Reed Solomon Code vs. Repetition in WiMediaUWB

Rabih Chrabieh and Koorosh AkhavanQualcomm, Inc., 5775 Morehouse Dr., San Diego, CA 92121, USA

Email: rabihc@ qualcomm.com, kakhavan@qualcomm.com

Abstract-WiMedia UWB is an OFDM system that is becoming Header MACthe de facto standard for high data rate Wireless Personal AreaNetworks. Low power consumption is essential for the success of Header IF

this technology. We propose, in this regard, to replace the Reed HeadernCheckSolomon code that protects header information by a simpler and Calculationoften better performing repetition code. The complexity of therepetition scheme is almost negligible and results in savings in HC ScrambledMACpower and silicon area. Furthermore, the scheme can be extended Append and Header + HCSto protect payload information. We propose ideas to improve the Scrambleperformance of short payloads and to achieve lower data rates. IF

ShortenedIndex Terms-Power demand, Reed Solomon code, repetition 6 Zero 6 Zero (23,17) 4 Zero

code, ultra wideband, WiMedia. Bits Bits RS Code Bits

PHY Tail Sc ambled Scrambled Tail RS Tail

I. INTRODUCTION Header Bits MAC Header HCS Bits Parity Bits Bits40 bits 6 bits 80 bits 16 bits 6 bits 48 bits 4 bits

Ultra-Wideband (UWB) is a new promising radio technol- Fig. 1. WiMedia's header construction.ogy for Wireless Personal Area Networks (WPAN). There areflavors for both low and high data rates. WiMedia UWB [1]is a high data rate standard, with current raw data rates II. HEADER PROTECTION BY REED SOLOMON CODEfrom 53.3 Mbps up to 480 Mbps. The standard is based on The header portion of the WiMedia physical layer frameOrthogonal Frequency Division Multiplexing (OFDM). Since structure contains critical information that is needed to decodeit is meant to equip a wide array of consumer electronics, the the rest of the packet, i.e. the payload. While the payload candesign stresses low cost hardware and low power consump- be transmitted at either low or high data rate, the header istion. Low power consumption is primarily achieved via duty always transmitted at low data rate to ensure high protectioncycling: packets are burst at high data rate and the device against channel impairments and noise.can nearly shutdown between packets, thereby saving power. WiMedia's first design of the header structure was to appendNevertheless, optimizing every piece of the system helps in 52 zero bits to 148 pre-specified data bits to make it compatiblereducing cost, silicon area and power. with the interleaver size (the Reed Solomon bits in Fig. 1 used

In this paper, we revisit the Reed Solomon (RS) code that to be zero padding). Hence, there was a waste of 52 bits thathas been recently added to the WiMedia standard in order to the receiver ignored.improve the protection of header information. The header is A few years later, WiMedia decided to replace the 52 wastedconstructed as shown in Fig. 1. zero bits by additional header protection. The main reason

In section II we describe the header information and the RS was to make sure that if in the future the payload coding iscode. In section III we propose to replace the RS code by a improved, the header coding is still stronger than the payloadrepetition code: same or better performance in most cases, less coding.hardware and less power demand. In section IV we suggest The WiMedia choice for the 52 padded bits was to use Reedusing the same repetition block to protect short payloads, Solomon code (Fig. 1). The design of the code is backwardand possibly to implement lower data rates (thus increasing compatible so that old devices that ignore the 52 padding bitsrange). In section IV-C we discuss how this repetition code can continue to function normally. The RS code easily satisfies thisbe occasionally substituted for WiMedia's Frequency Domain condition since it is a systematic code: the information bitsSpreading (FDS) and Time Domain Spreading (TDS): the are sent as is and parity bits are inserted in the position of therepetition code in this scenario provides better performance as 52 padding bits. Old devices ignore the parity bits and theira trade for its higher power consumption. We give simulation performance is unchanged. New devices can use the parity bitsresults and a qualitative analysis in section V, and conclude to enhance performance.in section VI. The RS code was chosen to be a (23, 17) systematic code,

1-4244-052 1-1/07/$20.00 ©2007 IEEE

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which is obtained by shortening a (255, 249) systematic code One example of repetition pattern we can propose is to[2]. This code is capable of correcting up to 3 bytes of errors in repeat all the coded bits from the convolutional encoder'sany of the 23 transmitted bytes. The code's parity is calculated upper branch (this is 148 repeated coded bits) and 8 morebased on PHY header (5 bytes), MAC header (10 bytes) and bits from the encoder's lower branch spaced apart by 54 bits.CRC (2 bytes). The CRC is needed to check that the decoding In other words, repeat the following coded bits: 0 to 441, inoperation succeeded. The total RS code's information is 17 steps of 3; and 2 to 380 in steps of 54.bytes. The parity bits consist of 6 bytes (48 bits out of 52). Other repetition patterns can be devised. For example, aThe remaining 4 bits out of 52 are used as tail bits for the simple scheme uses a fractional step to select what bits areconvolutional encoder. The total number of bytes for the RS repeated (more details in section IV).code, information plus parity, is 23 bytes. The total number of repeated bits is 156. There are two

After the header is encoded by the outer RS code, it is sent options:to a rate 1/3 inner convolutional encoder with a constraint . We append the repeated bits to the end to form 600 codedlength of 7 followed by an interleaver [3], [4] (Fig. 2.a). bits. This solution maintains backward compatibility with

------- older devices that ignore the repetition bits. But theRS Convolutional Interleaver disadvantage is some buffering requirements. The RS

Encoder i Encoder code too has buffering requirements, but possibly not as(a) WiMedia standard much.

------- . We insert the repeated bits in between the original bits.Convolutional

Encoder Repetition Interleaver This solution is the simplest from a hardware perspective--------- without a need for any buffering. However, backward

(b) Repetition scheme compatibility is lost. In this case, a MAC message or

Fig. 2. Header transmission blocks: (a) current standard, (b) proposed a special header bit may signal the type of header; old or

repetition code. Replaced blocks are denoted by dashed line. new header.

The total length of the header at the input of the con- IV. EXTENSION TO PAYLOADvolutional encoder is 200 bits. Thus, at the output of the A. Short Payloadconvolutional encoder, the total length is 200 x 3 = 600 codedbits (Fig. 3). The same repetition block suggested above can be extended

for use in the payload. Any short payload automatically, benefits, e.g. short voice packets transmitted every 20 ms. The

Header Convolutional Coded empty padding before the convolutional encoder is replacedBits EcdrBits(200) Encoder (600) with repetition after the convolutional encoder (Fig. 5).

Fig. 3. Convolutional encoder, rate 1/3. ConvoluPuncturer --0- InterleaverPadding Encoder

(a) WiMedia standardIII. HEADER PROTECTION BY REPETITION CODE

We now propose to use repetition instead of RS coding. Cnvoltn iRRepe tition Puncturer InterleaverRather than considering the 52 padding bits before the con-volutional encoder, we look at them after the convolutional (b) Repetition Schemeencoder (Fig. 2.b and 4). The 52 bits become 52 x 3 = 156

Fig. 5. Payload transmission blocks: (a) current standard, (b) proposedcoded bits. On the other hand, the useful information bits repetition code. Replaced blocks are denoted by dashed line.are 200 -52 = 148 bits. After the encoder they become148 x 3 444 coded bits. Therefore, we can send just 148 The repetition block is inserted between the encoder anduseful information bits through the encoder to obtain 444 puncturer (on the receiver side it is inserted between thecoded bits. Then we apply a repetition pattern, repeating 156 de-puncturer and the Viterbi decoder). Zero padding is notcoded bits, to fill up the gap and obtain 600 coded bits, as performed. Instead, the size of the zero padding area isrequired by the next stage (interleaver). supplied to the repetition block in order to compute the step

Codedsize between repeated bits. The repeated bits can be placed in

Header Bits Coded the area reserved for zero padding in order to maintain back-Bits (444) Bits ward compatibility. But this can mean substantial buffering.(148) Convolutional Repetition of (600) However, backward compatibility may not be necessary: a flag

Encoder 15 oedbtn the header can indicate that payload repeXtiton iS enabled.In this case, we mix the repeated bits with the original bits,

Fig. 4. Repetition after the convolutional encoder. and no buffering is required.

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The step size between repeated bits can be a fractional 0bps 640number that is cumulated until it crosses an integer boundary. Mbps C l Mbps Use high data TDS

. . , , , , . Convolutional Repetition rate InterleaverEvery time it crosses the boundary, we repeat one bit. Encoder every 15th bit and subsequent

B. Lower Data RatesFig. 7. Example of repetition instead of puncturing/TDS for 200 Mbps. The

The repetition block can also serve to decrease payload data rates of 600 and 640 Mbps are coded bit rates.rates below the current 53.3 Mbps in order to increase therange. The amount of repetition is signaled in the header. Therepetition block calculates an integer or fractional step size then repeat twice via TDS to obtain the final coded bit rate ofand repeats bits accordingly. For example, 53.3 Mbps can be 640 Mbps.divided by 4 to obtain a data rate of 13.3 Mbps, a spreading Our proposal is not to apply any puncturing after thegain of 6 dB which approximately doubles the range. encoder but rather to repeat a fraction of the 600 Mbps toThe repeated bits are inserted in between the coded bits. obtain the coded bit rate of 640 Mbps. In other words, repeat

The interleaver automatically distributes them over different once every 15th coded bit. Essentially, we combine puncturingsubcarriers and frequency bands. and TDS into a single repetition block.

However, at the increased range, the header itself has to The coded bit rate of 640 Mbps before the interleaver isbe transmitted at lower data rate via repetition. And more identical to the rate obtained by existing high data rates suchproblematic is the preamble issue: it has to be extended in as 480 Mbps. Hence, the interleaver and all subsequent blockslength and certain simple preamble detection algorithms may can be set in high data rate mode (no additional hardwarenot work. required). Also, the FFT runs twice faster as in high data rate

modes.C. More Optimum than FDS and TDS

There is one more feature of the repetition block. For certain V. SIMULATION RESULTSdata rates such as 80 Mbps and 200 Mbps, the current Fre- A. Header Protectionquency Domain Spreading (FDS) and Time Domain Spreading Fig. 8, 9 and 10 show header simulation results in Additive(TDS) are suboptimal forms of repetition. Two reasons: White Gaussian Noise (AWGN), and in IEEE 802.15.3's

. They apply repetition after puncturing, which results in Channel Model 2 (CM2) but without shadowing. Results fora coding loss, even in AWGN. CM3 are similar to CM2. In Fig. 9, frequency band hopping

. They apply repetition after interleaving (and they do is turned off. This is denoted by Fixed Frequency Interleavingnot interleave properly), which results in a diversity loss (FFI) in the WiMedia specification. In Fig. 10, frequency bandin non-AWGN channels, mostly when frequency band hopping is turned on. This is denoted by Time and Frequencyhopping is turned off. Interleaving (TFI). In TFI mode, we hop over 3 frequency

The worst case scenario exhibits more than 1 dB loss (cf. bands and we are allowed to increase transmission powersection V). The repetition block that we propose in this paper threefold (4.7 dB). The results give the Header Error Rateis an optimal form of repetition and recovers the entire loss. (HER) as a function of the signal to noise ratio, i.e., Eb/No.

Nevertheless, the puncturer and FDS/TDS have important The results show that the RS code outperforms the repetitionadvantages: they allow the hardware to run at lower speed and code only at high Eb/NO, i.e., at very low HER. This issave power. Hence, the repetition scheme can be occasionally when the RS code is very powerful because errors are highlyused to trade power for performance (Fig. 6). The header can concentrated. But this is not necessarily the regime we aresignal what scheme is in use. interested in. The regime of interest is the range of HER that

corresponds to a payload's Packet Error Rate (PER) muchI------- I-- above i0-. At this PER, a HER of about i0- is more thanPuncturer I nterleaver FDS/TDS _ sufficient.

Convolutional (a) WiMedia standard For the useful range of HER > 10- 4, repetition eitherEncoder outperforms RS coding or slightly under performs, by less

I1------- than 0.2 dB. Moreover, the repetition code is more immuneRepetition Interleaver to shadowing given the higher performance at low Eb/No.

(b) Repetition Scheme Repetition is a much simpler code that provides sufficientheader protection in the range of interest.

Fig. 6. The system can select between puncturing/FDS/TDS or repetition. Note that the performance in FFI mode (Fig. 9) appears tobe better than in TFI mode (Fig. 10) since in FF1 mode 6

The repetition scheme works as follows. Let us consider symbols are dedicated to channel estimation whereas in TFIthe example of 200 Mbps (Fig. 7). After the convolutional mode only 2 symbols are dedicated to channel estimation perencoder, the coded bit rate is 3 times higher, i.e., 600 Mbps. frequency band. However, since in TFI mode the UWB deviceCurrently we puncture to achieve a coded bit rate of 320 Mbps is allowed to transmit 3 times more power, this difference in

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100 original RS code is (255, 249), with which the repetition code............................... cannot com pete:in out of 249 bytes,there is no room

10~~~~~~....... for enough repetition. But after shortening it to (23, 17) the------ ........................ repetition code has a chance to compete: in 6 out of 17 bytes,

102 there is room for sufficient repetition.............. Here-isa-moredetaild.explnation.At.lo.HER,.ay....

-I-.......Repetition ........ ............ by esrte Rsa coredetfixes it.If atheeror. is 4lor moRe bayts th

103 bfera ieridsoingleerr ,vn of lngthalof thaeorde moft3obyes Tero

102 whether...the.packet..length--is-23--or 255..bytes.

1 0 .....o.... vntthe apacketsz. Tif werod venote the nheader informationtleg thu-e- No Protection ----mn fwogbt htetnsoe ,2 rmr

RedSolomon r................ cnepettion gainsis nteerr sls hn reult-- epetition

-1 0 1 2 3 4 5 6 Rpcoetition. Gaierrvntln11gth( +nbyt dB,(2)teViebEb/No (dB) deoe,imaryidpneto h legt mftepce.I

anlydeisendependetothe operating Eb/Notha Foreve th 255Fig.9. RS code vs. Repetition inC2AWNdFme. bytes,3tHengain isgaonlye0. dB, andsiteoisediffcultto3properl

0 o~~~~~~~~~~~~dsri25butes,athere eat redbis Fopratin 23bytes, thee gaionis0....................... 1.3 dBaindl wer ca en ts oothlyn tditib t theordepeito nbites. aTher

...........theconoltioal.ncder.Hece,reetiioninWiMdiaUW..o.. offers.. similar...gains..to..the .RS.code..

..............................(Fig.R 9)?e Thvie sans efise daiversit gainbhieteueetto1 0 decoder.acts.before he.Viterbi.decoder.nd.takes.full.advan

.....E/N (d) oss I TF mde thdeW aiMedia 3ecdinB rvdseog..................dierit, ndheceboh eptiio ad S ods ehve a

mode cannotbe dieclycopae on ths graphs..temreotmu.eetto.cd.Fi...sospalasimultionth raesuts forn200 Mbs inor25AddtiesWie. assa

bettr.thn.te.RScod.... Why?..........A.quc answe isthat....the... shOws the sameradbtheginTF odef hre sultsio given thes dpacetd

-3 .6 72.

100F, f 100 - .

0-AWN TD <>XXWNTS'\\

0 0 ON~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-2 -O-AWGN Rep'..\'.----.-2 -O-AWGN Rep<CM2TDS \ -A\-G- \ ACM2TDS A

|*-A*CM2 Rep i0000'0t 00i0000 000p-A*CM2 Rep :::::::A ::;:::: :::::

1 2 3 4 5 6 7 1 2 3 4 5 6 7Eb/No (dB) Eb/No (dB)

Fig. 11. Time Domain Spreading vs. Repetition for 200 Mbps payload, in Fig. 12. Time Domain Spreading vs. Repetition for 200 Mbps payload, inFF1 mode. TFI mode.

Error Rate (PER) as a function of the signal to noise ratio, We also used the proposed repetition scheme to develop newEb/NO. ideas for improving the system performance of short payloads,

In AWGN, we observe that the repetition code offers a achieving lower-than 53.3 Mbps data rates, and transmittingcoding gain of about 0.6 dB with respect to TDS. In addition, the existing data rates in a more optimum way than usingin CM2 the repetition code has a diversity gain of 0.6 dB in FF1 spreading such as TDS and FDS.mode and 0.3 dB in TFI mode. Hence, the total gain is 1.2 dBin FF1 mode and 0.9 dB in TFI mode. Despite spreading, the REFERENCEScurrent TDS scheme lacks some diversity in FF1 mode. [1] WiMedia Alliance, ECMA-368, High Rate Ultra Wideband PHY and

MAC Standard, 1st Edition, December 2005.VI. CONCLUSION [2] 5. Lin and D. J. Costello, Error Control Coding, 2nd edition, Prentice

Hall, 2004.We proposed to replace the Reed Solomon code in WiMedia [3] D. Tse and P. Viswanath, Fundamentals of Wireless Communication,

UWB by a simpler, better performing repetition code. The Cambridge university Press, 2005..............[4] A. Goldsmith, Wireless Communications, Cambridge University Press,

encoder/decoder complexity of the proposed repeXtiton scheme 2005.is almost negligible compared to that of Reed Solomon.

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