Luby Transform Coding Aided Iterative Detection for Downlink SDMA Systems

LUBY

TRANSFORM CODING

AIDED ITERATIVE

DETECTION FOR DOWNLINK

SDMA SYSTEMS

C.Y. Wei, T.D.

Nguyen, N.

Wu,

J.

Akhtman,

L.L.

Yang and

L.

Hanzo

School of

ECS.,

Univ.

of

Southampton, S017

1BJ,

UK.

Tel:

+44-23-80-593 125,

Fax:

+44-23-80-593 045

Email:

[email protected],

http://www-mobile.ecs.soton.ac.uk

ABSTRACT form(LT) codes[1]wereproposed forsolving this

prob-Divi- lem in the context of the conventional Internet, where the main cause of packet erasure is statistical

multiplexing-sionMultipleAccess(SDMA)systemusing iterative de- induced collisions, rather than fading and co-channel tection is

proposed,

which invokesa

low-complexity

near-

interference.

Inordertofill thepacket

erasures,

LTcodes Maximum-Likelihood (ML) Sphere Decoder

(SD).

The .. a f .

Ethernet-basedInternet sectionof the transmission chain

ulize

a

certa

fraction

of

redundant packets and,

as a inflicts random

packet

erasures, which is modelled

by

mbenefit,

we

can

dispense wth

anypacket acknowledge-the

Binary

Erasure Channel

(BE),

while the wireless

rents

In

other

words,

give

a

sufficiently

high fractio downlink

imposes

both

fading

andnoise. Anovel

Log-

of

redundant

packets the LT

decoder becomes

capable

Likelihood Ratio basedpacketreliability meric is used of

detefctien

pets

witheout

reltransm

for

identifying

thechannel-decoded

packets,

whichare

miThe

efficient design

of the

down-link wireless

trans-likely tobe error-infested. Packetshaving residual er-

mitte

hi

praount

i Te

fa

o

thetsake

o

Iev-rors must notbe passed on to the LT decoder for the

aud

high

t put The

fami oMultipl Iut

sakeofvoiingLT-dcodng-ndued erorproaga andMultiple Output (MIMO) systems employing

mul-tion.

Theaproposed

schemeoisncapableeof maintaininggan

tiple

antennas atboththe

transmitter

and receiver have

ion.fTesimalyslo

pcket er ratio

intetoinik

of

the

ability

to

satisfy

these

challenging requirements,

since

infiitheswirele

Intern f

ket

Eb

rror

rval

in.e

ofnabou

they

exhibita

substantially higher spectral efficiency

than

3dB.

_3dI3*

conventional single-antenna aided systems. The flexible

_{configuration}

ofaMIMO

system's

antennasallowsusto

satisfyanumber ofpotentiallycontradictory design

ob-1. INTRODUCTION jectivesin terms of the achievable multiplexing and di-versity gain[2,3].InthiscontextSpatialDivision

Multi-Intheconventional

Internett

theTransportControl

Prro-

ple Access (SDMA) constitutes an attractive MIMO

sub-tocol (TCP)is usedforrequesting thesource to

retrans-

class, which is capable ofachievinga high user capacity mitpackets that were lost owing to statistical multiplex- by supporting a multiplicity of subscribers within the ing. In addition to the packet-loss events inflicted by samefrequency

bamdwidth

[4,5].

statisticalmultiplexing,inthewireless Internetpackets

maybecorrupted owing to the hostile channel

condi-tions encountered and hence the retransmission over- M B

head maybecome excessive. A particularproblem in 3 h |

hostile wirelesschannels isthat the flood ofpacketac- A B E Chne

knowledgements requested by the plethora of Mobile

Station

(MS)

may overwhelmnot

only

the Base Station

(BS)

butthe entire network. Thisdeficiency may severely Uplinkwirielesschannel Internetchannel Downlink wirelesschannel

limit the effectivedatathroughput ofthe system. Thus

the

provision

of reliable

packet

transmission -

prefer-ably

without

invoking

an

acknowledgement-based

re-

Fig.

1. Data transmissionscheme

transmissionmechanism-isvital. In2002,

Luby

Trans-sg

Thefinancialsupportof theEUunder theauspices of the Phoenix

adNewcom project aswell as that the EPSRC UK is ratefull ac- In this treatise we considered the system

aided Down-LinkSDMAsystem(LT-DL-SDMA).Asshowniterativedecoding aided system, where extrinsic infor-inFigure 1, we considered the scenario, when Mobile mation is exchanged between the precoder's decoder Station (MS)Bwould like to receivedatapackets from and the convolutional channel decoder ofFigure4.

Fur-MSA, whereBS AandBareconnectedtoeach othervia thermore, based onthe soft-bit outputs of the channel either theconventional Ethernet-basedInternet orbya decoder, we introduced a packet

reliability

metric cal-dedicatedoptical fiber backbone. Inthisstudywecon- culation technique for

quantifying

the Packet Reliabil-sider the Ethernet-basedInternetaided scenario, which ity Information (PRI) forwarded to theLTdecoder for inflicts packetserasuresowingtostatisticalmultiplexing- informingitas towhether thepacketconsideredis suffi-induced packet collisionevents. First, the datapackets cientlyreliable foremploymentbytheLTdecoder.More are generated either bya conventional Ethernet-based explicitly, based on thePRI, the LT decodererases the terminalortransmitted fromMS A viathewireless up- unreliablepackets,

namely

those that are

likely

to

con-linkchannel to BSA. Then thedatapackets arerouted tainerrors,inordertoperfectlyrecoverall the

original

through the statisticalmultiplexingaided Ethernet-based data packets. Bycontrast, unreliable

packets

must not

BS-BSchannel, wheresome packets may be lost. These beforwardedtotheLTdecoder,sincetheywould inflict packet-loss events canbe modeled by the Binary Era- ahighnumberof further

propagated

errors,

depending

sureChannel (BEC) [6],whichischaracterizedbyasin- onthespecific

degree-distribution

of theLTcode

[11].

gleparameter, namely byitspacketdropping probabil- The rest of this paper is structured as follows. In

ity Pe. Finally, BS B receivesthedatapackets from the Section 2 we outline the transmission scheme consid-Internetand thentransmitsthemviathewireless down- ered. In Section 3 we detail theSDMA DL designand link channel toMS B. introducea measureof the normalized system

through-As shownin Figure 2, the LTpackets generated by put. The LT

decoding

aided receiver

employing

itera-MS A and receivedbyBS A are conveyed first via the tive detection is summarized in Section

4,

followedby Ethernet-based,lossyInternetmodeledby theBECchan- the

portrayal

of the above-mentioned

packet reliability

nel, while BSB at the

output

of BEC channel forwards calculation

algorithm

in Section5. Our

performance

re-the LTpackets to the target user. Since we focus our sultsare

provided

in Section 6.

Finally,

weconcludeour attention on theDL transceiver design inthis treatise, discourse in Section 7.

we assume that the packet source is either a fixed

ter-minalcorrectlyconnected tothe conventional Ethernet 2. SYSTEMOVERVIEW or, alternatively that no impairments are imposed by

the uplink wireless channel between MS A and BS A. Again, the system's schematic is outlined in gradually In our DL transmitter design, the LT packets are for- increasing detail in Figures 1 - 4. Let us consider, for wardedtotheconvolutional channel encoder ofFigure example, thetransmission of 13 000 LT encoded

pack-2followedby aninterleaver,aswellas a unity-ratein- ets, which were generated from 10 000 source packets

nerencoder[7]andfinallytothemodulator. The modu- byincorporating

30%

redundancy. At a packet erasure latedsignalistransmittedby the Multi-UserDL-SDMA rate ofP, =0.1 we will lose 1300 randomly positioned

scheme of Figure 3, which employs a spatio-temporal LTpackets, while the LT packets are routed over the

In-SDMA DLpre-processing technique proposed byChoi ternet. The LT packets, which do reach BS B will be and Murch

[8],

allowing for a specific user to receive transmitted via the wireless downlink channel to MS his/her dedicated signal, essentially free from Multi- B of Figure 1. The DL transmitter of the BS encodes

user Interference (MUI) inflictedbyother users. In or- thebits of the LT-encoded packets using both a convo-derto maintain ahigh datathroughputfor the system, lutional encoder and a unity-rate precoder, as shown

anovel detector suitable for the so-called rank-deficient in Figure 2. The rationale of using the unity-rate

pre-scenario is considered in theproposed DL-SDMA sys- coder serially concatenated with the convolutional

en-tem [9],where the number oftransmitters exceeds the coder is that it improves the convergence of the itera-numberofreceivers. While lineardetectors,suchasthe tive receiver, when its decoder exchanges extrinsic

in-Minimum MeanSquareError(MMSE)detector[4]were formation with the convolutional decoder of Figure 4 shown to perform unsatisfactorily inhigh-throughput [7]. When using the system parameters summarized

rank-deficient scenarios, the novel

Optimized

Hierar- inTable

1,

the DL-SDMA system employed the

Multi-chy

(OH)

RSA-aided ML detection method of

[10]

ex- UserTransmission (MUT) scheme of Figure 3 for trans-hibitsa relativelylow complexityeven inhighlyrank- mitting the data stream of MS B [9] in Figure 1. Figure deficient

scenalrios

and thus itsemployment is

mLeritolri-

4

detarils

the

desigln

of the MS's receiver, utilizing the

ous. so-called Optimized

HEierarchy

lReduced

Search

Algo-In orderto further increase the attainable

performnance,

rithm

(OH1RSA)

of [10], which is suitable for the

de-coder assistedby thePRIprovided by the convolutional element of

H(')

is characterized by a complex-valued

decoder

generates

therecoveredsource

packets

consti- scalar channel coefficient

H(k)

which

represents

the link tuting theoriginal data file. In ourforthcoming discus- between the i-th BStransmitantenna and theI-thMS

re-sions we willbrieflysummarize theoperationofMUT ceiver antenna of the k-th user,and each fadingMIMO

schemve

[9. utilized and outline the corresponding re- link is modeled by an

i.i.d.

complex Gaussian random ceiver design employing iterative decoding. variable having a variance of unity and a mean ofzero. Inorder to eliminate theMUI,letus now construct LT LT Interleaver the MUT preprocessor Tk of Figure 3. As outlined in

[9],

Pa BEC UnityRat Mod. Tkcanbe basedonthenulls ) of

H(i)

LEncoder Precoder calculated using

the

SVD[12] of

H(k)

expressedas:

DLTransmitter (k) = j(k) U ) 0 ° V(k)H (

Fig.2. Transmitterof the k-thuser

where

H(k) (k- (k+) (K) T

s(K)

>,.T(ff) 7 As advocated in [9], we will categorize the poten-(2)'---;@-<<-/ CHI(II) X i tial system design options ofan (M x N)-dimensional

S(1) msi

~~~~~~~~MIMO

system,

where M

and

N

refer

to the number

of

transmitandreceiveantennas. Toelaboratea little

fur-_K)

ASH2 .ther, the total number ofantennasemployed by all theK user terminalsis KNk. Letus nowintroducea measure

MlK <

.of

<~

thenormalized

system

load

expressed

as

Ms

(3)

Base Station N

Consequently, we may distinguish three different

sce-Fig.3. Multiusertransmission intheLT-DL-SDMAsys- narios asfollows:

temusing theusefulsingle-usertransmitterof Figure2

1. lightly-loaded

scenario, for Ls= 1;

2. fully-loaded scenario, for

L5

1;

LD-

LD-

t-r-v-

p 3. rank-deficient or 'over-loaded' scenario, for

Ls

>

H 1.

LT L0D-lap' DeincodaveCony. HFt D-PeoeUnit Rate4DtDtco__Dteto

DeoDecoder ecoder Lr LrPreoe Lapt 4. LTCODINGAIDEDRECEIVERUSING

PRI ate

ITERATIVE DETECTION

Fig.4. LTcodingaidediterativelydecodedMS receiver First, the detector constituting the first stage of the

re-design ceiver is theOHRSA [10], which is adapted for

employ-ment in oursysteminordertoreduce thecomputational

complexity imposed by theMLdetector usedby each of the MSs. Thederivation ofanexpressionfor the

low-3. MULTI-USER TRANSMISSION SCHEME

complexity

evaluation of the soft-bit information

associ-ated with the bitestimatesof theOHRSA detectorwas

Again, theMUT schemeconsidered isdepictedin Fig- alsogivenin [10].

ure 3. More specifically, the BS employs M transmit Later,iterative decoding iscarried outby

exchang-antennas for supporting KMSs, eachemployingNkre- ingextrinsicinformation between theunity-rateprecoder's

ceive antennas. decoder and the channel decoder. Figure 4illustrates

InLthiscontributioln we consideraflLat-fadingMIMO the iterative receiver

structure,

wvhere

L represents the channel. The MIMO channel corresponding to the k- LLRs. The super-script Detindicates the detector, P de-th user may be described by an (Nk x

Mi)-dimensional

notes the precoder, while Decrepresents the channel

extrinsic anda posteriori LLRs, respectively. First, the unity-rateprecoder's decoderprocessesthe soft-bit

out-putL/et4 of the detector generatedinthepreviousstage LT Packet size 120 bits and theaprioriLLRvalues

Lpr'

whichareappropriately L

arrangedby the interleaver areproducedfrom theex- distribution [11]

trinsic information LlYe of the channel decoder. Then Numberofinformation packets 10, 000

the extrinsic information L7 to be used

by

the

unity-

Numbero r paes 3 0

rate precoder's decoder is obtained from

L'pt

by sub- 01

tracting the a posterioriLLR values

Lapr.

Then, aspor- Recursive

Systematic

Code RSC(5,7)

trayedinFigure 4, the channel decoderprocesses Lpr, Interleaver length

10'

bits

whichwasgeneratedbythe deinterleaver '- fromLp, Modulation 4

QAM

and outputs the a posteriori LLRs LDe, to be used as a Number ofusersK 3

feedback for thenextdecodingiteration. When theiter- Numberoftransmit antennasM 6for

L,

=1,

ations arecurtailed, the channel decoderoutputs L/De,

8forL,=1.333

whichrepresentsthe hard decision based data bits. Number ofreceiveantennas

Nk

2

Normalized

Doppler frequency d.

f

=fD T=0.001

5. PACKETRELIABILITYCALCULATION

Inorderto assisttheLT decoderinsuccessfully decod- However, only 11 700 packets are transmitted by the BS ingthe receivedpackets,theLTdecoderrequiresamin- to MS B of Figure 1 owing to the 10% packet loss rate imumnumber of error-free unerasedpackets.

However,

of the BEC channel. It was found in our experiments

when the packets are transmitted through the hostile not shown here that the minimum number of packets

wirelesschannel,somepacketsmaynotbecorrectlyde- required for achieving a high probability of successful

coded. IftheLTdecoderprocesseserror-infestedpack- LT decoding is 11 000. Then we have toconsider two ets, the error will be propagated to all other packets, decoding scenarios, namely when the number of

erro-whicharerelatedtothisparticularpacket,asdetermined neous packets is higher than 11 700- 11 000= 700, as

by the LT code's degree distribution [11]. Hence we well aswhen it is lower than 700. In the former specific

haveto ensure thatonly error-freepackets areusedby case, the 11 000 packets chosen for LT decoding may

the LT decoder, and thereforewehave toidentify and contain some incorrectly decoded LT-encoded packets,

erase the incorrectly decoded packets. For the sake of which hence result in error propagation. However, in preventing errorpropagation, it is standardpractice to this scenario the best course of action is to stillforward

use Cyclic Redundancy Checking (CRC) for error de- the most reliable 11 000 packets for LTdecoding based tection, although this requires a substantial transmis- on thePRI. In other words, we remove the 700 most un-sionoverhead of 16bits,whichmaybeonthe orderof reliablepackets, because the chances are that this way

100,.

Hence here we introduce an attractive

technique

we may indeed succeed in

removing

all the incorrect

ofquantifying thereliabilityof the channel-decoded

pack-

packets andhence successfully LT decode all the source ets, whichis referred to asPacket Reliability Informa- packets.

tion(PRI). Thistechniqueimposesnotransmission

over-head. Basedonthis PRI,weidentifythe channel-decoded

packets, which aredeemedtobe error-infested. 6. PERAND BERPERFORMANCE

The PRIis calculated based on the Log Likelihood

Ratio (LLR) [13] of the bits. Hence we introduced an Herewe continue our discourse by

characterizing

the

LLR threshold, denoted as It. A channel decoded bit PER versuspacket-length performance of theinner en-is deemed reliable, if the absolute value of its LLR is coder/decoder scheme of Figure 5. As

expected,

the higher than It,where the thresholdIt hastobecarefully PERdegradesupon increasing the

packet-length,

since

chosen. By contrast, ifthe absolute value of the LLR the probability ofhaving residualerrors after channel

islower than It,it isdeemed unreliable. Therefore,the decoding increases upon increasing the

packet-length.

PRI ofa packet is simplycalculated as the percentage Further,itcanbe shown thatincreasingthe

packet-length

of the reliable bits in the channel-decoded packet. On increasestheLT-decodingcomplexity. Bycontrast, upon

increasing the interleaver length has the beneficial ef- 100 It-di-sdma-Pr:04-Oct-2006 E3 E E!

fect of reducing the PER owing torandomizing the bit- - -

---errors more efficiently. 1o-1 x----

-In this section, we characterize the achievable per- -

---X---formance of the LT-DL-SDMA

system

assisted

by

both i0-2 --

---a 16-bit CRC-b---ased ---and on theproposed LLR-based PRI

estimation scheme. The packet erasure rate Pe of the w0o-

--BEC was set to 0.1 and each. LT packet contained 120

bits. In

conjunction

with the CRC overhead, a source t-4N e-i

packet accommodated 136 bits. As seen in Table 1, we

Eb/NO=6,noiter=2

rwi

employed 4-QAM protected by the half-rate Recursive 1o- int

lengtht105-Systematic

Convolutional code

RSC(5,7)

having

a mem- int.

lengthl104

3

|

ory of three and using a 105-bitinterleaver, where(5,7) 1o6 LII 1_

60 120 180 240 300 360 420 480 540 600 660 720 780840 900 960

represent the generatorpolynomialsin octal format. A Packet length slow-fadingMIMO channel having a normalized Dopper

frequency of 0.001 was used. The system configuration Fig. 5. Inner PER performance of the LT-DL-SDMA studied supported K =3 usersand each user terminal schemehavinganormalized system load ofLs = 1.333

employedtwo receiver antennas. Finally, for the sake for different Eb/Novalues, packetsizes and interleaver of convenience, we assume that each MS is receiving lengths. Our system supports K=3users,where each

thesamenumber ofindependent data streams

Lt

from useremploysNA/ =2 receives antennas.

theBS, whichimplies that each user has the same data throughput.

Figure 6 portrays the PERperformance of the inner that the LLR-based PRI-aided scheme

slightly

outper-decoder scheme ofFigure 4 corresponding to the nor- formedits CRC-basedcounterpart,

owing

tothe

Eb/NO

malized system load of Ls

_of~~~~~~~~~

1.0,i,e. when the number

trnsi

anensi.

n h ubro ne penalty

imposed

by the 16-bit CRC overhead. It was pt

transmitted

toe

nuer

e

rinal-

shown in

Figure

6 that for

Eb/No

values in excess of

pendent

= t streams

tk=2.

IntheCRC-assistedscheme, about 3dB an

infinitesimally

low PER may be

achieved.

is Lt = M-

(K

-

1)

.Nk

=

2IntheCRCassistedschem.

, Our future research will focus on improving the

sys-the LT decoder iscapable of avoiding the decoding of error-infested packets. As stated above, in the

exam-ple considered the BEC erases 1300 packets out of 13 tweentheinner decodersand theouter LTdecoder.

000and hence 11700LT-encodedpackets will be

trans-mitted via the wireless downlink channel. Recall that 8. REFERENCES

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Nk,

=2receive antennas. All

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