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Halmstad University Post-Print

Incremental redundancy deadline dependent coding for efficient wireless

real-time communications

Elisabeth Uhlemann and Lars K. Rasmussen

N.B.: When citing this work, cite the original article.

©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Uhlemann E, Rasmussen L. Incremental redundancy deadline dependent coding for efficient wireless real-time communications. In: IEEE Conference on Emerging Technologies and Factory Automation, 2005. Piscataway, N.J.: IEEE; 2005. p. 417-424. DOI: http://dx.doi.org/10.1109/ETFA.2005.1612708 Copyright: IEEE Post-Print available at: Halmstad University DiVA http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-378

Incremental Redundancy Deadline Dependent Coding for Efricient WirelessReal-Time Communications

Elisabeth Uhlemannt T and Lars K. Rasmussen§tCentre for Research on Embedded

Systems, Halmstad UniversityBox 823, 301 18 Halmstad, [email protected]

TVolvo Technology CorporationTransport and Telematics ServicesDept. 6600, M1:6, Gotaverksg. 10SE-405 08 Goteborg, Sweden

§Inst. for Telecommun. ResearchUniversity of South Australia

Mawson Lakes SA 5095, [email protected]

Abstract

The concept ofdeadline dependent coding (DDC) hasbeen demonstrated as a promising design approach forefficient and reliable real-time communications overwireless channels. The main idea behind the concept ofDDC is to make all components of the communicationprotocol deadline dependent, tailoring the channel codeand the retransmission protocol to the specific real-timeconstraints. The DDCframework allows critical reliabil-ity and timing constraints to be readily evaluated as afunction of available system resources. Concatenatedcoding and iterative decoding within retransmissionprotocols enables additionalflexibility and new adaptivedesign options. Here, we introduce an incremental re-dundancy retransmission scheme in conjunction withconcatenated coding and show that this further improvesthe DDC scheme.

1. Introduction

Most embedded systems are expected to provide in-creasingly more complex and safety-critical services.Cooperation and communication between separated em-bedded systems typically found in a factory automationenvironment enables enhanced applications with strictreal-time and reliability requirements. Traditionally,communication in such production environments isbased on conventional wireline techniques. Wirelesscommunications, however, provides a new level of de-sign freedom and flexibility. Looking beyond simplereplacement of existing wireline solutions, entirely newapplications enabled exclusively by wireless communi-

This work was partly funded by the Knowledge Foundation, the na-tional Swedish Real-Time research initiative ARTES supported by theSwedish Foundation for Strategic Research and by Personal Comput-ing and Communication (PCC++) under Grant PCC-0201-09. L. K.Rasmussen is supported by the Australian Government under ARCGrant DP0558861 and by the Swedish Research Council throughChalmers University of Technology under grants 621-2001-2976 and723-2002-4533.

cations between system components can also be envi-sioned. This vision is supported by the ongoing wirelessrevolution when considering the trend towards coopera-tive embedded systems in all kinds of home equipment,automotive components, entertainment devices and lo-gistics services.

Even though wireless communication offers consider-able advantages for industry automation applications, thehostile wireless transmission environment has limited itsextensive use in systems with real-time constraints. In atypical wireless communication system, the channelconditions vary with time [1]. The inherent consequenceof this is a relatively high average error rate, making thewireless channel significantly less reliable in comparisonto copper wire and optical channels. Techniques for pro-viding strict reliability and deadline guarantees fortransmission over wireless channels must therefore bedeveloped.

The Deadline Dependent Coding (DDC) scheme pre-sented by the authors in [2] and formalized in [3] ad-dresses these issues. The purpose of DDC is to improvethe reliability of real-time communication over a wire-less channel by means of specifically tailored channelcoding. This is accomplished using forward error controlcodes in conjunction with a retransmission scheme, a so-called automatic repeat request (ARQ) scheme. TheReed-Solomon codes used in [2, 3] were replaced bypowerful concatenated codes with iterative decoding in[4]. Iterative techniques provide an entirely new level ofperformance and flexibility for DDC systems, makingthe approach very attractive. These schemes are closelyrelated to turbo coding, [5], which provides virtuallyoptimal use of the fundamental channel resources. Usingsuch strategies in a retransmission scheme also elevatesthe corresponding performance to levels close to funda-mental limits.

In this paper we keep the concatenated codes, but re-place the block repetition hybrid ARQ protocol used in[2-4] with a more efficient incremental redundancy (IR)hybrid ARQ (IR-HARQ) scheme. IR is tractable sinceno bits are transmitted more than once and hence repeti-tion of previously transmitted bits is avoided. IR wasfirst suggested in [6] and is considered here in the DDC

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framework. The redundant bits are ordered and parti-tioned for each transmission with the aim of obtaining ashigh reliability as fast as possible, using a minimum ofresources.

The paper is organized as follows. Section 2 reviewsthe idea and benefits of DDC for wireless real-timecommunications. In section 3 the purpose of using con-catenated coding for DDC is discussed, while section 4describes the concept of IR in hybrid ARQ protocols. Insection 5 the effect of correctly ordering the redundancybefore transmission is presented and its impact on theDDC scheme illustrated. Further, in section 6 the bene-fits of choosing correct packet lengths for each retrans-mission is discussed and the effect on DDC is demon-strated. Finally, section 7 contains our conclusions.

2. Deadline dependent coding

The objective of DDC is to enable efficient real-timecommunications in relevant applications for future mo-bile wireless communication networks. Development ofspecifically tailored channel codes makes the data linklayer and parts of the network layer protocols suitablefor reliable and efficient wireless real-time communica-tion.

Network protocols such as IP [7] have traditionallybeen designed for a best-effort approach regarding bothtimeliness and information reliability. The protocol suiteTCP/IP is a joint transport and network layer protocolsuite that provides reliable communication through errordetection and retransmission strategies, but offers onlybest-effort timeliness. Recently, quality of service (QoS)implementations extending into new IP standards havemade it possible to introduce priority algorithms, e.g.IPv6 [8]. Also the use of the UDP protocol in place ofTCP has made it possible to provide real-time multime-dia communication at best-effort information reliability.These extensions are based on modifications to protocolsoriginally designed for different purposes, which meansthat most existing protocol standards can only guaranteetimeliness or information reliability, but not both.

Besides TCP/IP there are a number of real-timecommunication protocols such as [9-11] that strives toensure delivery prior to deadlines. These protocols arebest-effort schemes in terms of information reliabilityand consequently do not give any guarantees or explicitprediction on the probability of correct delivery. Recentprotocols offering negotiable QoS in terms of timelinessrequirements have been suggested in e.g., [12, 13]. Theyassume, however, a reliable channel which is directlyavailable for optical wired applications. Unfortunately,in a mobile wireless environment, the encountered com-munication conditions are quite challenging compared towired communication in terms of signal degradation.The inherent error rate being significantly higher in awireless environment has prevented extensive use ofwireless communication in real-time systems with criti-

cal deadlines. The concepts of channel coding and re-transmission schemes must be introduced in order toprovide a reliable channel.

Another difficulty with a wireless channel is its lim-ited bandwidth. The radio spectrum is a limited naturalresource, assigned according to strictly enforced rulesand consequently additional bandwidth may be costly ormay not exist at all. Furthermore, wireless devices areoften battery powered and therefore put restrictions onthe maximal computational complexity and the transmit-ted signal power to prolong battery life. Moreover, giventhat we have a limited bandwidth, liming the transmittedpower also limits the inherent interference generated byother transmitters present in the local wireless multipleaccess system. All of this implies that the channel codeand the retransmission protocol have to be carefully tai-lored.

The main idea behind DDC is to make each compo-nent in the communication protocol deadline dependent.In addition to being subject to a real-time deadline, theinformation must also be delivered correctly with highprobability since information delivered before the dead-line, but in error, may have severe consequences. TheDDC communication protocol lets the timeliness and thereliability of delivered information constitute the QoSparameters required by the application. We thus considerthe probability of correct delivery, Pd, prior to reachingthe deadline tDL. Correct delivery implies that a certaintarget error rate, Pt, is met. Note that the target error ratecan never be equal to zero due to the presence of channelnoise [ 1 ].

Using these QoS parameters it follows that a protocollayer can negotiate values of the parameters with an up-per or a lower layer, thus enabling flexible admissioncontrol that provides a trade-off between the deliverytime and the quality of the delivered data. The values ofthe QoS parameters are requested by the application us-ing the communication system. The value of Pd controlshow reliable the transfer must be in a real-time perspec-tive, i.e., a measure of how critical the task is, and con-sequently, it does not say anything about delivery ofcorrect information after the designated deadline. Thenegotiation about the value of tDL reflects how soft thereal-time constraints on the deadline are.

One of the objectives of the wireless real-time com-munication protocol is to maximize the probability thatthe communication system will be able to accept thetransmission request with the required values of the QoSparameters. Besides maximizing the probability of deliv-ering the necessary information before a given deadline,the protocol should also attempt to minimize the requiredbandwidth, the transmitted energy and the average timerequired to successfully deliver the information. Thevalues of the QoS parameters are transformed into ac-tions to be taken by the link layer protocol in terms ofcoding and retransmission strategies specifically re-quired when using an unreliable channel. Consequently,

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the QoS parameters tDL and Pd are mapped onto a re-transmission protocol which plays the role of maximiz-ing the probability of correct delivery before the deadlineusing a minimum of resources. The DDC protocol thusperforms a series of transmissions triggered by the re-transmission protocol, providing increasingly more in-formation for decoding the closer we come to the dead-line.

3. Concatenated codes

The channel capacity formulated by Shannon [14] in-corporates into one composite parameter the effects ofchannel parameters such as thermal noise, constrainedbandwidth, and limited signal power. The significance ofthe channel capacity is that as long as the communica-tion rate is kept below the channel capacity, an arbitrar-ily low error rate can in principle be obtained if infinitelylong codes are used. Note that the term "long code" usedhere does not refer to the length of the informationframe, but rather the length of the codeword, or thelength of the code memory. Decoding complexity, how-ever, generally increases exponentially with code lengthand hence may prohibit the use of codes beyond a certainlength. At the same time as a long code will improve theperformance in terms of lowering the bit error rate(BER), it will also require more resources in terms ofmore bandwidth, more energy and above all, in this con-text, more time to transmit and decode. When a real-timecommunication system is considered, time is a limitedresource and hence we are not only concerned with lim-iting the length of the code in order to limit the decodingcomplexity but also to limit the overall communicationtime.

The channel capacity unfortunately only states whatcommunication rate is theoretically possible to achieve,but it does not say what codes to use in order to achievean arbitrary low BER for a particular rate. Therefore,there has been a gap between the theoretical limit and theachievable communication rates obtained using codes ofa manageable decoding complexity. Concatenated codesusing iterative decoding is a relatively new way of pro-viding long codes capable of virtually closing the per-formance gap while maintaining manageable decodingcomplexity. A turbo code is basically a concatenatedsystem of two simple component codes connectedthrough an interleaver in order to create a very long codeand also a very strong code [5, 15]. Optimal decoding ofsuch a system is intractable due to the length of the codeas determined by the size of the interleaver. However,the attractive characteristic of a concatenated system isthat iterative a posteriori probability (APP) decodingbased on exchanging soft reliability information betweenthe code components provides a low complexity sub-optimal decoding algorithm. This implies that each com-ponent decoder is used several times in the decodingprocess, usually once for each iteration. Hence, the soft

reliability information exchanged between the compo-nent decoders is iteratively refined and the interleaver isused as an integrated part of the code. The overall decod-ing complexity of the iterative decoding algorithm for aconcatenated code is lower than that required for a singlecode of the corresponding performance. The lower com-plexity is achieved by decoding each component codeseparately. The low-complexity decoders for the simplecomponent codes are used and iteratively reused severaltimes, instead of using one highly complex optimal de-coder for the full code.

In general, concatenated coding provides longer codesthat yield significant performance improvements at rea-sonable complexity investments. Given certain condi-tions, the iterative decoding algorithm performs close tothe fundamental Shannon capacity [5]. The ideas behindDDC have been extended by the authors in [4] to includethe principles of concatenated coding and powerful itera-tive decoding.

4. Incremental redundancy

Whenever a feedback channel is available, an ARQscheme [16] can be used. This implies that when apacket arrives, the receiver may choose not to accept it,but instead request a retransmission through the feed-back channel. This request can be done either by sendinga negative acknowledgement or simply by not sendingany acknowledgement. To determine whether or not aretransmission request should be generated, the receiverchecks the quality or the reliability of the receivedpacket. This two-way communication usually goes onuntil the receiver obtains a packet that is considered suf-ficiently reliable.A hybrid ARQ (HARQ) scheme [17] uses an error

control code in conjunction with the retransmissionscheme. Consequently, the received packet is first de-coded and a retransmission is requested only if the qual-ity of the decoding decision is too low, i.e. if the decodedsequence is below a certain reliability threshold. Thereare different methods of determining whether a decodingdecision is sufficiently reliable and hence different crite-ria for requesting a retransmission. The choice of methodsignificantly affects the character of the retransmissionscheme.

There are also different ways of handling packets re-sponsible for causing a retransmission. These "errone-ous" packets can either be dropped or they can be com-bined with one or more retransmitted packets. This pro-cedure of using the information in previously receivedpackets is termed packet combining and was first sug-gested in [18]. There are two different ways of usingpreviously received packets in order to improve per-formance, i.e. two different packet combining tech-niques, diversity combining, [18] and code combining,e.g., [19]. Diversity combining is typically implementedbefore the decoder on a symbol-by-symbol (or bit-by-

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bit) basis. Individual symbols from multiple identicalcopies of a packet are combined to create a single packetof the same length but with more reliable constituentsymbols. In contrast, a code combining scheme concate-nates several packets pertaining to the same frame on apacket-by-packet basis to form a codeword of lower rate,i.e., containing more redundant bits.

Further, there are different types of HARQ schemeswhich basically are defined by their respective packetcombining method. HARQ type-I, [17] uses no packetcombining and hence erroneous packets are simplydropped. HARQ type-Il, [20] uses code combining sothat increasingly longer codewords with lower and lowercode rate are formed for each retransmission. Finally,HARQ type-Ill, [21] uses diversity combining implyingthat identical packets are retransmitted and combined toform a new more reliable packet with maintained coderate. HARQ type-III is essentially packet repetition andconsequently just a variant of an HARQ type-II schemeusing a simple repetition code.

Previous versions of the DDC protocol [2-4] haveused HARQ type-Ill. In this work an HARQ scheme oftype-Il is used, i.e., a code combining scheme using IR.IR implies that the HARQ scheme responds to a re-transmission request by transmitting increasingly moreredundancy. This redundancy is then appended to thepreviously received packet, thus lowering the code rate.This way more advanced codes than repetition codes canbe created by the retransmissions. IR is usually accom-plished by so-called rate compatible punctured codes.Puncturing a code implies that certain code bits are re-moved before transmission so that the overall code rateis increased. The receiver needs to know the so-calledpuncturing pattern, so that erasures can be inserted in-stead of the punctured bits before decoding starts. Thepunctured bits can then later be sent in a retransmissionand thus bit by bit complete the lower rate codeword inthe receiver. A family of rate compatible codes impliesthat all code bits belonging to a particular code in thefamily also belongs to all other codes with a lower coderate in that family. The transmitter and receiver onlyneed to share a puncturing table to determine which codebits are to be transmitted next, and the receiver simplyinserts erasures for all redundant bits that have not yetbeen received. That way, starting with a high rate codethe transmitter only needs to transmit complementaryredundant bits to get to the next lowest rate code, andhence incremental redundancy can be accommodated.

5. IR transmission order

Since no repetition of previously transmitted paritybits is made in an IR scheme, the following notation isadopted. A data frame is a sequence of k information bitspassed through an encoder with code rate k / n, and thusgenerating a codeword of length n with n - k parity bitsor redundant bits. This code is termed the mother code.

The codeword is then partitioned into M . 1 IR-blocksas follows. For i = 1, 2, ..., M, let f denote transmissioni and let ci denote the number of redundant bits includedin f, such that ZM1c= n-k and 0 < c < n-k. Notethat f includes the k information bits as well as cl re-dundant bits, whereas for i >1, f includes only theredundant bits ci.

When f for i < M, is received, the decoder insertsthe newly arrived redundant bits at their respectiveplaces and consequently decodes a codeword of lengthni = k + ZY=i c1 If the reliability of the decoding deci-sion is too low, transmission f+1 is requested. The de-coder output is delivered to the user application as soonas decoding is successful or whenever the maximumnumber of packets M has been received. The targetframe error rate Pe can thus be obtained by proper de-sign of the mother code.

As an example mother code we have chosen a parallelconcatenated single parity check (SPC) code. Our SPCcode takes a block of seven information bits and adds asingle parity bit to it. We use three SPC codes concate-nated in parallel and separated by two interleavers ofsize 7.49 = 343. Each encoder thus adds 49 redundantbits to every data frame of size 343. Consequently,k=343 and n-k=3 49=147. We assume that thismother code will provide the required level of P

Further, we assume that tDL and the round trip delayallows a maximum of M = 7 transmissions or partitionsof the mother codeword. For simplicity we will choosethe packet sizes according to Table 1. This implies that24 of the 147 available parity bits should be included inthe first retransmission should it become necessary.

Table 1. Packet sizes for the schemesused in Figure 1. Here k = 343, n - k = 147and M= 7.

Tfi f2 If3 IA4 f5 Tf6 lf7Ci T 0 24 25 24 T25 T24 l25ni l343 l367 392 416 T441 T465 l490

An interesting question is now whether it matters howthese 24 redundant bits are chosen, i.e., we are interestedin knowing whether one particular puncturing patternleads to successful decoding faster than another. Due tothe regular structure of the chosen mother code, there aretwo cases that are particularly interesting: choosing all24 bits among the parity bits generated by the same en-coder or choosing them randomly from all available en-coders. We term the first option dimension-wise punctur-ing and the latter random puncturing.

By means of Monte-Carlo simulations we comparetwo schemes using random puncturing and dimension-wise puncturing respectively. Both schemes use the samemother code and packet lengths according to Table 1.The codewords are transmitted using binary phase shift

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200 250 300 350 400time units

Figure 1. Comparison of two differentpuncturing patterns or transmission or-ders; random and dimension-wise, plot-ted at signal-to-noise ratio 4 dB.

keying (BPSK) over an additive white Gaussian noise(AWGN) channel. To get an upper bound on perform-ance, perfect error detection (PED) is used as the re-

transmission criterion and thus retransmissions will takeplace whenever a bit error occurs. Further, we assume an

error free feedback channel, implying that no retransmis-sion requests are ever lost or misinterpreted. In Figure 1

the QoS parameter Pd is plotted as a function of time forthe two different schemes. The time is given in timeunits rather than exact time since the latter would requireknowledge of application specific parameters, such as

distance between sender and receiver, transmissionspeed, decoder hardware architecture, etc. The round tripdelay in this example is 60 time units and the first trans-mission arrives at time unit 0. Hence, every 60 time unitadditional parity bits will arrive if requested by the re-

transmission criterion.The iterative decoder will initiate iterations as soon as

parity bits belonging to two or more component decodershave been received. For the scheme using dimension-wise puncturing this does not occur until the fourthtransmission has been received. For the scheme usingrandom puncturing this may occur already in the secondtransmission arriving at time unit 60. An activation of a

component decoder is assumed to take one time unit inthis example. Since the chosen mother code consists ofthree component codes, one iteration takes three timeunits since all component decoders have then been acti-vated once. Looking at the dash-dotted curve in theenlargement figure within Figure 1, small steps can benoticed for time unit 61 to 67 corresponding to iterativerefinements of Pd. Once one iteration has been com-

pleted at time unit 63, additional activations yield more

and more diminishing returns.Further, we can see that the scheme using random

puncturing results in the value of Pd being lowered attime unit 121, when iterations start after having received

the third transmission. This is due to the fact that theiterative decoding process is restarted every time addi-tional redundancy arrives. This implies that some infor-mation bits that were decoded correctly and thus im-proved Pd are now temporarily reset when the iterativeprocess is restarted. Since a retransmission occurs evenif only one bit is in error, decoding is restarted even fordata bits that were correctly decoded. This is why thelevel of Pd drops at e.g. 121 time units. Note that thevalue of Pd does not drop to the same level every timethe decoding process is restated, since all packets neednot be retransmitted.

From Figure 1 we can also see that dimension-wisepuncturing is superior to random puncturing and thusalso that the IR transmission order influences the per-formance. The better the puncturing pattern - the fasterthe level of Pd increases and the earlier the correct resultcan be delivered.

The curves in Figure 1 at plotted at a signal-to-noiseratio of 4 dB. At higher signal-noise ratios, the gain ofdimension-wise puncturing is even higher [22]. Only forvery high noise levels can random puncturing have aslight advantage. The performance of a particular punc-turing pattern depends on the structure of the code. Inthis case, dimension-wise puncturing has an additionaladvantage in that only component decoders for whichparity bits have been received need to be activated. Thismeans that if only parity bits pertaining to one compo-nent encoder have been received no iterations areneeded. This can be seen in Figure 1 where the solidcurve lacks any small refinements until transmission fourhas been received at time unit 180. When parity bitsfrom two component decoders arrive, iterations includeonly these two decoders. This results in a less complexdecoding procedure since one iterations entails only twoactivations.

The above results are based on an AWGN channel. Ina wireless network, channel types such a block fadingchannels and other burst-error channels may be encoun-tered. Concatenated coding is well-suited for such chan-nels, as the parity bits in each dimension are based onencoding interleaved versions of the information bits.The decoding process therefore involves interleaved ver-sions of information bits, allowing for some randomisa-tion of burst errors. Further, the IR-HARQ scheme pro-vides some inherent time diversity.

6. IR packet sizes

The truncated HARQ scheme considered here impliesa limited number of retransmissions, which is controlledby the QoS parameters set by the real-time constraints.We assume that tDL together with knowledge of the bittransmission rate of the system will determine the maxi-mum number of retransmissions allowed in order to getthe required redundancy across in time. This means thatwhile Pd determines the necessary amount of redun-

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dancy, the bit transmission rate and tDL determines howmany blocks the redundancy can be partitioned into, andhence also the maximum number of round-trip delaysthat can be afforded.

Given that we have a mother code that yields the re-quired Pd after the M allowed retransmissions, we wouldlike to limit the total amount of transmitted redundancyin order to use as little of the available resources as pos-sible. This implies that we would like to maximize thecode rate of the system. In the previous section it wasconcluded that a good puncturing pattern will lead to ahigher Pd earlier in time. This implies fewer retransmis-sions and a higher code rate. In this section we will showthat by optimizing the amount of redundancy used ineach transmission the code rate can be maximized, givena particular puncturing pattern.

The code rate of a non-ARQ system is rc = k / n, butfor an ARQ-system we can only get an average code ratesince the retransmissions yields a variable code ratebased on the current channel conditions. Assume that wehave an IR-HARQ system that is limited to two packets,M = 2, i.e., a packet of n1 = k + cl is transmitted firstand thereafter a block of c2 parity bits is transmittedonly when necessary, resulting in a packet of lengthn2= k + c1 + C2 . Consequently, when using this scheme,some of the frames have been accepted using a code rateof only k / (k + cl ), whereas others needed a code rate ofk / (k + c1 +c2 ) . The average code rate of this IR-HARQsystem is the mean of these two code rates. Since a coderate in some sense is a velocity, the harmonic mean mustbe used according to

M=2 = (a kI +b 1 ') (1)rc ky k

where a and b are the percentage of frames of the respec-tive rate. We can express the average code rate as a func-tion of the probability of a retransmission, PARQ, accord-ing to [23]

Mrc

k(3)M

k+c1 +ZCiPARQ (n-j)i=2

The average code rate can be maximized by choosingoptimal values on ci for i = 1,2,...,M. Recall that wehave designed the mother code to cater for achieving therequired level of Pd. This implies that in the last trans-mission, CM should always include all the remainingparity bits that have not yet been transmitted accordingto CM = n - k - ZjM= ci. For M transmissions this resultsin an M -1 dimensional discrete maximization problemaccording to [23]

_ _ ~~~~MIcl,~ C2 ..., CM-1 I = arg max rc ICl ,C2 ... CM-1

(4)

where rC' is given by [23]

kMr _::::

M-1

k +c1 + Z CiPARQ (ni-I ) + CMPARQ (nM-l)i=2

(5)

In Figure 2 a Monte-Carlo simulation of a scheme us-ing the fixed packet sizes from Table 1 is compared toone using optimal packet sizes obtained analytically us-ing (4). Both schemes use dimension-wise puncturingand hence the solid curve in Figure 1 is the same as thesolid curve in Figure 2. The packet sizes for the two dif-ferent schemes are given in Table 2.

Table 2. Packet sizes for the schemes usedin Figure 2.

|ni n2 |n3 |n4 ns5 n6 |n7

Fixed: 343 367 392 416 441 465 490

Optimal: 422 427 433 441 457 473 490

M=2 k

k+cl+ C2PARQ (nl )(2)

In a Monte-Carlo simulation, PARQ can be determined bycounting the number of retransmissions actually madeduring the simulation. Note that the probability of a re-transmission depends on the packet length n1 in an IR-HARQ system. Using PED yields PARQ (ni) equal to theframe error rate after decoding a codeword of length ni.Generally, the more redundancy that is included in n1the smaller PARQ (nl) will be. Including more redundancyin the first transmission, however, also implies that themaximal average code rate is reduced. The expression in(2) can be generalize to M number of transmissions as[23]

The scheme using fixed packet sizes has received allof the parity bits from the first dimension after threetransmissions and all parity bits from the second dimen-sion after five transmissions. The scheme using optimalpacket sizes have received all the parity bits from thefirst dimension and also some parity bits from the seconddimension already in the very first transmission. Hence,the scheme with optimal packet lengths will start iterat-ing immediately after the first transmission. Again it isassumed that a new transmission arrives every 60 timeunit if the retransmission criterion requires additionalparity bits and that one activation of a component de-coder takes one time unit.

It can be seen that using optimal packet sizes yieldssignificant performance improvements in terms of

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0.998 _

0.997

200 250 300 350 400time units

I

... Reset all val- - -Continue the

Figure 2. Comparison of IR schemes us-ing fixed packet lengths and optimizedpacket lengths. Plotted at signal-to-noiseratio 4 dB.

maximizing the average code rate. This implies that weus less redundancy and therefore less resources, but alsothat the average communication time is reduced. Usingall seven retransmission corresponds to the worst case

since each retransmission increases the probability thatthe frame is correctly decoded and further retransmis-sions becomes unnecessary.

The curves in Figure 2 are again plotted at a signal-to-noise ratio of 4 dB. A higher signal-noise ratio results ina different set of optimal packet lengths as reported inTable 3. As can be seen less and less redundancy is re-

quired in the first transmission as the signal-to-noiseratio increases. If simple transmitters and receivers are

used, the optimization of packet lengths may be doneusing a look-up table as in Table 3. However, if morecostly receivers are available the choice of packetlengths can be done adaptively based on the current es-

timated channel conditions.

Table 3. Optimal packet lengths for differ-ent signal-to-noise ratios in dB.

[dB] n| n2 n3 n4 n5 n6 n7

2.6 457 460 464 469 475 482 490

4.0 422 427 433 441 457 473 490

5.3 387 392 405 416 427 441 490

6.6 343 364 379 392 426 441 490

8.0 343 369 381 392 467 478 490

9.0 343 374 384 392 424 441 490

10.0 343 378 386 392 469 479 490

11.0 343 380 383 387 390 392 490

050 1 00 1 50 200 250 300 350 400time units

Figure 3. A scheme not restarting the it-erative decoding process each retrans-mission is compared to one that does.Plotted at signal-to-noise ratio 4 dB.

A scheme that does not restart the iterative decodingprocess each time additional parity bits arrive will gaineven further time. In Figure 3 two schemes using dimen-sion-wise puncturing and optimal packet lengths are

plotted. One restarts the iterative process each time a

new transmission arrives (the solid curve in Figure 3,which is also the same as the dash-dotted curve in Figure2), whereas the other does not (the dashed curve inFigure 3). The scheme that does not restart the iterativeprocess requires fewer iterations to converge. If an itera-tion is very complex or energy demanding, this proce-

dure may be advantageous.

7. Conclusions

The DDC scheme using IR evaluated here constitutesa flexible and robust communication scheme that care-

fully manages the available resources while keeping thereal-time constraints. The QoS parameters deadline tDLand probability of correct delivery prior to the deadlinePd determines the required redundancy and the maxi-mum number of retransmissions allowed. An admissioncontrol system using this protocol is able to provide a

trade-off between the worst case delivery time and thequality of the delivered data. Service requests can there-fore be accepted, rejected or renegotiated depending on

the available resources. The retransmission scheme en-

ables early termination of the communication, as soon as

the required quality has been obtained. Thereby the use

of available resources is kept at a minimum. Using pow-

erful concatenated codes with iterative decoding enablesimproved fault-tolerance over an unreliable wirelesschannel. It is shown that by choosing an appropriatetransmission order and optimal partition of the redun-dancy, the required level of Pd can be obtained at an

even earlier point in time.

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_..

ues every IR transmissione ongoing iterative process

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0.999

0 50 100 1 50

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References

[1] J. G. Proakis, Digital Communications, 3rd ed.,McGraw-Hill, New York, NY, 1995.

[2] H. Bengtsson, E. Uhlemann, and P.-A. Wiberg, "Proto-col for wireless real-time systems," in Proc. EuromicroConference on Real-Time Systems, York, UK, June1999, pp. 168-174.

[3] E. Uhlemann, T. M. Aulin, L. K. Rasmussen, and P.-A.Wiberg, "Deadline dependent coding - a framework forwireless real-time communication," in Proc. Interna-tional Conference on Real-Time Computing Systems andApplications, Cheju Island, South Korea, December2000, pp. 135-142.

[4] E. Uhlemann, T. M. Aulin, L. K. Rasmussen, and P.-A.Wiberg, "Concatenated hybrid ARQ - a flexible schemefor wireless real-time communication," in Proc. IEEEReal-Time Embedded Technology and ApplicationsSymposium, San Jose, CA, September 2002, pp. 35-44.

[5] C. Berrou, A. Glavieux, and P. Thitimajshima, "NearShannon limit error-correcting coding and decoding:turbo codes," in Proc. International Conference onCommunications, Geneva, Switzerland, May 1993, pp.1064-1070.

[6] D. M. Mandelbaum, "An adaptive-feedback codingscheme using incremental redundancy," IEEE Transac-tions on Information Theory, vol. 20, no. 3, pp. 388-389,May 1974.

[7] J. F. Kurose and K. W. Ross, Computer Networking - ATop-Down Approach Featuring the Internet, Addison-Wesley, 2000.

[8] A. Leon-Garcia and I. Widjaja, Communication Net-works: Fundamental Concepts and Key Architectures,McGraw-Hill, 2000.

[9] W. Zhao, J. A. Stankovic, and K. Ramamritham, "Awindow protocol for transmission of time-constrainedmessages," IEEE Transactions on Computers, vol. 39,no. 9, pp. 1186-1203, September 1990.

[10] S.-K. Kweon, K. G. Shin, and Q. Zheng, "Statisticalreal-time communication over Ethernet for manufactur-ing automation systems," in Proc. IEEE Real-TimeTechnology and Applications Symposium, Phoenix, AZ,May 1999, pp. 192-202.

[11] A. G. Argawal, B. Chen, W. Zhao, and S. Davari,"Guaranteeing synchronous message deadlines with thetimed token medium access control protocol," IEEETransactions on Computers, vol. 43, no. 3, pp. 327-339,March 1994.

[12] T. F. Abdelzaher, E. M. Atkins, and K. G. Shin, "QoSnegotiation in real-time systems and its application toautomated flight control," IEEE Transactions on Com-puters, vol. 49, no. 11, pp. 1170-1183, November 2000.

[13] J. Kim and K. G. Shin, "Performance evaluation of de-pendable real-time communication with elastic QoS," inProc. International Conference on Dependable Systemsand Networks, Gothenburg, Sweden, July 2001, pp. 295-303.

[14] C. E. Shannon, "A mathematical theory of communica-tion," Bell System Technical Journal, vol. 27, pp. 379-423 and pp. 623-656, October 1948.

[15] G. D. Forney, Jr., Concatenated Codes, M.I.T. Press,Cambridge, MA, 1966.

[16] S. Lin, D. J. Costello, Jr., and M. J. Miller, "Automatic-repeat-request error control schemes," IEEE Communi-cations Magazine, vol. 22, no. 12, pp. 5-16, December1984.

[17] J. M. Wozencraft and M. Horstein, "Digitalised commu-nication over two-way channels," in Proc. Fourth Lon-don Symposium on Information Theory, London, U.K.,September 1960.

[18] P. Sindhu, "Retransmission error control with memory,"IEEE Transactions on Communications, vol. 25, no. 5,pp. 423-429, May 1977.

[19] S. Lin and P. S. Yu, "A hybrid ARQ scheme with parityretransmission for error control of satellite channels,"IEEE Transactions on Communications, vol. 30, no. 7,pp. 1701-1719, July 1982.

[20] D. Chase, "Code combining - a maximum-likelihooddecoding approach for combining an arbitrary number ofnoisy packets," IEEE Transactions on Communications,vol. 33, no. 5, pp. 385-393, May 1985.

[21] S. Kallel, "Complementary punctured convolutional(CPC) codes and their applications," IEEE Transactionson Communications, vol. 43, no. 6, pp. 2005-2009, June1995.

[22] E. Uhlemann, Adaptive Concatenated Coding for Wire-less Real-Time Communications, Ph.D. thesis, ChalmersUniversity of Technology, Goteborg, Sweden, Septem-ber 2004.

[23] E. Uhlemann, L. K. Rasmussen, A. J. Grant, and P.-A.Wiberg, "Optimal incremental-redundancy strategy fortype-II hybrid ARQ," in Proc. IEEE International Sym-posium on Information Theory, Yokohama, Japan, June2003, pp. 448.

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