Improving wireless packet throughput using hybrid-II ARQ and physical layer side information

Improving Wireless Packet Throughput Using Hybrid-I1 ARQ

and Physical Layer Side Information

infomution

Cheing-hong Lin and Jingshown Wu

Room 519

Department of Electrical Engineering and Graduate Institute of Communication Engineering

National Taiwan University Taipei, Taiwan 106 17

R.0.C

high-rate c&

Abstract

-

In this paper, the physical layer side information is

employed to improve the throughput of the hybrid-I1 ARQ

protocol in the binary phase shift keying wireless communication

system. With the combination of the hybrid-I1 ARQ and the

n-bit-marked error correction scheme, the packet throughput is

improved significantly. The numerical examples show that the

throughput of this combination scheme may have a maximum

gain about 0.26.

I. INTRODUTION

Wireless communications possess the convenient mobility property, which is very desirable. However, the air link, which may be effected by noise, multi-path fading, Doppler frequency shift, introduces significant errors in a mobile computing system. The conventional automatic-repeat-request (ARQ) protocol, which is designed for the wired transmission environment, can effectively control errors for the higher layers. Because of the high error rate for air link, the ARQ protocol becomes not very effective as it used in the wired

transmission environment [ 13. The forward-error-correction

(FEC) scheme is a well-known method to control errors. Directly applying FEC scheme and the ARQ protocol on a mobile computing system can reduce errors at the expenses of transmission bandwidth, because a packet with FEC has a lot of redundant bits [2]. When the bit error rate (BER) is not so

high, say lo4, this direct combination of ARQ and FEC wastes

the bandwidth, which is very undesirable.

The Hybrid-I1 ARQ scheme using FEC codes, which is devised based on the concept that the parity-check bits for error correction are sent to the receiver only when needed, increases the bandwidth efficiency and reduces the average packet delay [ 3 ] . Two linear codes are used in this scheme; one

is a high-rate (B, B-k) code CO, which is designed for error

detection only, the other is an invertible half-rate (2k, k) code

C,, which is designed for simultaneous error correction and

error detection. The packet formats are depicted in Fig. 1. The operation procedure of the hybrid-I1 ARQ is described as following. At first, the transmitting node sends the packet with the high-rate code. When the packet is received successfully, the receiving node sends an acknowledgement (ACK) back to the transmitting node. Otherwise, the receiving node sends a negative acknowledgement (NAK) back and the transmitting node will transmit the corresponding invertible half-rate code for correction. If the packet is successfully corrected, the receiving node sends an ACK back. On the contrary, the receiving node sends a NAK for the retransmission of the high-rate code packet and drops the former one. If the retransmitted one is correct, an ACK will be sent. Otherwise, it will be corrected by the former corresponding invertible half-rate code. If the packet still can’t be corrected, the packet with the corresponding invertible

invertible half-rate code high-rate code

Fig. 1. The packet formats of hybrid-I1 ARQ.

half-rate code will be dropped and a NAK will be sent for the retransmission of the packet with the corresponding invertible half-rate code. This procedure will be repeated until the packet

received successfully [4].

On the other hand, the n-bit-marked error correction scheme employs the physical layer side information to increase the correctness of every transmitted packet for improving the throughput [SI. In this scheme, the transmitting node doesn’t

have to change the structures of the physical layer and the data

link layer. In the receiving node, a side information generator

is added. The receiver structure with binary phase shift keying

demodulator and the side information generator is shown in

Fig.2. We mark the bit, which is in Conditions I1 and 111.

In this paper, we combine the,n-bit-marked error correction and the hybrid-I1 ARQ scheme. The operation procedure of this combined scheme is very similar to that of the hybrid-I1 ARQ scheme. The only difference is that we use the n-bit-marked error correction scheme to increase the correctness of every hybrid-I1 ARQ packet to improve the

throughput. The operation procedure of

this

combined scheme

is described as following. At first, the transmitting node sends the packet with the high-rate code. If the packet is received successfully by employing the n-bit-marked error correction scheme, the receiving node sends an ACK back to the

transmitting node. Otherwise, it sends a NAK back to request

for transmitting the packet with the corresponding invertible

half-rate code.

This

packet is also received by employing the

n-bit-marked error correction scheme. If it is correct or can be corrected by the n-bit-marked error correction scheme, the receiving node sends an ACK back. If not, it also can be used to correct the information packet. If the packet is successfully corrected by the corresponding invertible half-rate code, the receiving node sends an ACK back. On the contrary, the receiving node sends a NAK for the retransmission of the packet with high-rate code and drops the former one. If the

retransmitted one is correct or can be corrected by the

n-bit-marked error correction scheme, an ACK will be sent.

~~

‘The work IS supported in part by the National Science Council, R.0.C

ride information generator

Fig.2: receiver structure

Otherwise, the former packet with the corresponding invertible half-rate code will be used to correct the packet.. If the packet still can't be corrected, the packet with the corresponding invertible half-rate code will be dropped and a NAK will be sent for the retransmission of the packet with the corresponding invertible half-rate code. This procedure will be repeated until the packet received successfhlly.

11. THE THROUGHPUT ANALYSIS

The throughput of the hybrid-I1 ARQ scheme is effected

by the values of 41 and 42. 41 is the conditional probability

that the packet can be recovged by .the second transmitted packet when the first transmitted packet is detected error. 42 is the conditional probability that the packet can be recovered by the third transmitted packet when the first and second transmitted packets are detected error and can not be recovered by the packet with the invertible half-rate code.

For the combination the hybrid-I1 ARQ and the n-bit-marked

scheme, 41 can be expressed as

(1)

41 = ( P c + P n ) + Pd&l 4 1 - P c

-

P f l ) ,

where P, is the probability of the first packet is received

successfully without invoking the correction algorithm. P,, is

the probability that the erroneous packet is successfully

recovered by the n-bit-marked error correction scheme. Pdcl is

the probability that the first and second transmitted packets are erroneous and can't be corrected by the n-bit-marked error correction scheme but can be recovered by invertible high-rate

code. PddCI can be expressed as

where Pdc is the probability that the first and second

transmitted packets are erroneous but can be recovered by

invertible high-rate code. PA is the probability that the first and

second transmitted packets are detected errors, the first transmitted packet can be recovered by the n-bit-marked error correction scheme and the first and second packets can be

recovered by the half-rate code. PAI is the probability that the

first and second transmitted packets are detected error, the second transmitted packet can be recovered by the n-bit-marked error correction scheme and the first and second packets can be recovered by the half-rate code. PB is the probability that the first and second transmitted packets are

detected error, both can be recovered by the n-bit-marked error correction scheme, and the first packet can be recovered by the half-rate code. The probabilities, P A and, Pal are equal. Pddcl

can also be expressed as

(3)

We assume that there are N marked bits in the first transmitted packet and among them h marked bits are in the

first k bits of the packet. Let t be the correction power of the

invertible half-rate code and n is the maximum number of

marked bits of the n-bit-marked error correction scheme. The

probability PA is given by

Pddcl = Pddc - 2PA i-PB

(4)

where

P,

is the BER, B is the number of bit in a packet. P I is the probability that the signal energy of a received bit is larger

than r (the threshold of side information generator). P2 is the

probability that the energy of a received bit is fallen in the (0, r)

region. P3 is the probability that a received bit is fallen in the (0,

-r) region. The detailed derivation of PA is presented in the

Appendix.

where PI<, is the probability that a packet with one to (t-j)

errors in the first k bits can be recovered by the

n-bit-marked error correction scheme and PIU is the probability that a packet with one to t errors in the first k bits can be recovered by the n-bit-marked error correction scheme. Similarly, when the n-bit-marked error correction scheme is

employed, q2 is given by

1-1

C A l ( i ) s , ( t - i)[l - A(0) - s(t - i ) - s2 (i)] ( 8 )

,=O

and

A(i) = C:pe'(l - P.)~-' (9)

where P, is the probability of the first packet is received

successfully without invoking the correction algorithm.

P,

is

the probability that the erroneous packet is successfully

recovered by the n-bit-marked error correction scheme. A(i)

is the event that the first k bits of the thud transmitted packet contain exactly i errors. A I(i) is the event that the first k bits of the third transmitted packet contain exactly i errors and can not be corrected by the n-bit-marked error correction scheme.

S(j) is the event that the first k bits of the third transmitted packet contain one to i errors. S,(i) is the event that the first k

bits of the third transmitted packet contain one to i errors and

can not be corrected by the n-bit-marked error correction scheme. S,(i) is the event that the first k bits of the third transmitted packet contain ( t - j + l ) to k errors and can be corrected by the n-bit-marked error correction scheme.

Denote that

Y

= 41 +42 - q1q2

Then the throughput of the combination scheme with receiver buffer of size N has a lower bound as

q 2 6, /(6, + 6, + 6 , N ) (17)

where

The throughput versus

BER

with t= 3, 5 or 10 are plotted in

Figs.3-5. In Fig.3, the maximum gain is 0.26. Here the gain is

defined as the difference of the throughput of the hybrid4

A R Q

and that of the combination of the hybrid-I1

A R Q

and the n-bit-marked error correction scheme. The maximum gains are

0.24 and 0.17 for t=5, n=10 and t=10, n=15 as shown in Figs.4

and 5. It is observed that the proposed scheme can increase the packet throughput significantly at BER around 1.5x103, where

the throughput of the conventional selective repeat

A R Q

is

almost zero.

Iv.

CONCLUSION

In this paper, we combine the hybrid-I1

A R Q

and the

n-bit-marked error correction scheme to improve the throughput performance. We take the advantages of using side information and FEC codes. The numerical results show that this scheme can improve the throughput significantly. The maximum gain of this combination scheme is 0.26 at BER around 1.5~10'. This scheme needs computation power in the

receiver. It is expected that when the cost effective digital

signal processing integrated circuit chip is available, this

scheme can be practical.

0.9 . 0.8 . 0.7 . 0.6 .

g

0.5 .

e

0.4 . 0.5 . 0 2 . 0.1 .

Fig.3.The throughput of the combination of n-bit-marked

error correction (n= 3, 5 or 10) and hybrid-I1

A R Q

with

hybrid4 ARQ (1=5 ) --- ride-information (n=3) aide-information (n=5) 0 8 - - - ride-information ("=lo) - z 0 7 - E 0 6 - I O 4 - 5 3 0 5 - P 0 3 - 0 2 0 1 0

Fig.4.The throughput of the combination of n-bit-marked

error correction (n= 3, 5 or 10) and hybrid41 ARQ with

t=5. The buffer size is 128 and the packet size is 524.

11

- -

___-

.,

hybrid-11 ARQ (t=lO )

... ade-mforrnalion [n=V

--- side-information (n-IO)

-:. side-information(n-15)

- . 0.8

Therefore, when h=O, the total probability of PA can be expressed as

PA =

2

k;-'P,H-NkP2 + P3)N - PzN@C:P.'(/ - p ) k - ' ] - ( I - P)E}

N = l ,=O

(A.4)

Next, we assume N=l and h=land PA is expressed as

If N=2 and h=l, then PA is given by

If N=3 and h=l, then PA is given by

0.6 - P 9 0 5 - j O 4 . 0 3 - 0.2 . O l - 01 lo" 10" 10.' 10.' 10.' \ 1 +b@kF;B"4k4+412-4'

1 1

-(l-ef (A.7) bit e m r rata

Fig.5.The throughput of the combination of n-bit-marked

error correction ( ~ 5 , 10 or 15) and hybrid-I1 ARQ with

t=lO. The buffer size is 128 and the packet size is 524.

If N=n and h=17 then can be expressed as

APPENDIX

First, we assume that N=l and h=O. Then PA can be

(A.8) expressed as

(A.1)

If N=2 and h=O, then PA can be expressed as Therefore, when h=l, the total probability of PA can be

expressed as

Then, when h=2, the total probability of PA can be derived as

Therefore, the total probability of PA is given by " "

p* =

c

CCfc;:;p:-N

h=ON=h

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Shu Lin and Daniel J. costello, Jr., Error Control Coding :

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[2]

[3]

1701-1719, July 1982.

[4] Yu-Ming Wang and Shu Lin, 'A modified selective-repeat

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G.

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