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INCREMENTAL REDUNDANCY (IR) SCHEMES FOR W-CDMA HS-DSCH

Amitava Ghosh1, Kenneth Stewart2 , Rapeepat Ratasuk1, Eoin Buckley2, and Raja Bachu2

1 Advanced Radio Technology, GTSS, Motorola, Arlington Heights, IL, USA 60004

2 Personal Communications Sector, Motorola, Libertyville, IL, USA 60048

email: {qa0047, qa2191, rratasu1, w50105, frb024c}@email.mot.com

Abstract – This paper compares two Hybrid Automatic

Repeat Request (HARQ) schemes using Incremental

Redundancy (IR) which have been proposed for the UMTS

(W-CDMA) High Speed Downlink Shared Channel (HS-

DSCH). Their relative throughput performance is reported

for various channel conditions. It is shown that the two-

stage rate-matching scheme

performance compared to the alternative scheme for certain

coding rates and under some channel conditions.

has marginally worse

I. INTRODUCTION

The two fundamental forms of HARQ are Chase

combining and incremental redundancy (IR). In Chase

combining [1], each retransmission repeats the first

transmission or part of it. In IR, each retransmission

provides new code bits from the mother code to build a

lower rate code [2]. While Chase combining is sufficient to

make Adaptive Modulation and Coding (AMC) robust, IR

offers the potential for better performance with high initial

and successive code rates, at higher SNR estimation error

and FER operating points (i.e., a greater probability that a

transmission beyond the first will be needed), albeit at the

cost of additional memory and decoding complexity. The

consensus in the 3GPP UMTS standards bodies is to

explicitly define and allow IR, while retaining Chase-like

operation as a subset of IR since the memory requirements

at the User Equipment (UE) for the highest data rate is

derived based on Chase combining.

In this paper, two types of IR schemes for W-CDMA

HS-DSCH are discussed: a) IR based on two-stage rate

matching and b) IR based on block interleaving. The IR

based on two-stage rate matching [3][4][9] is the agreed

upon IR scheme for HS-DSCH. It uses two stages of rate

matching where the first stage is used to match the amount

of coded bits to the UE buffering capability and the second

stage is used to generate the different redundancy versions.

It may be noted that the first stage will be bypassed in case

the UE has full buffering capability. IR based on block

interleaving was proposed in [5][6]. The approach uses a

block interleaver in the channel coding chain followed by a

redundancy version selector and a virtual bit priority

mapper. The block interleaver rows and columns are

permuted according to UMTS-Release ’99 internal turbo

interleaver and 1st interleaver algorithms. This technique

simplifies the Release-’99 channel coding chain by

removing the rate-matching block. The block interleaver

acts both as a rate-matcher and channel interleaver followed

by a virtual bit priority mapper. In this scheme, orthogonal

re-transmissions (i.e., each transmission contains unique

parity bits) are guaranteed and as such the performance of

this scheme is optimal. Section II describes the W-CDMA

HS-DSCH IR scheme based on two-stage rate matching.

Section III provides a brief description of the IR scheme

based on block interleaving. Simulation results comparing

these two methods are then presented in Section IV.

Finally, conclusions are drawn in Section V.

II. HARQ BASED ON TWO-STAGE RATE-

MATCHING

The 3GPP HARQ scheme for HS-DSCH is shown in

Figure 1. This scheme is based on the rate-matching

algorithm defined in Section 4.2.7 of [7] and can support

both self-decodable and non self-decodable transmissions.

The First Rate Matching block is used to adjust the number

of available coded bits at the Node-B to the virtual UE’s

buffer size. The maximum number of soft bits available in

the virtual IR buffer is signaled from higher layers for each

HARQ process. The Second Rate Matching block is then

used to rate-match and select the set of coded bits for

transmission, given the redundancy version (RV) selected.

Two parameters control the generation of the

redundancy versions, a self-decodability parameter s and eini

variation parameter r. The goal of the eini variation

parameter is to enable robust retransmissions by

orthogonalizing available redundancy versions that contain

the same self-decodability parameter s. The number of

RV’s allowed for HS-DSCH is limited to 8. HARQ second

stage rate matching is done with the general method

described in 4.2.7.5 of [7]. The initial (eini), increment (eplus)

and decrement (eminus) value of variable e in the rate

matching pattern determination algorithm are based on the

RV parameters s and r. The parameter s can take the value

Systematic

bits

Parity 1

bits

Parity2

bits

RM_P1_1

RM_P2_1

RM_P1_2

RM_P2_2

RM_S

First Rate Matching

Second Rate MatchingVirtual IR Buffer

Nsys

Np1

Np2

Nt,sys

Nt,p1

Nt,p2

bit

separation

NTTI

bit

collection

Ndata

C

W

Figure 1. IR Scheme for HS-DSCH based on two-

stage rate-matching.

0-7803-7589-0/02/$17.00 ©2002 IEEEPIMRC 2002

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0 or 1 to distinguish between prioritizing systematic and

parity bits. The parameter r (range 0 to rmax) changes the

initial error variable eini in the case of puncturing. In case of

repetition both parameters r and s change the initial error

variable eini. The parameters Xi, eplus and eminus are calculated

as per Table 1 shown below.

Systematic

RM S

Parity 1

RM P1_2

Parity 2

RM P2_2

Xi

eplus

eminus

N

−

sys

N

sys

N

syst sys

N

,

1

p

N

1

p

Na⋅

1,1

ptp

NNa

−⋅

2

p

N

2

p

Na⋅

2,2

ptp

NNa

−⋅

Table 1. Parameters for the second-stage rate matching.

Denote the number of bits before second rate matching

as Nsys for the systematic bits, Np1 for the parity 1 bits, and

Np2 for the parity 2 bits, respectively. Denote the number of

physical channels used for the Coded Composite Transport

Channel (CCTrCH) by P. Ndata is the number of bits

available to the CCTrCH in one radio frame (defined as

Ndata=P×3×Ndata1, where Ndata1 is given in [7]). The rate

matching parameters are determined as follows.

For

21

pp sys data

NNNN

++≤

, puncturing is performed

in the second rate matching stage. The number of

transmitted systematic bits in a retransmission is

{

datasyssyst

NNN

, min

,

for a transmission of self-decodable

type and

(

max

,

datasyst

NNN

decodable case. For

>

data

N

N

performed in the second rate matching stage. A similar

repetition rate in all bit streams is achieved by setting the

number of transmitted systematic bits as follows

}

=

)

0 ,

+

{}

N

21

pp

N

+

+

−=

in the non self-

, repetition is

21

pp sys

N

+

=

2

,

2

psys

data

sys syst

NN

N

NN

(Eq. 1)

The number of parity bits in a transmission is then

−

2

=

,

1,

syst data

pt

NN

N

(Eq. 2)

and

−

2

=

,

2,

syst data

pt

NN

N

(Eq. 3)

for the first and second parity stream, respectively. The

parameter a in Table 1 is chosen using a = 2 for the first

parity stream and a = 1 for the second parity stream.

The rate matching parameter eini is calculated for each

bit stream according to the redundancy version parameters r

and s using

1 mod

1)(

max

r

+

−

−=

plus

plus

i ini

e

e

rXre

(Eq. 4)

in case of puncturing, and

()

1 mod

1

2

2)(

max

r

+

−

+−=

plus

plus

iini

e

e

e

rsXr

(Eq. 5)

in case of repetition, where r ∈{0,1,…,

the total number of redundancy versions allowed. Note that

r

varies depending on the modulation mode (for 16-

r

= 2 and for QPSK,

max

r

-1} and

max

r

is

max

QAM,

maxmax

r

= 4).

Subsequently, the bits out of the 2nd rate-matching stage

are mapped based on priority via the HARQ bit collection

unit, and interleaved via one or more Release ’99

interleavers based on the modulation level (QPSK or 16-

QAM). The HARQ bit collection is achieved using a

rectangular interleaver of size

rows and columns are determined from:

col row

NN

×

. The number of

row col

row

NFN

MN

/

)( log2

=

=

(Eq. 6)

where M is the modulation size and F is the number of

coded and rate-matched bits to be transmitted. Data is

written into the interleaver column by column, and read out

of the interleaver column by column. The parameter Nt,sys is

the number of transmitted systematic bits. Intermediate

values Nr and Nc are calculated using:

=

col

syst

r

N

N

N

,

(Eq. 7)

and

colr

col

syst

c

NN

N

N

N

⋅

−=

,

(Eq. 8)

If Nc=0, the systematic bits are written into rows 1…Nr.

Otherwise systematic bits are written into rows 1…Nr+1 in

the first Nc columns and rows 1…Nr in the remaining Nc

columns. The remaining space is filled with parity bits. The

parity bits are written column wise into the remaining rows

of the respective columns. Parity 1 and 2 bits are written in

alternating order. In the case of 16-QAM for each column

the bits are read out of the interleaver in the order row 1,

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row 2, row 3, row 4. In the case of QPSK for each column

the bits are read out of the interleaver in the order row1,

row2, row 3, row 4. The interleaving after the bit collection

unit is done using two Release ’99 2nd interleaver with fixed

size (32x30). For QPSK, only one interleaver is used

whereas for 16-QAM, there are two identical interleavers of

the same fixed size. For 16-QAM, the first two bits out of

the bit collection unit are read into the first interleaver and

the next two bits are read into the 2nd interleaver and so on.

III. HARQ BASED ON BLOCK-INTERLEAVING

This scheme was proposed in [5][6]. A block diagram

illustrating the functionality of this simpler scheme is shown

in Figure 2. It consists of a slightly modified Release ’99

interleaver, a redundancy version selector, and a Bit Priority

Mapper. The HARQ functionality is implemented by the

block-interleaver and the redundancy version (RV) selector.

Turbo

Coder

Systematic

Parity

Bit Priority

Mapper

R’99

interleaver + Row

rearrangement

R’99

interleaver + Row

rearrangement

RV selector

RV selector

Figure 2. Simpler IR/BPM Scheme.

A. Block Interleaver

The encoder used here is the rate-1/3 Turbo encoder

specified in [7]. The un-punctured codeword bits are

separated into a systematic and a parity stream denoted by

S x,,

k

p, 1,

k

p, 2

} (i.e.,

∈

k

{{0,0}, {0,1}, {1,0}, {1,1}}).

Each stream is read into an

interleaver while the tail bits are buffered separately and are

later appended onto the un-punctured instantaneous

codeword (where the instantaneous codeword is the

codeword transmitted in a specific transmission time

interval). Thus, the 12 buffered tail bits are always

transmitted. As an example, if the first transmission is at

R=3/4 and the number of information bits is 600, then 600

systematic, 188 parity are read from the Systematic and

Parity interleaver respectively into the Virtual Bit Priority

mapper. Finally the 12 tail bits are read. The number of

columns in each interleaver is always fixed at 30 while the

number of rows is variable (dependent on the number of

information bits) and is determined in exactly the same

manner as the turbo code internal interleaver defined for

Release ’99 in step 2 of section 4.2.3.2.3.1 of 25.212.

kP x, respectively where

∈

kS x,

{0,1} and

∈

kP x,

{

kP x,

colrow

NN

×

block matrix

Data is read row-wise into each interleaver, with

dummy bits padded if

N

<

????

to the procedure used for the Release ’99 second interleaver.

To facilitate flexibility in supporting variable coding rates,

both columns and rows are permuted prior to reading out of

the block matrix contents. The same column permutation is

proposed for both the systematic and parity interleavers and

is defined in [7]. The proposed row permutations are derived

directly from the intra-row permutations of the Release ’99

Turbo code internal interleaver.

col row

NN

×

. This is identical

B. Redundancy Version Selector

The redundancy version selector determines the subset

of systematic and parity bits to be transmitted over the air.

A salient feature of this method is that the selector does not

suggest a particular order of transmission. Using this simple

approach the selected redundancy version sequence may be

chosen to support Chase, partial and full IR schemes. Each

redundancy version j contains a starting column

either the systematic or parity interleaver (i.e.

∈

j

{0,…7},

},{

PSi∈

and

procedure for computing

j

α is as follows. First, compute

j

α in

},{ ki

). The

j∈α

for

∈

k

},, 1 {

max_,

coli

N

?

colP colS vr

NNN

max_, max_,

2×+=

(Eq. 9)

then

) 4 ,

j

mod(2

8

) 4 ,

j

mod(2

N

VR

vr

j

⋅−

⋅⋅

=

(Eq.10)

for ∈

j

{0,…7}. Finally, calculate

j

α via

},{

jj

VRS

=α

(Eq. 11)

if

colSj

N VR

max_,

<

and

−

=

2

,

_,

colSj

j

NVR

P

???

α

(Eq. 12)

otherwise. This gives four unique starting columns evenly

spaced throughout the lowest code rate supported by the

mobile. Coded bits are read from the selected starting

columns column-wise either

(

) 1 ,(

+×

row

Nk

,

) 2,(

+×

row

Nk

, …) for

decreasing order (

) 1,(

−×

row

Nk

{4,5,6,7}. Coded bits continue to be read until the end

(

) ,(

row

NNk

××

???????

for

∈

j

{0,1,2,3}) or start (

{4,5,6,7}) of the interleaver is reached. Reading then

continues column wise from the other interleaver iˆ,

(

},{

ˆ

PSi ∈

,

ii ≠

ˆ

) either from the first column or the last

column.

in increasing

{0,1,2,3}) or in

order

′

iy

′

iy

∈

j

′

iy

,

) 2

−

,(

×

′

row

Nkiy

, …) for

∈

j

iy

′

1 , iy′ for

∈

j

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As an example, consider the case shown in Figure 3

where the encoded message consists of 720 bits with the UE

able to support the full rate 1/3 code. Assuming the

redundancy versions chosen for transmission are RV0 and

RV2 and each transmission consisting of 960 bits, then the

first transmission will consist of codeword bits followed by

the 12 tail bits and the second transmission will consist of

the codeword bits followed by the 12 tail bits.

C. Virtual Bit Priority Mapper

Priority bit mapping is based on utilizing the differing

bit reliability offered by higher order constellations (16-

QAM or higher). Since the systematic portions of a

codeword are of greater importance to decoder performance

than the parity portions, they should be placed in positions

of high reliability when higher order constellation is used.

Since channel interleaving has already implicitly been

performed, codeword bits can be read directly from the

Systematic and Parity puncturing block interleavers, to form

the desired 16-QAM symbol in a simple and straightforward

manner.

IV. SIMULATION RESULTS

The effective code rate is defined as ni/ni+np where ni is

the number of information bits and np is the number of

unique parity bits, after the second transmission is plotted as

a function of the initial code rate for the above two schemes

(assuming full buffering) in Figure 4. The two schemes

have identical results for initial code rates lower than 1/2.

At higher code rates, however, the rate-matching scheme

cannot select only unique parity bits in the second

transmission, thus resulting in a higher effective code rate.

The block interleaving approach, however, is able to select

all unique parity bits in subsequent transmissions. As a

result, the optimality of the block interleaving based

approach is evident from the figure since the block-

interleaving approach could

transmissions as opposed to the two-stage rate-matching

scheme.

guarantee orthogonal

Next, the two IR schemes are compared using a

symbol-level simulator for HS-DSCH. The results presented

here assume ideal channel estimation, QPSK/16-QAM

modulation and non self-decodable re-transmissions. Table

2 lists additional relevant simulation parameters.

Parameter Value

Carrier Frequency 2GHz

Channel conditions AWGN, Flat Fading

HSDPA frame Length 2 msec (3 slots)

Ior/Ioc Variable

Fast fading model Jakes spectrum

Channel Coding R=1/3 Turbo

Max no. of Decoder Iter 8

Metric for Turbo Coder Max-Log-Map

Turbo Interleaver Random

Table 2. Simulation Parameters.

Figure 5 compares the spectral efficiency of the two

schemes under static AWGN channel for N=720 bits, R=3/4

and QPSK modulation. In this case, the block-interleaving

based scheme has a marginal advantage over the rate-

matching scheme at Ior/Ioc greater than –1.2 dB. Figure 6

compares the spectral efficiency vs. Ior/Ioc of the two

schemes using QPSK modulation, N=720 bits, R=3/4 code

under Rayleigh fading channel at 3 km/h. For the rate-

matching approach, we assume s=1, r=0 on the first

transmission, s=0, r=0 on the second transmission, s=0, r=1

on the third transmission, and s=1, r=1 on the fourth

transmission for the rate matching approach. A maximum

of 4 re-transmissions were allowed for the packet for both

the above cases.

Figure 7 compares the performance using 16-QAM

modulation at 120 kmph using R=3/4 code for a message

size of 1,440 bits. For the rate-matching approach, we again

select s and r as outlined above. It may be observed from

both the figures that the block interleaving approach

outperforms the two-stage rate-matching scheme by

approximately 0.5 dB under fading channel conditions.

V. CONCLUSIONS

The block-interleaving scheme has the following

advantages over the 3GPP two-stage rate-matching scheme.

First, the systematic and parity interleavers in Figure 2 are

analogous to the second rate-matching block combined with

the Release ’99 interleavers in that they interleave as well as

rate match. As such, a single set of backwards-compatible

interleavers serve as a simple approach for RV selection,

SystematicParity

Nrow=24

NS,max_col=30

NP,max_col=30

RV0

RV1RV2 RV3

RV5

RV6 RV7

RV4

Column 1 Column 20 Column 5

Column 15

Figure 3. Example of Redundancy Version Selector

and Codeword Selection.

Page 5

symbol mapping etc. Second, the performance of the block-

interleaving approach is superior to IR based on two-stage

rate-matching by approximately 0.5dB. Third, for the two-

stage rate matching scheme, the rate-matching patterns must

be determined for every redundancy version selected,

whereas in the block-interleaving approach only the index of

the starting location is needed. Lastly, not all re-

transmissions are guaranteed to have unique parity bits due

to the rate-matching algorithm, which degrades incremental

redundancy performance.

ACKNOWLEDGEMENTS

The authors would like to acknowledge Bob Love and Brian

Classon for their invaluable comments.

REFERENCES

[1] D. Chase, “Code combining—A maximum-likelihood

de-coding approach for combining an arbitrary number

of noisy packets”, IEEE Trans. Comm., Vol. COM-33,

No. 5, pp 385-393, May 1985.

[2] S. Lin and D. J. Costello, Error Control Coding:

Fundamentals and Applications. New York: Prentice

Hall, 1983, pp. 477-494.

[3] R1-01-1045, Ericsson, “Physical-layer Hybrid-ARQ

functionality”, 3GPP RAN1#22, Korea.

[4] R1-01-1196, Siemens, “Rate Matching and Incremental

Redundancy for HSDPA”, 3GPP RAN1#22, Korea.

[5] R1-01-1244, Motorola, “Revised:HARQ Scheme Using

Incremental Redundancy”, 3GPP RAN1#22, Korea.

[6] R1-02-0285, Motorola, “Enhancement for IR for

HSDPA”, 3GPP RAN1#24, USA.

[7] 3GPP “HSDPA-Physical Layer Aspects”, 3GPP

TS25.212, V5.0.0.

[8] R1-02-0234, Motorola, “Enhancement of IR for

HSDPA”, 3GPP RAN1#24, USA.

[9] R1-01-1026, TI, “Two Stage Rate Matching for 3GPP

HSDPA”, 3GPP RAN1 Ad-Hoc, Sophia Antipolis.

0.30.40.5 0.6

Initial Code Rate

0.70.80.91

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

Effective Code Rate

Block Interleaver Based

Two−Stage Rate Matching Scheme

Figure 4. Effective Code Rate Comparison of IR based

on two-stage rate-matching and block interleaving.

−2 −1.8−1.6 −1.4−1.2 −1−0.8−0.6 −0.4 −0.20

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Ior/Ioc (dB)

Spectral Efficiency

Spectral Efficiency for N=720, QPSK, R=3/4, AWGN Channel

Block Interleaver Based

Two−Stage Rate Matching Based

Figure 5. Spectral Efficiency for N=720, QPSK, R=3/4,

AWGN Channel.

−10−505 10 15

0

0.5

1

1.5

2

2.5

3

Ior/Ioc (dB)

Spectral Efficiency

Spectral Efficiency for N=720, QPSK, R=3/4, Flat Fading (3 km/h) Channel

Block Interleaver Based

Two−Stage Rate Matching Based

Figure 6. Spectral Efficiency for N=720, QPSK, R=3/4,

Flat Fading channel (3 km/h).

−12 −10−8 −6−4−202

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Ior/Ioc (dB)

Spectral Efficiency

Spectral Efficiency for N=1440, 16−QAM, R=3/4, Fading (120 km/h) Channel

Block Interleaver Based

Two−Stage Rate Matching Based

Figure 7. Spectral Efficiency for N=1440, R=3/4, 16-

QAM, Flat Fading channel (120 km/h).