CROSS-LAYER OPTIMIZATION FOR RAPTOR CODE ENABLED VIDEO TRANSMISSIONOVER MOBILE WIMAX

Victoria Sgardoni, David R. Bull and Andrew R. Nix

Department of Electrical and Electronic Engineering; University of Bristol; Bristol; BS8 1UB; UKvicoria.sgardoni, Andy.Nix@bristol.ac.uk

ABSTRACT

This paper explores the use of application layer systematic

Raptor codes for real-time video transmission over mobile

WiMAX networks. We study the relation between channel

errors at the PHY, MAC and application layers and the Rap-

tor code parameters. Modulation and Coding Scheme (MCS)

link adaptation is taken into account in order to estimate

the amount of channel resources required to accommodate

the additional Raptor overheads. Low Raptor code rates are

shown to place a very high demand on the channel resources.

A cross-layer optimization approach is proposed to select

the Raptor code parameters and the MCS mode jointly to

maximise transmission efficiency. Simulation results show

that a 28% gain in channel capacity can be achieved together

with an extension in operating range of 4dB.Index Terms—mobile WiMAX, Raptor codes, link

adaptation, transmission efficiency, goodput, channel

bandwidth

I. INTRODUCTION

Currently there is an increasing interest in high quality

video applications on mobile devices. There are predictions

that mobile traffic will increase 39 times over the period

2010-2014 [1]. This is mainly due to a significant rise

in smartphone video applications. The efficiency of future

wireless networks must be optimized to meet the conver-

gence of video and data. At the same time strict Quality

of Service (QoS) is required for each of the competing

user streams. It is well-known that video transmission over

wireless networks is challenging because of the time-varying

channel quality and the high data rates and QoS demands of

video. The latest mobile broadband standard, IEEE 802.16,

offers high user data rates and support for video applications.

The need for additional cross-layer adaptive strategies to

further enhance wireless network efficiency and to provide

the high QoS required was also identified in [1],[2].Rateless codes, such as Raptor codes, have been initially

studied for wireless video broadcasting in [3][4]. The error

correcting capability of Raptor codes, even in severe chan-

nel conditions, is well established. The 3GPP Multimedia

Broadcast and Multicast Services (MBMS) [5] has embraced

Raptor codes for broadcasting services over UMTS wireless

networks. [6] has studied their performance for file delivery

over WiMAX using FLUTE. More recently [7] has evaluated

the performance of Raptor codes for H.264 video streaming

over DVB-H networks. Furthermore, [8] investigates the

delivery of IPTV data with the use of data partitioning

and Raptor codes over mobile WiMAX. In [8] the authors

identify the need to predict the amount of redundant data

according to channel loss in order to reduce the FEC data

overhead.

The use of rateless Raptor codes introduces additional

overheads that place high demands on wireless network

resources. In view of the importance of energy and band-

width efficiency, it is necessary to carefully control the

Raptor code overhead. A high overhead Raptor code places

a very high demand on the channel resources, and in some

cases it is unrealistic to implement over a shared cellular

network. Therefore, there is a need to accurately estimate the

amount of redundancy suitable for the level of packet loss

occurring over the wireless channel. The rateless property

of Raptor codes can be exploited to select the Raptor code

rate according to the specific channel conditions and the

data Modulation and Coding Scheme (MCS). Furthermore,

the MCS selection performed via a link adaptation scheme

should take into account the use of Application Layer

Forward Error Correction (AL-FEC), such as Raptor codes,

and the additional error robustness that this provides. A

cross-layer optimization approach should be adopted where

the Raptor code parameters and the MCS are jointly selected,

aiming for error free (or quasi error free) transmission

with the best possible use of valuable bandwidth. Previous

works, such as [7],[8], do not take into consideration the

MCS used during transmission. Adaptive MCS offers itself

a form of error robustness, however this is at the expense

of throughput. Alternatively higher throughput modes can

be chosen at the expense of higher error rates. Typically

link adaptation is used to select the more error robust MCS

modes at the expense of reduced throughput in poor channel

conditions. To the best of our knowledge, no study has

been reported on the relation between MCS selection at the

MAC/PHY layer protocols and Raptor code parameters at

the application layer.

In this work the use of Raptor codes is studied for real-

time high data rate video transmission over mobile WiMAX.

Through simulation we investigate how the choice of Raptor

code parameters, namely code rate and source block length,

is influenced by the MCS mode chosen at the 802.16e MAC

layer during link adaptation. We then design a cross-layer

optimization methodology to jointly select the MCS and

Raptor code parameters, according to the wireless channel

conditions. This optimization is constrained by the maximum

acceptable Packet Error Rate (PER) at the application layer.

Here we aim to deliver quasi error free data to the video

application. A time-correlated channel model is used, to

accurately describe the bursty nature of the error mechanism

in a fading channel [9]. This enables us to study the relation

between errors at the PHY, MAC and application layers and

the Raptor code parameters.

II. BACKGROUND

II-A. Raptor codes

Raptor codes are a class of binary rateless or fountain

codes [10] first introduced in [11]. Due to their excellent

error correcting capability they have become part of various

standards, including the 3GPP MBMS [5], DVB-H and

IETF RFC 5053 [12]. A rateless code can generate as

many encoding symbols as desired from the source symbols.

The Raptor encoder partitions incoming data packets into

several blocks, known as source blocks. Each source block

consists of a number of source symbols, K, each of length

T bytes. For each source block a number of repair symbols

also of length T are generated. At the receiver the Raptor

decoder will recover a source block with high probability if

any of K(1+δ) symbols (source or repair) are successfully

received, where δ is real and δ > 0. Only slightly more

encoded symbols than the K source symbols are required

to recover the source block. Raptor codes operate very close

to an ideal erasure code. Raptor codes as specified in 3GPP

MBMS are systematic codes. They consist of an outer high

rate block code (LDPC pre-code) followed by the so-called

Luby Transform LT coder. Source symbols are encoded into

intermediate symbols using a block code, such that the first

K encoded symbols are equal to the source symbols. This

is achieved by using a code constraints processor using a

specific code constraint matrix A, defined in [12] and [5].

The encoding and decoding algorithms are described in [5].

The rateless property of Raptor codes is inherited from the

inner LT code. The low encoding and decoding complexity

of these codes is mainly a result of the sparse inner LT code.

II-B. IEEE 802.16e

Medium Access Control (MAC) Layer - The 802.16e MAC

layer [13] includes a number of adjustable features, such as

adaptive MCS, ARQ, packet fragmentation and aggregation,

variable size MAC Protocol Data Units (PDU), application

specific service flows and PDU scheduling based on QoS.

Our simulated video data is sent as a constant bit rate service

with Unsolicited Grant Service (UGS) scheduling. Packets

from the higher layers arrive in the convergence sublayer

(CS) of the MAC as MAC Service Data Units (SDUs). Based

on their QoS requirements, MAC SDUs are classified into

service flows. There is the option for SDU fragmentation

Table I: 802.16e Link Speeds

# link speed bits per slot total data rate (Mbps)

0 QPSK 1/2 48 6.14

1 QPSK 3/4 72 9.21

2 16 QAM 1/2 96 12.29

3 16 QAM 3/4 144 18.43

4 64 QAM 1/2 144 18.43

5 64 QAM 2/3 192 24.58

6 64 QAM 3/4 216 27.64

and SDU partitioning into ARQ blocks of fixed size. MAC

SDUs can be fragmented, or alternatively one or more SDUs

can be packed into a MAC Protocol Data Unit (PDU). The

MAC PDU is the data unit exchanged between the BS and

MS MAC layers. Once a PDU has been constructed, it is

placed in the appropriate service flow queue and managed by

the scheduler, which determines the PHY resource allocation

(i.e. bandwidth and OFDMA symbol allocation) on a frame-

by-frame basis.

Physical Layer (PHY) - The mobile WiMAX standard has

adopted Scalable-OFDMA (S-OFDMA) [14]. Our mobile

WiMAX PHY layer simulator is described in [15]. The

payload data is modulated using the full range of link speeds

(MCS modes) as defined in the standard [14] and shown

in Table I. Assuming a PUSC DL [14], the modulation

symbols allocated to a sequence of slots in each DL OFDMA

frame are assigned to a number of logical subchannels.

An OFDMA slot is the minimum possible data allocation

unit. For PUSC DL it is defined as one subchannel by two

OFDMA symbols.

Wideband Channel Model - The channel model follows

the ETSI 3GPP spatial channel model (SCM), as described in

[9]. A time varying “urban micro” tapped delay line (TDL)

was generated for each channel snapshot. The TDL consists

of 6 time-correlated fading taps with non-uniform delays.

The carrier frequency is 2.3 GHz and the FFT size is 1024.

III. SYSTEM DESIGN AND OPTIMIZATION

The Raptor code performance over a mobile WiMax net-

work is studied via the simulation of UDP packets through

the transport, MAC and PHY layers of 802.16e. The MAC

and PHY layers are implemented according to the standard

[14]. A time correlated fading channel is assumed. The

fading channel is modeled using the 3GPP SCM [9], for

a Single Input Single Output (SISO) system. The 802.16e

MAC and PHY simulator described in [16] is used to model

the MAC SDU and ARQ Block loss process. Automatic

Repeat Request (ARQ) retransmissions are not enabled as we

want to study the performance of Raptor codes and typically

in a broadcast scenario ARQ is not used. A stream of

incoming RTP/UDP packets, at constant bitrate, are Raptor

encoded at the application layer using a systematic Raptor

encoder/decoder developed according to the standard [5].

The Raptor encoder collects n RTP/UDP packets to form

Fig. 1: cross-layer Raptor simulation

source blocks of size K ·T , consisting of K source symbols

of length T (Bytes). For simplicity we assume that all

RTP/UDP packets are of fixed size SP . For each source

block of K source symbols, a number of repair symbols

R, of length T , are generated by the Raptor encoder. The

number of repair symbols R generated in addition to the K

systematic symbols depends on the chosen Raptor code rate

c, defined as c = K

K+R. The encoded symbols generated

from each source block are then packed into n + l new

RTP/UDP packets for transmission over the wireless IP

network, as shown in fig. 1.

It is assumed that two flows of encoded UDP packets

(source and repair) arrive to the MAC layer and any packet

headers from the intermediate layers are ignored. At the

MAC layer each UDP packet is mapped to one MAC SDU

and then transmitted according to the 802.16e MAC layer

protocol. It is assumed that the MAC scheduler uses the UGS

QoS scheme, but is Raptor-aware and therefore resources

allocated must take into account source and repair data,

according to the selected Raptor code rate c. Also resources

used vary according to the data modulation MCS. At the

MAC layer the MAC SDUs can be segmented into ARQ

Blocks.

At the receiver the MAC waits to acquire all the ARQ

Blocks forming a MAC SDU before reassembling the SDU.

Each SDU is then mapped to one UDP packet, delivered

through the transport layer to the application layer. At

the application layer the Raptor decoder receives the UDP

packets transmitted. According to the standard [14] an SDU

will not be delivered to the higher layers if any of its ARQ

Blocks are in error. This policy however, aggravates the SDU

packet error rate seen at the receiver by comparison to the

ARQ Block error rate. For example, for an SDU consisting

of 20 ARQ Blocks, with a BLER of 10% just 2 ARQ Blocks

are in error. However, if the whole SDU is discarded then the

error rate at the application layer for this SDU rises to 100%.

Much larger overheads are then required for the AL-FEC.

Since the AL-FEC is in place, system performance would

greatly benefit if SDUs with missing ARQ blocks were

delivered to the Raptor decoder. The traditional IP receiver

policy is to ignore a significant amount of correctly received

data because packets are discarded if any segment within an

IP packet is corrupted. The detrimental effect of this policy

on wireless systems is studied in [17]. In [17], [18] a Perme-

able Layer Receiver (PLR) is proposed, in conjunction with

Raptor AL-FEC, allowing the forwarding of partly received

packets to the higher layers. In accordance with the PLR

assumptions, in the case of a mobile WiMAX network the

ARQ Block error rate at the MAC layer would correspond

to the received symbol error rate at the Raptor decoder.

A key assumption in this case is that the Raptor symbol

boundaries would be known at the MAC layer. During the

segmentation of each SDU into ARQ Blocks Raptor symbol

boundaries would be exactly aligned with the ARQ Blocks.

The alignment of ARQ blocks to symbols ensures that ARQ

Block errors can be directly mapped to Raptor symbol errors.

Thus the ARQ Block error rate (BLER) would be directly

analogous to the Raptor symbol error rate. If the boundaries

between ARQ Blocks and symbols were not aligned, the

Raptor symbol error rate would increase by comparison to

the BLER and more symbols would be considered lost at

the Raptor decoder than symbols actually in error. This

would deteriorate the Raptor decoding performance, calling

for more repair symbols. For a Raptor-aware system design

it is essential to use tight coupling between the application

layer data format and the MAC/PHY layer data structures.

The performance benefits of this kind of alignment were also

observed in [7] for DVB-H networks.The Raptor decoder collects the UDP packets correspond-

ing to each encoded source block. If the total number of

source and repair symbols received for a source block is

M ≧ K(1 + δ) (for real δ > 0) then the Raptor decoder

is able to correct the missing symbols and deliver all the

source UDPs error free to the application layer (i.e. the video

decoder). If, however, Raptor decoding fails then the Raptor

decoder will deliver only the correctly received UDP packets.The simulator evaluates the following as a function of

mean channel SNR, MCS, mobile station (MS) speed, source

block length K and Raptor code rate c:

• ARQ BLER at the MAC receiver

• SDU error rate at the MAC receiver, if no Raptor AL-

FEC is applied

• UDP PER after the Raptor decoder

• received goodput at the video decoder with/without

Raptor AL-FEC

• the channel resources, i.e. the OFDMA slots, required

for data transmission, including source and repair Rap-

tor data. An OFDMA slot is the minimum possible data

allocation unit in mobile WiMAX .

We define goodput G as the number of correct bits received

per second at the application layer (i.e. the video decoder),

given by

G =(1− PER) ·N · Ps

TN

(1)

where PER is the UDP packet error rate at the application

layer, N is the total number of source UDPs transmitted, Ps

is the UDP packet length in bits and TN is the transmission

duration in seconds.

In this paper we choose the appropriate Raptor code rate

c to minimise the bandwidth requirements and to maintain

a target PER according to a QoS requirement. The most

appropriate link speed (i.e. MCS) for the channel conditions

is selected, taking into account the Raptor code rate c. We

also investigate if higher link speeds can be used at a given

SNR, as a direct result of the use of Raptor codes. We use as

a metric of transmission efficiency the function goodput-per-

slot, in bps/slot, defined as the goodput over the total num-

ber of OFDMA slots, B, required for video transmission.

Both are calculated during the transmission simulation. The

goodput-per-slot is a function of the mean channel SNR, the

MCS mode, the Raptor code rate c, the source block length

K and the symbol length T : F (SNR,MCS, c,K, T ) = G

B.

An analytic expression for this function is not available and

simulation is used to provide the required data. We maximise

the goodput-per-slot function at each mean channel SNR

value, applying the constraint that the UDP packet error

rate attained must remain below a maximum acceptable

threshold, EUDP . This maximisation results in the highest

goodput for the least amount of WiMAX PHY layer re-

source. The target EUDP defines the QoS offered by the

system: a quasi zero value of EUDP offers near error free

transmission, whereas higher values (e.g. 3%) are used for

applications with greater error tolerance. The methodology

proposed identifies the pair of MCS, m and Raptor code

rate, c, (m, c) that delivers maximum goodput-per-slot at

each mean channel SNR value, for a source block length

K and a given target EUDP . The symbol length T remains

constant.

IV. SIMULATION PARAMETERS

Fig. 2 shows the block diagram of the simulator. Simula-

tions were performed based on 25,000 channel samples. The

mean channel SNR was simulated for values in the range

from 12dB to 22dB. The mobile station (MS) speed was set

at 1 km/h.

To simplify the interface between the PHY link level

and the MAC simulator, while modelling dynamic system

behaviour, a technique known as Effective SINR Mapping

(ESM) is used. This compresses the SINR per subcarrier

vector as a single ESINR. The technique is described in

detail in [19]. The Effective SINR technique enables us to

compute the instantaneous packet error rate for each channel

Fig. 2: Simulator diagram

realisation, based on the instantaneous fading response for a

packet length equal to the ARQ block size.

The simulator captures the transmission of 2,000 UDP

packets, 815 Bytes each, transmitted at 1.03 Mbps through

the 802.16e PHY and MAC layers. Each MAC SDU was

fragmented into ARQ Blocks, each 32 Bytes long. PDU

packing and Block re-arrangement within the PDUs was not

enabled. Table II details the simulation parameters used for

the MAC layer. The Raptor encoder was used to encode the

simulated UDP packets with symbol length T = 32 Bytes.

K was configured to one of two values, 1040 and 1820, and

code rates c were analysed in the range from 0.5 to 0.9.

V. ANALYSIS OF RESULTS

The error correcting capability of Raptor codes depends

on the symbol error rate encountered when a source block is

Raptor decoded. According to theory, if enough redundant

symbols are received such that there are slightly more

than K, then the decoding success of the raptor code is

guaranteed. Therefore if the symbol error rate is known, the

amount of redundancy and hence the associated code rate c

can be determined accordingly. Fig. 3 shows the goodput

attained in the 1 km/h channel for different link speeds

when no Raptor codes are applied and no ARQ mechanism

is enabled at the MAC layer. For a data input bitrate of

1.03Mbps it can be seen that only link speed 0 (QPSK 1/2)

can deliver data with approximately 3.5% loss at 12dB mean

channel SNR.

In Fig. 4 the UDP PER after Raptor decoding is shown vs

MCS mode for a mean channel SNR of 14 dB. The range of

Table II: WiMAX Simulator Parameters

Parameter Value

OFDMA

Carrier frequency 2.3 GHz

Channel Bandwidth 10 MHz

FFT length 1024

Subcarrier frequency spacing 10.94 kHz

Frame length 5ms (48 OFDMAsymbols)

Guard Interval 1/8

DL subcarrier Permutation Scheme PUSC DL

Number of active DL subcarriers 840

Number of subchannels 30 DL / 35 UL

Data subcarriers per subchannel 24

OFDMA data symbols 22 DL/15 UL

DL capacity 330 slots

DL/UL ratio 60/40

MAC

MAC SDU size 815 B

ARQ Block size 32 Bytes

PDU Packing NO

SDU Fragmentation YES

ARQ not enabled

QoS scheduling UGS

12 14 16 18 20 220

200

400

600

800

1000

1200

SNR dB

goodput

Kbps

QPSK 1/2

QPSK 3/4

16QAM 1/2

16QAM 3/4

64QAM 1/2

64QAM 2/3

64QAM 3/4

Fig. 3: goodput vs SNR vs MCS (no AL-FEC)

Raptor code rates is varied from 0.4-0.9. It can be seen that

for modes higher than 3 no code rate in the simulated range

can deliver error free data. For MCS mode 2, code rates

of 0.4-0.7 attain a zero UDP PER (or very close to zero)

and similarly for mode 1. The question therefore is which

code rate to select and which MCS mode, 1 or 2, assuming

that all combinations deliver a PER below the maximum

acceptable target EUDP . The figure shows the undoubted

error correction capability of Raptor codes when compared

with the minimum PER achieved without the use of Raptor

codes. Apart from the improvement in PER, there could also

be an improvement in the channel resources required, as

modes 1 and 2 operate at higher throughput than mode 0.

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

mode

PE

R

c=0.4

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

MAC no ARQ

Fig. 4: UDP PER at SNR=14 dB for all MCS modes and

code rates

However, the throughput improvement offered by a higher

MCS mode is counterbalanced by the Raptor redundancy

required to meet EUDP .

The simulator calculates the number of slots required for

each user data burst during the transmission, according to

the MCS mode and Raptor code rate. Fig. 5 shows the total

channel capacity required, in slots, for the transmission of

2000 UDP packets vs MCS mode, for a range of Raptor code

rates. It also shows the channel capacity required to transmit

the source data when no Raptor coding is used as FEC (and

without ARQ retransmissions). As expected, we observe that

the capacity required increases linearly as the Raptor code

rate decreases and more repair symbols are generated. As

a reference, fig. 5 also shows the total number of slots

available, taking into account the total number of OFDMA

frames in the transmission, when K=1820. The requirements

of low code rates, such as c= 0.5, on the channel resources

at low link speeds are excessive and would be unrealistic

in situations where the channel is shared amongst a large

number of users.

Fig. 6 shows an example of goodput-per-slot vs MCS

mode for a range of Raptor code rates. The mean channel

SNR is 12 dB and K=1820. We observe that there are

clear maximum values for link speed 2. The goodput-per-

slot function displays similar maximum points for all the

other mean channel SNR values.

The maximum point of the goodput-per-slot function is

estimated for a particular code rate and MCS mode, for

each mean channel SNR, with the constraint PERUDP ≤

EUDP . The calculation is based on our simulation data for

EUDP = 0.01. Table III shows the pairs of MCS mode

and code rate that maximise the goodput-per-slot function

for each mean SNR for K=1820 and K=1040. The mode

selection at each SNR is different to the standard [13]

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

9x 10

5

mode

channel slo

ts

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

MAC no Raptors

total slots K=1820

Fig. 5: channel capacity in slots required per MCS mode,

K=1820

0 1 2 3 4 5 60

1

2

3

4

5

6

mode

go

od

pu

t/slo

t b

ps/s

lot

c=0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

Fig. 6: goodput-per-slot vs MCS mode, K=1820 for mean

SNR=12dB

because it is based on the UDP packet error rate after Raptor

decoding, and depends on the target EUDP used in the

optimization process. We also observe that K=1040 requires

generally lower code rates, or reduced throughput MCS

modes (one MCS mode lower) for the same mean channel

SNR. Therefore transmission with K=1040 is less efficient

as it requires more redundant data and lower throughput

modes.

From Table III we observe that code rate 0.7 is the

minimum code rate for K=1820. The simulator estimates

the goodput attained when code rate 0.7 is applied for

transmissions for all mean channel SNRs (as for example

when broadcasting). In Fig.7 it is clear which mode attains

maximum goodput at each SNR with code rate c=0.7: for

example at 12 dB mode 1 has the highest goodput and at 14

dB it moves to mode 2. By comparison, Fig. 8 shows the

goodput vs SNR when a higher code rate, c=0.8, is used.

Table III: Goodput optimized MCS and code rate pairs

SNR dB mode coderate c

mode coderate c

K=1820 K=1040

12 1 0.7 0 0.8

14 2 0.7 2 0.5

16 2 0.8 2 0.65

18 3 0.7 2 0.85

20 3 0.8 3 0.65

22 5 0.7 3 0.8

12 14 16 18 20 220

200

400

600

800

1000

1200

SNR dB

goodput

bps

mode=0

1

2

3

4

5

6

Fig. 7: goodput vs SNR for c=0.7, K=1820

We observe that lower modes are now required to attain

the maximum goodput at each SNR value, hence channel

bandwidth is wasted. Similarly, if a lower code rate than

0.7 was used, channel resources would be wasted because

of unnecessary redundancy. This explains how the goodput-

per-slot metric enables us to make the most efficient use of

bandwidth for a desired level of QoS.

Fig. 9 shows goodput-per-slot vs SNR when the optimum

pairs of MCS and c from Table III are used, for the two

values of K. This graph is a measure of the transmission

efficiency for the two cases. We observe that in the particular

channel conditions (MS speed 1 km/h) the larger value of K

offers improved efficiency, since the goodput-per-slot values

are higher at all SNR values. This is expected according to

Raptor theory for larger K values. Efficiency is improved in

terms of the channel resources required to attain the same

level of PER, which is shown in fig.10.

Fig. 10 shows the channel resources (i.e. OFDMA slots)

required for each SNR value in three cases: a) when the

optimum pairs (m, c) are used at each SNR, for K=1820,

b) for optimized pairs (m, c) for K=1040 and c) for a

suboptimal choice where mode 1, c=0.65 and K=1820

12 14 16 18 20 220

200

400

600

800

1000

1200

SNR dB

goodput

bps

mode=0

1

2

3

4

5

6

Fig. 8: goodput vs SNR for c=0.8, K=1820

12 14 16 18 20 223

4

5

6

7

8

9

10

11

SNR dB

go

od

pu

t/slo

t b

ps/s

lot

K=1820

K=1040

Fig. 9: goodput-per-slot vs SNR for the selected pairs of

MCS mode and code rate

are used. In all cases transmission is error free, attaining

maximum goodput (see fig. 7 for K=1820). However, fig. 10

clearly shows that fewer channel resources are required when

the optimal values (m, c) are used for K=1820. At SNR=14

dB with K=1820 about 80,000 less slots are required than in

the suboptimal case, i.e. about 28% gain. Similarly it shows

that the amount of slots required when K=1040 is more than

when K=1820, by about 50,000 at the lower SNR values.

Finally fig. 11 shows the goodput attained when Raptor

codes are used with the optimum pairs (m, c) at each SNR.

The required error free data rate of 1.03 Mbps is attained

at all SNRs. The plot for goodput attained without the use

of Raptor codes or ARQ, with mode 0 (QPSK 1/2), shows

that there is about 3.4% data loss at 12 dB. Transmission is

not quasi error free until approximately 16 dB. Since mode

0 is the most robust mode, this practically means that a high

quality video service at quasi error free QoS could not be

offered below 16dB, in a 1 km/h MS speed channel. At 16-

18 dB only mode 0 would be able to deliver quasi error free

data, at the expense of low throughput. Thus, Raptor codes

with optimum selection of parameters, essentially extend the

operating range of a high QoS video service by 4-5 dB.Analysis of the goodput and channel capacity required has

shown that there is an optimum combination of MCS and

Raptor code parameters for which the amount of channel

resources required to attain a target packet error rate at the

receiver is minimised, depending on the channel conditions.

Using this approach transmission efficiency can be increased

with joint MCS mode and Raptor code rate selection.

12 14 16 18 20 2250

100

150

200

250

300

350

SNR dB

slo

ts x

1000

K=1820 optim (m,c)

K=1820 m=1 c=0.65

K=1040 optim (m,c)

Fig. 10: channel capacity in slots vs SNR

12 14 16 18 20 22950

960

970

980

990

1000

1010

1020

1030

1040

1050

SNR dB

goodput

Kbps

K=1820 optim (m,c)

m=0 no Raptors

Fig. 11: goodput vs SNR with optimised Raptor

parameters and without Raptors

VI. CONCLUSIONS

Although AL-FEC with Raptor codes has the power to

deliver error-free data our results show that the redundant

data can impose unwanted demands on the channel resources

of a mobile WiMAX network. Raptor code rates allow

the use of higher MCS modes and the PHY layer link

adaptation process must be made aware of the use of Raptors

in a cross-layer design. In order to maximise transmission

efficiency the selection of the Raptor code rate and the source

block length K must be performed jointly with the the

selection of the MCS mode. The metric goodput-per-slot

has been proposed to improve the transmission efficiency

and drive the selection of the most suitable pair of MCS

mode and Raptor code rate for any given channel SNR

and Raptor length K, according to a target PER at the

application layer. Results show that this approach achieves

a 28% reduction in the amount of radio resource required in

a mobile WiMAX network, by comparison to what a fixed

mode, fixed code rate would require, in order to deliver error-

free video. Results also show that with the optimum selection

of parameters when Raptors are used, the operating range of

a high QoS video service is extended by 4-5 dB, compared to

what non-Raptor enabled multicasting over mobile WiMAX

can offer.

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