Integrated Packet Loss and Error Control Schemes in Wireless Multimedia Data Links Jinsong Wu
Jacek Ilow
CDMA BTS Algorithm Development Nortel Networks, Calgary, AB Canada
[email protected]
Electrical and Computer Engineering Dalhousie University, Halifax, NS Canada
[email protected]
Abstract - This paper describes a novel Forward Error Correction (FEC) based technique, VHPG FEC, which combats packet losses and packet errors simultaneously. The scheme proposed uses a twodimensional (2-D) coding approach in which, at the encoder, information carrying packets are arranged vertically to form the 2-D matrix. The first code is applied along the horizontal direction to form the redundancy packets mainly to recover from lost packets; the second code is applied along the vertical direction within the individual packets to minimize the bit error rate (BER). Within the group of packets, the overall effect of this scheme is the reduction in the effective packet loss and the BER without need for retransmission. The scheme is applicable in environments where the packet loss is not exclusively a result of high BER and where the transmission time constraints are critical. The adaptive extension of the scheme proposed, AVHPG FEC, is introduced to deal with dynamic wireless channel characteristics. Performance of the VHPG coding is analyzed through theoretical calculations to illustrate the choice of coding parameters for various channels.
1. INTRODUCTION
1.1 Background Traditional FEC and ARQ error control schemes [1], which deal with packet level errors, are not efficient enough to confront the wireless communications environments with high BER and packet loss to meet guaranteed Quality of Service (QoS) in multimedia applications with stringent delay constraints. Another common error control method for combating burst bit error within packets is interleaving, but it is not advantageous when the inter-packet level has high BER and packet loss. Many existing solutions for providing QoS in wireless networks, such as [2] and [3], are based on the higher network layers. In the context of multimedia packet networks, limited adaptive wireless data link solutions, such as [4], have been explored. The focus of this paper is to meet the requirements of bounded delay and jitter in real-time wireless applications at the data link layer. The approach presented relies on a relatively low rate FEC code, and, with the multimedia traffic considered, the proposed solution is particularly applicable to new generations of broadband wireless access networks.
1.2 Problem formulation The critical observation that packet loss is not exclusively caused by erroneous transmission constitutes the foundation for the work described in this paper. Hard handoff, the process of buffer overflow, and network congestion are several possible reasons for packet loss independent of the BER level within the packets.
The construction of redundancy packets using FEC with erasure decoding to decrease the packet loss and to ensure the fixed transmission delay and jitter has been proposed at layers higher than data link in [5] where erasures correspond to lost packets. All the previous work in this area assumes that once the packet (either redundancy or information) is received, it has no or very few errors in higher network layers. However, such an assumption requires an extremely powerful FEC code at the physical layer or ARQ at the lower layers. The first option, combined with a redundancy level packet, could introduce prohibitive overhead, while the second option could probably recover lost packets itself. Considering the drawbacks of conventional error-control schemes for wireless multimedia applications and the flaws of the newer FEC-based packet loss control schemes, this paper presents a novel approach at the lower layers, especially the data link layer, to combat packet errors and loss at the same time, using an integrated FEC method. The breakthrough of the proposed method comes from applying FEC along two dimensions: first, across the information packets to construct the redundancy packets, and second, within individual packets to protect them against erroneous transmission. The distinguishing feature of the coding scheme proposed is that, unlike in conventional 2-D codes, the columns of the 2-D code (packets) are transmitted as independent entities.
2. VHPG FEC
2.1 Basic ideas The 2-D FEC scheme presented here, Vertical-Horizontal Packet Group FEC (VHPG FEC) [6], flexibly utilizes the product of conventional 1-D Reed-Solomon (R-S) codes in vertical and horizontal directions because of their superior performance in the presence of burst errors such as those in wireless links. At the receiver, the 1-D R-S decoding with hard decisions is performed first within the packet to reduce the BER and then within the group of packets 1-D erasure R-S decoding is employed to possibly recover from lost (“erased”) packets. The VHGP FEC coding scheme is characterized by the number of parameters that could be adapted to varying wireless channel conditions so that the throughput and the reliability of the data could be balanced.
2.2 Structure and possible implementation Fig. 1 shows the group of packets coding matrix. The packets belonging to a specific group are arranged column-wise into a matrix. In the figure, VH(m,n) stands for the mth bit of the nth packet. The core idea in the proposed VHPG FEC code is that coding is applied to a group of numbered packets, and the packets
0-7803-7206-9/01/$17.00 © 2001 IEEE
685
Nh − Kh
parity-
check packets to allow for packet loss recovery. Individual bits are aligned horizontally to form
Kv
Nv − Kv
information rows and
parity rows. Here, the Reed-Solomon (R-S) codes are used in two (horizontal and vertical) dimensions, hence the name of this novel coding scheme. This VHPG FEC refers to coding along the vertical dimension as intra-packet level coding (non-erasure decoding is used), and to coding along the horizontal dimension as inter-packet level coding (erasure decoding is used). Dv and Dh are respectively vertical and horizontal R-S coding minimum distances.
VH(1,NV-1)
VH(2,NV-1)
..
VH(NH-2,NV-1)
VH(NH-1,NV-1)
VH(0,NV-2) ..
VH(1,NV-2) ..
VH(2,NV-2) ..
.. ..
VH(NH-2,NV-2)
VH(NH-1,NV-2)
..
..
..
..
..
..
..
..
..
..
..
..
..
..
VH(0,3) VH(0,2)
VH(1,3) VH(1,2)
VH(2,3) VH(2,2)
.. ..
VH(NH-2,3) VH(NH-2,2)
VH(NH-1,3) VH(NH-1,2)
VH(0,1)
VH(1,1)
VH(2,1)
..
VH(NH-2,1)
VH(NH-1,1)
VH(0,0)
VH(1,0)
VH(2,0)
..
VH(NH-2,0)
VH(NH-1,0)
(N v ,K v, D v )
VH(0,NV-1)
Vertical Intra-Packet FEC
Packet Level Time Line
From Fig. 2, it is evident that, unlike in INTRAPHS, the choice for the INTERPHS length in bits is more flexible. In general, the parameters in the VHGP scheme with INTRAPHS and INTERPHS will depend on the requirements for delay and jitter performance as well as the burst packet loss situations.
Intra-packet Horizontal Coding Direction of packets transmission (packet loss recovery and error correction) nh 00000000000000 11111111111111
10 001010 1010 110 10 1000 1011 00 11 0 1 00 101010 11 00 11 0 1 0 1 00 0 11 1 0 1 00 10 11 00 11 0 1 0 1 00 0 11 1 0 11 1 0001 101010 00 11 0 1 0 1 00 11 0 1 0 1 00 00 0 11 1 0 11 1
kh
kv
information packets and
nv
Kh
(error correction)
matrix consists of
Direction of symbol transmission within the packet
are transmitted independently of each other. In VHGP code, each
0 1 1 0 0 1 0 01 1 0 01 01 1 0 1 0 1 0 01 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 01 1 0 01
11 00
Individual Packets 0 1 vertical horizontal m1 0 symbols v1 0 symbols
0 1 Inter-packet Horizontal Coding 11111111111111 00000000000000 n mh
(Nh,Kh,Dh) Horizontal Inter-Packet FEC
h
In the horizontal packet level FEC, the R-S encoding and decoding unit is called a horizontal virtual packet. Two kinds of horizontal virtual symbols in a virtual packet are possible. One is called the intra-packet horizontal symbol (INTRAPHS); the other is called the inter-packet horizontal symbol (INTERPHS). INTRAPHS: the whole horizontal R-S symbol is constructed from bits belonging to the same packet. INTERPHS: here, one horizontal R-S symbol uses only one bit of each vertical packet. The parameters for the horizontal R-S code are as follows: mh horizontal symbol length in bits; nh – number of horizontal symbol, dmin.h - horizontal coding minimum distance in symbols. The corresponding parameters for the vertical R-S code are: mv, nv and dmin.. The symbol level architecture of the coding scheme proposed is documented in Fig. 2.
686
000 111 11 00 11 00 11 00
kv
There is a number of possibilities in implementing VHGP encoding and decoding. One possible implementation is to encode the horizontal level of the VHPG codes first, but this order will incur higher delay. The recommended approach is to perform the encoding in three steps: (1) the vertical level encoding of information packets; (2) partial construction of the redundancy packets using the horizontal code; (3) vertical encoding of in the redundancy packets. The proposed sub-optimum decoding sequence of a 2-D code [1] is that vertical level decoding is completed first and then follows horizontal level decoding. After vertical decoding, at the horizontal level decoding, two issues need to be considered: for horizontal decoding (1) the errors come from the undetected vertical decoding errors; (2) the erasures come from the detected vertical decoding errors and packet loss, which in the case of this paper are independent phenomena.
kh 11111111111 00000000000 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 00 11 00 11 0 1 0 1 00 11 0 1 00 11 00 11 00 11 0 0 00 11 0 1 000 111 00 11 00 001 11 01 1 0 1 00 11 11 0 1 000 0 111 1 00 11 00 11 0 1 0 1 00 11 000 111 00 11 00 11 00 11 0 1 0 1 00 11 0 1 00 11 00 11 00 11 0 0 00 11 0 1 00 00 001 11 01 1 0 1 00 11 11 0 11 1
nv
Fig. 1 Vertical-Horizontal Packet Group (VHPG) view.
Individual Packets
11 00 00 11 mh
horizontal symbols
1 0 0 1 0 1
vertical m1 0 v1 0 symbols
Fig. 2 Inter- and intra-packet symbol based horizontal coding.
3. AVHPG FEC The trend in the design of FEC schemes for wireless packet radio networks is to dynamically optimize the FEC code and ARQ parameters based on estimates of the channel conditions. The objective of traditional adaptive coding schemes is to reduce the packet error rate. However, in the case considered in this paper, when the packet loss does not depend exclusively on the packet being in error, these traditional adaptive coding schemes will not be successful to combat packet losses and errors simultaneously. This is the reason for developing an adaptive extension of the VHPG FEC. The Adaptive Vertical-Horizontal Packet Group (AVHPG) FEC [6] based on the channel state conditions adjusts the parameters of vertical and horizontal codes, such as: (i) mv and mh: the R-S vertical and horizontal symbol length in bits, and (ii) nh and nv: the number of horizontal and vertical symbols. Here, cases (i) and (ii)
are mentioned separately because shortened or extended R-S codes could be applied. In general, in the AVHPG coding scheme, there are more parameters available to optimize performance over timevarying channels than in 1-D codes; thus, the proposed adaptive scheme could be more flexible than the conventional adaptive FEC schemes. Besides traditional random bit errors (BER) based Gilbert-Elliot (two-state) channel model (Fig. 3-a), AVHPG FEC also adopts three additional Gilbert-Elliot channel models in which the “Good” and “Bad” channel states (Fig. 3-b) are (i) burst errors in bits (burst error bit length or BEBL), (ii) randomly lost packets (packet loss rate or PLR), and (iii) burst of lost packets (burst packet loss number or BPLN). The two-state models and the mapping of the channel states into the AVHGP FEC code parameters describe the procedure of adaptive protocol processing. The adaptive scheme proposed adjusts the coding rates of vertical and horizontal error control to follow the changes in bit error and packet loss, respectively. The scheme optimizes the vertical packet symbol length in bits to follow the changes in packet burst errors. The scheme is adaptive to packet burst loss by changing the INTERPHS length in bits during periods of high burst packet loss and high detected decoding errors. When no burst loss happens, INTRAPHS horizontal coding is preferential.
Low BER
error
perr . The probability for reaching the erasure state is p era
We assume that the generic binary R-S code has the parameters: the number of coded symbols n = 2 − 1 with m being the number of bits to represent the R-S symbol and the minimum distance in m
d min = n − k + 1 . The probability p of the symbols: particular symbol being confused with another symbol is related to the channel bit error rate
p ce
in binary transmission as
pe = 1 − (1 − pce ) m
(1)
The UDSC model with non-erasure decoding is obtained from Fig.5 by removing the erasure state. Received Symbol
Transmitted Symbol 1- p err - p era
0
0 p
α
α
p
α2
Input Code-Word Symbol
(each)
α3
p p
.
High BER
α2
p
m
p err/2 -1
p
p s
m
2 -1
α Fig. 3-a model.
.
Conventional (BER based) Gilbert-Elliot channel
.
α3
Output Code-Word Symbol
m
2 -1
α p era
erasure
Fig. 4 2m-ary Uniform Discrete Symmetric Channel model with erasure. Good State
Bad State
The decision delivered by the R-S decoder in this paper can be classified as follows: Correct decision when the corrected code word after error correction is the same as the transmitted code word described by the
Fig. 3-b Generalized Gilbert-Elliot channel model.
probability of correct code word ( Pc );
4. ERROR PERFORMANCE CALCULATIONS The reliability and throughput performance of the proposed VHPG coding scheme can be determined through the series of combinatorial calculations [6]. Because of the space limitation, we only outline the procedure to obtain the closed-form expressions for the performance of the VHPG scheme in terms of the effective symbol error rate after vertical and horizontal decoding. To analyze the overall performance, one needs to consider first the performance along the vertical direction, and then along the horizontal direction. To obtain analytically tractable results, at the starting point, we introduce the uniformly distributed symmetric channel (UDSC) models with non-erasure and erasure decisions [7] [8]. The latter model is presented in Fig. 4 with α being the R-S coded symbol transmitted independently with the same probability of symbol i
687
Decoder (undetected) error when the corrected code word after error correction is different than the transmitted code word: this is u
described by the probability of undetected error ( PE ). Decoder failure (detected error) when the decoder cannot decide which code word was transmitted: this situation is described by the d
probability of detected error ( PE ). Using the code word (in our case packet) error performance analysis of the R-S codes over UDSC presented in [7] [8], the following are the formulas of packet error correcting probabilities for the non-erasure and erasure decoding cases, respectively:
pc.nera (m, perr , d e , n) =
de −1 2
∑ v =0
n v perr (1 − perr )n−v v
In the packet networks, the performance metrics need eventually to be converted to the packet level. Using Fig. 2 again, the number (2)
real
of real (vertical) packets ( N v
N
INTRAPHS scheme is
N
de 2 d −2v e
n n − v w v pc.era (m, perr , pera , de , n) = ∑ ∑ pera (1 − perr − pera )n−v−w perr v=0 w=0 v w
(3)
real v
To apply the above results to VHPG scheme, we observe that the decoding along the vertical and horizontal directions in VHPG uses non-erasure and erasure R-S decoding, respectively. In VHPG, the packet and symbol error rate after vertical FEC (intra-packet) decoding is obtained using non-erasure R-S decoding formulas such as (2) with parameters of the vertical code:
p pkt . c.v =
∑ u =0
nv u perr. v (1 − perr .v ) nv −u u
(4)
The key point in the horizontal performance analysis is that the packet loss, combined with the failures of the decoder in the vertical direction, contributes to the horizontal symbol erasures for intrapacket coding so that for the horizontal intra-packet symbol encoding
pera .h = p pkt .d .v + PL − p pkt .d .v ⋅ PL PL
where
is packet loss probability, and
(5)
p pkt .d .v is
detected
packet error probability after vertical error control. With this observation, the horizontal virtual packet correct reception probability after horizontal error correction,
p vpkt .c.h
1
The actual calculations of probability of horizontal level undetected errors in VHPG coding scheme are very complex because even for the case of 1-D R-S code with erasure decoding, the formulas are quite involved. To check the validity of our results, Fig. 4 shows the erasure decoding performance (symbol error rate) using the contour plot as a function of symbol error and erasures rates along the x and y directions, respectively. The 1-D R-S code employed has the parameters: m=3 and dmin =4. i.e., the length of the code word in coded symbols is n = 2 number of information symbols in the
m
This code used is capable of correcting one coded symbol error. The performance results in Fig. 5 calculated using the closed-form expression (3) are in good agreement with simulation results. In addition, the contour plot for 1-D R-S coding provides a good point of reference for the choice of the 2-D R-S code. After R-S erasure decoding,packet error probability(log10),m=3,dmin=4 -1 -1 -1
-2
v =0
where the horizontal effective symbol error probability after is derived from the vertical symbol
for INTERPHS
-4 -4.5
(7)
-5 -4.5
for INTRAPHS
Given this, the effective correct decoding probability in the vertical-horizontal packet group after VHPG FEC is calculated as: virt
p grp .c.vh = ( pvpkt .c.h ) K h
-1
( n v − d e .v ) m v mh nv − d v
-3.5
-3
={
which from Fig. 2 is:
-3
-4
K
virt h
K
-2.5
-7
horizontal virtual packets
-4
-5
-2 -6
-5
error calculations. Using (6), we can get the performance of the VHPG at the group of packet level by calculating the number of virt h
-4
-2
perr .h
-2
-3
-6
vertical error decoding
-2 -3
-1.5
symbol erasure probability(log10)
∑
and the word is
-3
u=0
code
-1
∑
−1= 7
k = 2 m − 1 − (d min − 1) = 4 .
is obtained
nh nh − u u nh −u−v (6) v perr.h pera .h .(1 − perr.h − pera.h ) u v
(8)
688
(9)
5. PERFORMANCE SIMULATIONS
-1
dmin. h −1 2 d min. h −2 u −1
N vreal
p pkt .eff .ud .vh = 1 − p pkt .eff .c.vh = 1 − ( p grp .c.vh )
from (3) as: pvpkt.c.h =
= nn ⋅ mh . Applying the principle that the group of packets
is correct when all the packets are correct, the effective (undetected) packet decoding error probability is:
where de=dmin-1 is the minimum distance of the R-S codes adopted.
d min . v −1 2
) in the VHPG coding with
= nn and with INTERPHS scheme
real v
-4
-3.5 -3 -2.5 -2 symbol error probability(log10)
-1.5
-1
Fig. 5 Packet error probability for R-S (7,4) code with erasure decoding.
To give an insight into the choice of parameters in VHGP and AVHGP FEC coding schemes for different values of BERs and PLRs, the effective packet error probabilities after VHPG decoding are provided for the cases of mv=4, mh=4 in Tables 1, 2, and 3. The effective packet error probabilities, which include effective undetected packet error probability and effective detected packet error probability, in each table are calculated as a function of Dv and Dh(the vertical and horizontal R-S decoding minimum distances, Dv=
d min.v , Dh= d min.h ).
6. CONCLUSIONS
The common characteristics in these tables are that with the increase of the distances of vertical and horizontal R-S coding, the effective packet error probabilities are decreased. Furthermore, the crucial observation in all tables is that these performances are not symmetrical between vertical and horizontal levels.
Dv=5
Dv=7
Dv=9
Dv=11
Dv=13
Dh=3 1.00E+00 8.51E-01 3.50E-01 4.06E-02 1.18E-03 Dh=5 7.92E-01 5.53E-01 8.89E-02 2.11E-03 6.76E-06 Dh=7 4.75E-01 2.30E-01 1.09E-02 4.04E-05 1.29E-08 Dh=9 1.78E-01 5.23E-02 5.70E-04 2.90E-07 9.04E-12 Table 1 Effective packet error probability after AVHPG FEC, under mv=4, mh=4, BER:6.00e-02, PLR:0.00e+00 Dv=3 Dh=3
Dv=5
One interesting phenomenon in Table 3 is that, although the BER is 0, even if the distances of the horizontal R-S coding are the same, after AVHPG FEC, the effective packet error probabilities are different by using different distances of vertical R-S coding. In fact, in the horizontal level, the VHPG FEC protects only the information bits and horizontal redundancies of the packets, and different distances of vertical R-S coding lead to the differences in the number of actual protected bits within the packets.
Dv=7
Dv=9
Dv=11
The main contribution in this paper is the introduction of a new approach for the integrated error and packet loss control in wireless packet networks within the FEC. Specifically, a novel VHPG coding scheme and its adaptive extension, AVHPG, were proposed. Their performance has been investigated under different wireless channel and packet loss conditions. The new schemes are based on the concept of two-dimensional (2-D) Reed-Solomon codes, and the novelty of this design is that the columns (packets) within one 2-D code word are transmitted as independent entities. As a result, they undergo different corrupting processes in the systems, and erasure decoding allows for the recovery of the 2-D code words that otherwise would be in error. The development of these new schemes has been motivated by the stringent quality of service (QoS) requirements in multimedia applications.
References
Dv=13
[1] Shu Lin and Daniel J. Costello, Error Control Coding: Fundamentals and Applications, Prentice Hall, published in New Jersey, Oct 1982
1.50E-01 1.27E-01 1.03E-01 7.81E-02 5.28E-02 2.68E-02
Dh =5 1.02E-02 8.50E-03 6.80E-03 5.11E-03 3.41E-03 1.71E-03 Dh =7 2.49E-04 2.07E-04 1.66E-04 1.24E-04 8.28E-05 4.14E-05
[2] A. Alwan, R. Bagrodia, N. Bambos, M. Gerla, L. Kleinrock, J. Short, and J. Villasenor, Adaptive mobile multimedia networks, IEEE Personal Communications, vol. 3 2 , pp. 34 51, April 1996
Dh =9 2.28E-06 1.90E-06 1.52E-06 1.14E-06 7.59E-07 3.80E-07 Dh =11 7.45E-09 6.20E-09 4.96E-09 3.72E-09 2.48E-09 1.24E-09 Dh =13 6.95E-12 5.76E-12 4.61E-12 3.46E-12 2.30E-12 1.15E-12 Table 2 Effective packet error probability after AVHPG FEC, mv=4, mh=4, BER=1.00e-04, PLR=1.00e-01 Dv=3 Dh=3
Dv=5
Dv=7
Dv=9
Dv=11
[3] B. Belzer, J. Liao, and J.D. Villasenor, Adaptive video coding for mobile wireless networks, Image Processing, 1994. Proceedings. ICIP-94., IEEE International Conference, vol. 2 , pp. 972 -976, 1994
Dv=13
3.61E-07 3.01E-07 2.40E-07 1.80E-07 1.20E-07 6.01E-08
[4] P. Lettieri, Curt Schurgers, and M.B. Srivastava, Adaptive link layer strategies for energy efficient wireless networking, Wireless Networks, 5, pp. 339-355, 1999
Dh =5 2.38E-12 1.99E-12 1.59E-12 1.19E-12 7.94E-13 3.97E-13 Table 3 Effective packet error probability after AVHPG FEC, mv=4, mh=4, BER=0.00e+00, PLR=1.00e-03
In the case of BERs not being sufficiently small as shown in Table 1, horizontal error control is helpful even if PLR=0. In Table 1 (with very high BER), by comparing the case of (Dv=5, Dh=7) with the case of (Dv=7, Dh=5), it seems that increasing the distance of horizontal control is more efficient than increasing that of vertical control. However, comparing (Dv=9, Dh=7) with (Dv=7, Dh=9), it seems increasing the distance of vertical control is more efficient than increasing that of horizontal control. Thus the efficiency of increasing the distance of either vertical control or horizontal control is not always consistent. A tendency is that, when the distance of the horizontal error control is sufficiently large, increasing the distance of the horizontal error control seems more efficient than increasing the vertical error control.
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[7]
Stephen B. Wicker and Vijay K. Bhargava, Editors, ReedSolomon Codes and Their Applications, IEEE Press, published in New Jersey, 1994
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