximately for a given blocklength, there two options for theinformation blocklength , namely, , resulting ina slightly higher rate, or, , resulting in a slightlylower rate.

Fig. 5. Uncoded 16-QAM symbol- and bit-error rates on the AWGN channel.

TABLE ICANDIDATE REED–SOLOMON CODESOVER GF(2 ) WITH RATES AROUND

R = 4=5 AND R = 9=10

Table I shows candidate Reed–Solomon codes within 0.5%redundancy of the required rates and having blocklengths (inbits) roughly corresponding to those examined in [4], [10] forthe FM system.

III. REED–SOLOMON DECODING ALGORITHMS AND

PERFORMANCE

To discuss Reed–Solomon decoding algorithms in a commonframework, we introduce some notation.1 For a more thoroughintroduction to these codes, see [11], [12]. Giveninforma-tion symbols, the transmitter chooses the appropriate codeword

from an Reed–Solomon code overGF( ). This codeword is appropriately modulated, transmittedover the channel, and demodulated as discussed Section II. Dueto channel distortion, the received signalgenerally differs from the transmitted codeword, and the re-ceiver must form an estimate of the transmitted codewordfrom the received signal.

1To differentiate between scalar and vector quantities, the latter is denoted inboldface. For example, the vector of scalarsx ; x ; . . . ; x is denoted byx.


Maximum-likelihood decoding is optimal in terms of mini-mizing the probability that the receiver’s estimatediffers fromthe transmitted codeword ; however, maximum-likelihooddecoding has complexity that grows exponentially in the in-formation blocklength and, importantly for audio applications,does not offer a flag mechanism for error concealment in theaudio decoder. As practical alternatives to maximum-likelihooddecoding, we consider decoding algorithms based on alge-braic bounded-distance decoders such as, e.g., hard-decisiondecoding (HDD), successive-erasure decoding (SED), andfixed-erasure decoding (FED), of the Reed–Solomon codeslisted in Table I, all of which offer block error flags.

These algorithms work with a decision vector, being the maximum-likelihoodsymbol

decision based only upon the received signal. The decisionvector takes values in GF( ) , thereby allowing for reducedcomplexity algebraic error-correction algorithms to be appliedto obtain an estimate of the transmitted codeword. Whenthe number of symbol decision errors betweenand isless than the decoding radius of the code, anerrors-only decoding routine decodes to the correct codeword,so that . When the number of decision errors betweenand some other codeword is less than the decoding radiusof the code, an errors-only decoding routine decodes to theincorrect codeword , contributing to the undetectederror rate of the code. If neither of the above two conditionsare met, an errors-only decoding routine flags a block error,contributing to the flag rate of the code. Traditionally, theperformance of errors-only decoding is evaluated in terms ofthe sum , often referred to as the probabilityof not decoding correctly or simply block error rate, but foraudio applications we are interested in the flag and undetectederror rates individually. Error events are defined similarlyfor an errors-and-erasures decoding routine, but with a largerdecoding radius depending upon the number of erasures.

We now summarize HDD, SED, and FED, and presentsimulation results for the candidate Reed–Solomon codesin Table I. Our simulations utilize the algebraic errors-onlyand errors-and-erasures decoding routines provided in [13]for decoding Reed–Solomon codes. Both routines can beused for shortened codes by simply padding the input wordswith zeros and removing these zeros at the output of thedecoding routine. However, the decoding routines, particularlythe errors-and-erasure decoding routine, may decode to acodeword without the leading zeros; instead of accepting thiscodeword, a decoding failure results.

A. Hard-Decision Decoding

Hard-decision decoding (HDD) applies an algebraicerrors-only decoding algorithm to the symbol decision vectorto generate either a codeword estimateor a block error flag.

Fig. 6 shows flag rates and undetected error rates forHDD of the Reed–Solomon codes over GF() listedin Table I. Fig. 7 shows similar results for the codes.These simulation results suggest that using longer codes of thesame rate with hard-decision decoding reduces the block error,flag, and undetected error rates at moderate to high SNR. Theseresults are in contrast to the results obtained in [4] for CRC

Fig. 6. Flag error rateP (squares) and undetected error rateP (circles)versusE =N in dB for theR = 4=5Reed–Solomon codes with hard-decisiondecoding (HDD). The successively lower curves correspond to the longerblocklength codes listed in Table I.

Fig. 7. Flag error rateP (squares) and undetected error rateP (circles)versusE =N in dB for the R = 9=10 Reed–Solomon codes withhard-decision decoding (HDD). The successively lower curves correspond tothe longer blocklength codes listed in Table I.

codes with error detection only: increasing the blocklength in-creased the flag rate and decreased the undetected error rate,leading to the choice of a medium-blocklength CRC code forbetter matching to the audio decoder.

B. Successive-Erasure Decoding

Increasing the blocklength of the Reed–Solomon code canreduce the undetected error probability beyond that required bythe audio decoder. For example, for the ,Reed–Solomon code, there appears to be nearly four orders ofmagnitude between the relative frequency of block error flagsand undetected errors, while the audio decoder only needsroughly two or three orders of magnitude separation [2]. Audioquality can be significantly improved by reducing the flag rateas much as possible, while maintaining reasonable undetectederror rates. Successive-erasure decoding (SED) [14]–[16]


should reduce the flag rate at the expense of increasing theundetected error rate, and potentially allow for a better matchto the error concealment algorithm in the audio decoder. SEDapplies an algebraic errors-and-erasures decoding algorithmto the symbol decision vectorwith increasingly more of thesymbol decisions erased, thereby generating a list of candidatecodewords from which the “best” candidate can be selected.

In our SED algorithm, successive symbol decision erasuresare generated from continuous-valued reliability informationobtained from the symbol decision device. In the most generalsetting [16], the reliability information is captured by a matrix,

, whereis a vector indicating the reliability of the all possible symboldecisions. Specifically, for the received sample, indi-cates the reliability, e.g., likelihood or (generalized) distance,of making the hard-decision that symbolwas transmitted inslot . We note that the earliest methods [14], [15] fuse theinformation in each vector into a single scalar value indi-cating the reliability of the hard-decision. The method in [16]maintains separate reliabilities for all possible symbol decisionsin each slot, and, in particular, appears to be more effective fornonbinary signaling alphabets as employed in our application.SED reduces computation over maximum-likelihood decodingby never combining the reliability information in the matrixinto codeword reliabilities.

To briefly summarize the algorithm of [16], candidate code-words are generated via successive erasures as follows:

1) Each Reed–Solomon symbol in GF() is trans-mitted as two consecutive 16-QAM symbols, so foreach RS-symbol , the 16-QAM demodulator com-putes squared Euclidean distances and ,

between the two complex-valued channeloutputs and all of the symbols in the constellation. Allpossible pairs of distances are added toform the Reed–Solomon reliability vector.

2) For each RS-symbol, construct the index set

such that

Then Reed–Solomon symbol is theminimum-distance (maximum-likelihood) symboldecision.

3) Let , so that represents thereliability of the second-most likely symbol decision rel-ative to that of the most likely symbol decision. Smallimplies that the decision in RS-symbolis unreliable, be-cause the received signal is nearly equidistant to at leasttwo possible symbols. Construct the index set

such that

Then RS-symbol contains the most unreliableReed–Solomon symbol decision, RS-symbolcontainsthe second-most unreliable Reed–Solomon symboldecision, and so forth.

4) Set .

Fig. 8. Flag error rateP (squares) and undetected error rateP (circles)versusE =N in dB for theR = 4=5, (30; 24) Reed–Solomon code withsuccessive-erasure minimum-distance decoding (SEMDD). The successivelylower squared curves and successively higher circled curves correspond togrowing the list of candidate codewords by one.

5) Erase RS-symbols and apply anerrors-and-erasures decoding routine to generate apotential candidate codeword for the list.

6) If , set [14] and goto step 5);otherwise, select from among the candidate codewords onthe list.

SED may select from the list of candidates the “best”codeword according to one of several criteria. For example,a successive-erasure bounded-distance decoding (SEBDD)algorithm chooses the unique codeword within the generalizeddecoding radius of the code [14]–[16], if this codeword canbe found on the list; otherwise, SEBDD flags a block error.As another example, successive-erasure minimum distancedecoding (SEMDD) chooses the codeword on the list withsmallest Euclidean distance from the received signal [15], if anycodewords can be found on the list; otherwise, it flags a blockerror. In this paper, we focus on SEMDD because it offers lowerflag rates and more closely approximates maximum-likelihooddecoding than SEBDD on an additive white Gaussian noisechannel.

The SED algorithm outlined above can be readily modifiedto accommodate a concatenated coding scheme using outerReed–Solomon codes over GF() and inner trelliscoded 32-QAM; however, such a system requires a soft-outputViterbi algorithm (SOVA) for TCM, adding to the decodercomplexity in a concatenation approach. We also point out that,although in our simulations we execute the errors-and-erasuresdecoding routine to generate each possible candidate code-word, several authors have developed more computationallyefficient SED algorithms that may be useful for implementationpurposes [17]–[19].

Fig. 8 shows the flag rate and undetected error ratefor SEMDD of the , Reed–Solomon codeover GF( ) listed in Table I. Fig. 9 shows similar results forthe , code. These results suggest that, for16-QAM modulation and these Reed–Solomon code rates, SED


Fig. 9. Flag error rateP (squares) and undetected error rateP (circles)versusE =N in dB for theR = 9=10, (30; 27) Reed–Solomon code withsuccessive-erasure minimum-distance decoding (SEMDD). The successivelylower squared curves and successively higher circled curves correspond togrowing the list of candidate codewords by one.

offers at most 0.5 dB at the expense of much higher undetectederror rates; hence, the added complexity of SED may not beworthwhile for digital audio applications in the AM band.

C. Fixed-Erasure and Errors Decoding

For fixed partial-band interference situations as depicted byFig. 2, we also consider fixed-erasure decoding (FED), a de-coding algorithm similar to SED except that a specific set ofsymbols arealwayserased, and at most one candidate code-word is generated. For uniform interference channels, SED isgenerally more effective because it has more flexibility in termsof the symbols it erases. For nonuniform interference, particu-larly for partial-band interference, channels, as arise, e.g., in theHIBOC AM system at some locations with second-adjacent in-terference [2], FED may be more effective than HDD and SEDbecause, given side information about which symbols containhigher levels of interference, FED can erase those symbols thatare known to be less reliable, rather than the general procedureperformed by SED. Then errors and erasure decoding is per-formed for the Reed–Solomon code.

An adaptive system employing HDD and FED might operateas follows. A pilot tone is used to indicate the presence of over-lapping interference in the highest and/or lowest tones, and thismeasurement provides the decoding algorithm with the numberof tones that are subjected to interference. The pilot could bea fixed pilot tone for the lowest and highest frequency or a“roaming pilot tone” which is on only part of the time for a cer-tain frequency and which jumps around among the tones. Withno partial band interference, HDD can be employed. When thepilot indicates that partial-band interference is present, the de-coder switches over to FED with the symbols transmitted on theinterfered tones erased. We note that the complexity increasefor this two mode operation is marginal, but requires modifi-cation to the transmitter for the insertion of pilot tones. Oncea mode has been selected, the decoder remains in that modeuntil the channel measurements from pilot data suggest a mode

Fig. 10. Flag error rateP (squares) and undetected error rateP (circles)versusE =N in dB for theR = 4=5, (64; 51) Reed–Solomon code withhard-decision decoding (top curve) and fixed-erasure decoding (bottom curves)in the presence of partial band interference. The SNR in the 10 jammed 16-QAMsymbols (5 RS symbols) is�10 dB relative to theE =N .

change. When the pilot indicators are close to their decisionthreshold, the decoder can, in principle, decode using both HDDand FED and select the candidate codeword, if either, that de-codes successfully.

Fig. 10 shows the flag rate and undetected error ratefor HDD and FED of the , Reed–Solomoncode over GF( ) in the presence of partial band (5 RS sym-bols) interference (10 dB lower SNR relative to thenumber). As we have seen, the HIBOC AM systems proposedin [2] use OFDM modulation. In this case 5 out of 64 RS sym-bols, or 10 16-QAM symbols, are exposed to severe interfer-ence. This will typically be the highest or lowest frequencies inthe HIBOC AM spectrum. The performance of HDD and FEDare shown, with the understanding that the performance of SEDwould be, at best, that of FED. This example set of simulationssuggests that FED can be very beneficial in HIBOC systems inthe AM band, when the receiver can obtain enough knowledgeof the channel conditions for FED to be appropriate.

Fig. 11 shows the same case as in Fig. 10, but without partialband interference. The better of the two upper error probabilitycurves in Fig. 11 shows the performance with HDD. The worseof the two curves shows the performance with FED in this case,where no partial band interference is present. Clearly, there isno need for FED in this case, but Fig. 11 shows the penalty inperformance when the incorrect mode is chosen. (Also note thatthe lower of the two upper curves in Fig. 10 is identical to theupper curve in Fig. 11.) Fig. 11 also shows the undetected errorrate for the FED case without interference.

IV. DISCUSSION ANDCONCLUSIONS

Designing error control systems for digital audio applica-tions depends on many parameters and channel conditions.Among these parameters are the audio coding rate, type oferror mitigation and screening for undetected errors, channelcoding rate, channel decoding algorithm, system complexity,


Fig. 11. Flag error rateP (squares) and undetected error rateP (circles)vs. E =N in dB for theR = 4=5, (64; 51) Reed–Solomon code withhard-decision decoding (bottom curve, squares) and fixed-erasure decoding(top curve, squares and curve with circles) in the presence of background noisewithout partial band interference.

etc. We have considered a number of these issues with respectto Reed–Solomon codes for HIBOC systems in the AM band,either in isolation with uncoded 16-QAM modulation or,in principle, in concatenation with trellis coded32-QAM.

In particular, we have examined several Reed–Solomon de-coding algorithms that use different levels of soft symbol infor-mation and modem erasures. In contrast to the error-detectingCRC codes optimized for HIBOC systems in the FM band,longer error-detecting and correcting Reed–Solomon codes arepreferred for HIBOC systems in the AM band. When no innertrellis coded modulation scheme is used, some error correctionis preferred in the Reed–Solomon decoding. At a given rate,the longest Reed–Solomon code appears to give the best per-formance, since the flag probability is much lower than for acodeword length better matched to the audio decoder averageframe length. Such a choice renders the error concealment lessefficient on the rare occasions it is called for, because mul-tiple audio frames can be erased as a result of an uncorrectableerror in a long channel code block. The probability of unde-tected errors also decreases with code word length at a givenrate, which is another benefit. Successive-erasure decoding ap-pears to offer little benefit for the additional complexity, at thehigh rates and long blocklengths considered for the HIBOC AMsystems in this paper. However, for nonuniform interferencechannels, as may arise in HIBOC AM systems with significantsecond-adjacent analog interference, successive-erasure and es-pecially adaptive fixed-erasure decoding methods offer consid-erable improvement over hard-decision decoding.

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J. Nicholas Laneman (S’93) was born in St.Charles, MO, USA. He received B.S. degrees inelectrical engineering and in computer sciencefrom Washington University, St. Louis, MO, in1995. He earned the S.M. degree in electricalengineering in 1997 from the Massachusetts Instituteof Technology (MIT), Cambridge, MA, where he iscurrently pursuing the Ph.D. degree.

Since 1995, he has been affiliated with theDepartment of Electrical Engineering and ComputerScience and the Research Laboratory of Electronics,

MIT, where he has held a National Science Foundation Graduate ResearchFellowship and served as both a Teaching and Research Assistant. During1998 and 1999, he was also with Lucent Technologies, Bell Laboratories,Murray Hill, NJ, both as a member of the Technical Staff and as a Consultant,developing robust source and channel coding methods for digital audiobroadcasting. He has 4 patents pending. His current research interests lie in thebroad areas of communications and signal processing, with particular emphasison resource-efficient wireless network algorithms and architectures. He is amember of Eta Kappa Nu and Tau Beta Pi.


Carl-Erik W. Sundberg (S’69–M’75–SM’81–F’90)was born in Karlskrona, Sweden on July 7, 1943. Hereceived the M.S.E.E. and Dr.Techn. degrees fromthe Lund Institute of Technology, University of Lund,Lund, Sweden, in 1966 and 1975, respectively.

Currently he is a distinguished member of theTechnical Staff in the Media Signal ProcessingResearch Department at Agere Systems. He waswith Bell Laboratories, Lucent Technologies,Murray Hill, NJ from 1984 to 2000. Before 1976,he held various teaching and research positions

at the University of Lund. During 1976, he was with the European SpaceResearch and Technology Centre (ESTEC), Noordwijk, The Netherlands, asan ESA Research Fellow. From 1977 to 1984, he was a Research Professor(Docent) in the Department of Telecommunication Theory, University of Lund,Lund, Sweden. He has held positions as Consulting Scientist at LM Ericsson,SAAB-SCANIA, Sweden, and at Bell Laboratories, Holmdel. His consultingcompany, SUNCOM, has been involved in studies of error control methodsand modulation techniques for the Swedish Defense, a number of privatecompanies and international organizations. His research interests includesource coding, channel coding, digital modulation methods, digital audiobroadcasting systems, fault-tolerant systems, digital mobile radio systems,spread-spectrum systems, digital satellite communications systems, and opticalcommunications. He has published over 90 journal papers and contributedover 130 conference papers. He has 62 patents, granted and pending. He iscoauthor ofDigital Phase Modulation, (New York: Plenum, 1986),Topicsin Coding Theory, (New York: Springer-Verlag, 1989) andSource-MatchedDigital Communications(New York: IEEE Press, 1996).

Dr. Sundberg has been a member of the IEEE European-African-MiddleEast Committee (EAMEC) of COMSOC from 1977 to 1984. He is a memberof COMSOC Communication Theory Committee and Data CommunicationsCommittee. He has also been a member of the Technical Program Committeesfor the International Symposium on Information Theory, St. Jovite, Canada,October 1983, the International Conference on Communications, ICC’84, Am-sterdam, The Netherlands, May 1984, the 5th Tirrenia International Workshopon Digital Communications, Tirrenia, Italy, September 1991, the InternationalTelecommunications Symposium, ITS’94, Rio de Janeiro, Brazil, August 1994and for the 2000 International Zurich Seminar, Zurich, Switzerland, February2000. He has organized and chaired sessions at a number of internationalmeetings. He has been a member of the International Advisory Committeefor ICCS’88 to ICCS’98 (Singapore). He served as Guest Editor for the IEEEJournal on Selected Areas in Communications in 1988–1989. He is a memberof SER (Svenska Elektroingenjörers Riksförening) and the Swedish URSICommittee (Svenska Nationalkommittén för Radiovetenskap). In 1986, heand his coauthor received the IEEE Vehicular Technology Society’s Paper ofthe Year Award and in 1989, he and his coauthors were awarded the MarconiPremium Proc. IEE Best Paper Award. He is a Fellow of the IEEE since 1990.He is listed in Marquis Who’s Who in America and Who’s Who in the World.

reed–solomon decoding algorithms for digital audio broadcasting in the am band

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