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A Model-Based Approach to Evaluation of the
Efficacy of FEC Coding in Combating Network
Packet Losses
VENKATA GIRI.MADDIPATI(*)
GIET,RAJAHMUNDRY
DEPT.OF.COMPUTERSCINCE &ENGG,
maddipati.venkatagiri@gmail.com
RAJASEKHAR.SWARNA
GIET,RAJAHMUNDRY
DEPT.OF.COMPUTERSCINCE &ENGG,
swarnarajasekhar@gmail.com
Abstract—We propose a model-based analytic approach for evaluating the overall efficacy of FEC coding
combined with interleaving in combating packet losses in IP networks. In particular, by modeling the
network path in terms of a single bottleneck node, described as a � queue, we develop a recursive procedure
for the exact evaluation of the packet-loss statistics for general arrival processes, based on the framework
originally introduced by Cidon et al., 1993. To include the effects of interleaving, we incorporate a discrete-
time Markov chain (DTMC) into our analytic framework. We study both single-session and multiple-session
scenarios, and provide a simple algorithm for the more complicated multiple-session scenario. We show that
the unified approach provides an integrated framework for exploring the tradeoffs between the key coding
parameters; specifically, interleaving depths, channel coding rates and block lengths. The approach facilitates
the selection of optimal coding strategies for different multimedia applications with various user quality-of-
service (QoS) requirements and system constraints. We also provide an information-theoretic bound on the
performance achievable with FEC coding in IP networks.
Index Terms—Autocorrelation function, FEC coding, interleaving, packet-loss processes, residual packet-loss
rates,
single-multiplexer model.
I. INTRODUCTION
THE packet transport service provided by
representative packet-switched networks, including
IP networks, is not reliable and the quality-of-service
(QoS) cannot be guaranteed. Packets may be lost due
to buffer overflow in switching nodes, be discarded
due to excessive bit errors and failure to pass the
cyclic redundancy check (CRC) at the link layer, or
be discarded by network control mechanisms as a
response to congestion somewhere in the network.
Forward error correction (FEC) coding has often
been proposed for end-to-end recovery from such
packet losses. However, the use of FEC in this
application provides a double-edged sword. From an
end user’s perspective, FEC can help recover the lost
packets in a timely fashion through the use of
redundant packets, and generally adding more
redundancy can be expected to improve performance
provided this added redundancy does not adversely
affect the network packet loss characteristics. On the
other hand, from the network’s perspective, the
widespread use of FEC schemes by end nodes will
increase the raw packet-loss rate in a network
because of the additional loads resulting from
transmission of redundant packets. Therefore, in
order to optimize the end-to-end performance, the
appropriate tradeoff, in terms of the amount of
redundancy added, and its effect on network packet-
loss processes, needs to be investigated under
specific and realistic modeling assumptions.
In this paper,we provide a study of the
overall effectiveness of packet-level FEC coding,
employing interlaced Reed-Solomon codes, in
combating network packet losses and provide an
information- theoretic methodology for determining
the optimum compromise between end-to-end
performance and the associated increase in raw
packet loss rates using a realistic model-based
analytic approach. Intuitively, for a given choice of
block length we expect that there is an optimum
choice of redundancy, or channel coding rate, since a
rate too high (low redundancy) is simply not
powerful enough to effectively recover packet losses
while a rate too low (high redundancy) results in
excessive raw packet losses due to the increased
overhead which overwhelms the packet recovery
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capabilities of the FEC code. The optimum channel
coding rate results in an optimum compromise
between these two effects.
In order to analytically investigate this
tradeoff, we consider a simplified network scenario
described in terms of a single bottleneck node,
modeled as a multiplexer. For networks with reliable
transmission media, where transmission errors are
negligible, buffer overflows due to congestion in
routers are the major cause of packet losses. In a
packet-switched network, a flow of packets crosses a
chain of routers before it reaches the destination
node. Most of the packet losses from a flow occur in
the router which has the smallest bandwidth.
Therefore, we can model the whole chain of routers
in terms of this single bottleneck node. Both
theoretical analysis and experimental results justify
this assumption [1]–[3].Asingle-multiplexer model
for this bottleneck node is widely used to analyze the
associated queueing-related packet losses, e.g., losses
due to buffer overflows and excessive delays. Since
the correlation level of the packet-loss process has
great impact on the FEC efficacy, we investigate this
dependence using the autocorrelation function of the
packet-loss process.
The performance of FEC in recovering
network packet losses has been studied in many
papers [4]–[13]. In [4], the use of redundant parity
packets was proposed to reconstruct lost data packets
and the corresponding performance evaluation
indicated that residual packet-loss rates can be
reduced up to three orders of magnitude. However, in
[4] for analysis purposes the packet-loss process
resulting from the single-multiplexer model was
assumed to be independent and, consequently, the
simulation results provided show that this simplified
analysis
considerablly overestimates the performance of FEC.
By modeling the single-multiplexer as an or queue,
Cidon et al. [5] proposed a recursive algorithm to
compute the packet-loss statistics (block errror
density), through which the exact residual packet-loss
rate after decoding was computed. Surprisingly, all
numerical results given in [5] indicate that the
resulting residual packet-loss rates with coding are
always greater than without coding, i.e., FEC is
ineffective in this application. However, in [5] only a
single parity packet is used1 and the block length was
constrained to the range . As we show later, these
conclusions are somewhat misleading and result from
inappropriate parameter choices. In [6]–[8], more
general arrival processes were considered and coding
tradeoffs assessed but performance results were
obtained using large deviation bounds to characterize
the packet-loss processes and were not exact. In [9]–
[12],
Altman et al. derived analytical
formulas for the frame-loss probabilities for the
single-multiplexer model using multi-dimensional
probability generating functions and show that the
frame loss probabilities can be reduced if a
sufficiently large amount of redundancy is added.
However, contrary to [4], [5], in these works the
authors used the frame-loss probability as the
evaluation metric for FEC performance, because it
was assumed that the failure to recover any lost data
packet will lead to the loss of all the data packets in
that block. For ATM networks, this assumption is
valid since the loss of a single cell does result in the
discarding of the whole message. However, for other
networks, like IP networks, this is not the case. In IP
networks, packet-level FEC coding can be performed
across several IP packets. Even if any lost data
packets cannot be recovered, the correctly received
data packets in the same coding block may still be
useful. For example, in the application of video over
IP, when some lost video packets cannot be
recovered, the correctly received video packets in the
same coding block need not be discarded and can
even be used to estimate the information in lost video
packets using an appropriate error concealment
scheme. As shown in Section II, in many cases, the
FEC performance predicted by using the frame-loss
probability is not only quantitatively different, but
also qualitatively different, from that reflected by the
packet-loss probability. Although the asymptotic
analysis (when block size goes to infinity) for the
frame-loss rates in [9]–[12] can provide some insight
into FEC performance on IP networks, the
methodology and specific conclusions developed in
these works are not useful for a comprehensive
evaluation of FEC effectiveness on IP networks since
they are based on an inappropriate evaluation metric.
II. PRELIMINARIES
A. Single-Multiplexer Network Model
If a network’s performance is limited by a single
bottleneck node, the network can often be modeled in
terms of a single multiplexer. As illustrated in Fig. 1,
the single-multiplexer model is a queueing system
which consists of three components: 1) an arrival
process for packets from different sources with
corresponding packet arrival rates , ; 2) a buffer
which can hold up to packets, which are assumed
served in first-come-first-served (FCFS) order; and 3)
an output link with average packet service rate . We
assume if a packet finds a full buffer upon arrival, it
will be discarded. For analytical convenience, we
assume the packet service times are independent and
identically distributed (i.i.d.) with an exponential
distribution and average packet service time .With
denoting the overall packet arrival rate, the
normalized load to the system is (1) Although the
assumption of exponential service time may not be
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accurate in some situations, it enables us to obtain
some analytical results and gain some insight on the
effects of packet-loss processes due to buffer
overflows.
B. Source Model
We assume the packet arrival process for each source
is a renewal process, i.e., for any source the packet
interarrival times are i.i.d. with arbitrary probability
density function . In particular, we consider the case
of the Erlang interarrival time distribution When
(assuming is fixed), the variance of converges to 0
and the interarrival time becomes deterministic with
period . With appropriate parameter choice, this case
can represent constant bit rate (CBR) sources. For the
hyperexponential distribution, the average arrival rate
C. System Model for FEC Performance
Evaluation
Consider the communication system model illustrated
in Fig. 2. We suppose there are homogeneous and
independent sources sharing the single-multiplexer
and each source generates packets with average rate .
The FEC coder for each source applies an interlaced
Reed-Solomon code [6], [8], [15] to the packets from
the source, which means for every block of source
information packets it creates an additional parity
packets to the network. The channel coding rate is
given by . As a result of the channel coding, the
packet arrival rate into the network will increase to .
Let the random variable denote the number of lost
packets within a block. If , we assume all the lost
packets within that block can be recovered by the
channel decoder. Assume denotes the block-error
distribution, i.e., the probability that packets out of
are lost. Therefore, the expected number of lost
packets within a block is (6)
and the expected number of lost information packets
within a block is (7) Finally, the effective information
packet loss rate after channel decoding is (8)
D. Evaluation Metric: Packet-Loss Probability or
Frame-Loss Probability?
In some networks, such as ATM networks, the failure
to recover a single packet results in the loss of the
entire frame (block). In this case, the frame-loss
probability is a more suitable metric than packet-loss
probability for evaluation of FEC performance, as
used in [9]–[12]. The frame-loss probability is given
by (9) Figs. 3 and 4 illustrate comparisons of the FEC
performance predicted by packet-loss probability
with that predicted by
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Fig. 3. Performance difference between coding and
without coding as a function of the number of
information packets in each frame, single session ��
Other system parameters are as follows: system load
buffer size , 1 parity packet used
Fig. 4. Performance difference between coding and
without coding as a function of the number of
information packets in each frame, multiple session
�� _ __. Other system parameters are as follows:
system load _ _ ___, buffer size _ ___, 1 parity
packet used.
frame-loss probability. The curves show the
differences of the residual packet-loss probabilities
and frame-loss probabilities with coding and without
coding, denoted by and , respectively. Fig. 3 shows
the case of a single session and Fig. 4 shows the case
of multiple sessions . Other system parameters are
indicated in the corresponding figure captions. When
one of the differences is positive (i.e., or ), this
implies that using redundant packets does not
improve the corresponding performance metric ( or );
that is, use of FEC is ineffective. From Figs. 3 and 4
it should be clear, at least for the cases considered,
these two performance metrics can lead to totally
different conclusions, both quantitatively and
qualitatively, concerning the effectiveness of FEC. In
particular, in either case the results indicate that, for
the corresponding choice of system parameters, the
use of FEC is ineffective for all block lengths based
on but can provide improved performance based on
provided the block length is chosen large enough. As
described above, in this paper we focus on IP
networks and use packet-loss probability to evaluate
the FEC performance.
E. Autocorrelation Function of Packet-Loss
Processes
For a packet-loss process we use the autocorrelation
function to characterize the dependence between the
packet-loss events over time. Let the random
sequence represent the packet- loss process, with 1
denoting loss and 0 denoting reception. If is
stationary, then the autocorrelation function of is
given as (10) where is the lag and is the expectation
of the sequence
III. FEC PERFORMANCE WITH A SINGLE
SOURCE
A. FEC Without Interleaving
We begin our analysis with the simplest case: there
is only one user for the multiplexer . As (8)
illustrates, the key quantity in evaluating the residual
packet-loss rate after FEC decoding is , the block-
error distribution for an arbitrary number of
consecutive packets. In [5], Cidon et al. propose a
recursive algorithm to compute for the finite buffer
queue with Poisson arrivals and exponential service
times, denoted as the queue. In order to analyze the
packet losses for more general arrival patterns, in
what follows we first describe the extension of the
algorithm to the queue, i.e., the finite buffer queue
with general i.i.d. interarrival times and exponential
service times. 1) Analysis of Block-Error
Distribution: Suppose there is only one source
sharing the multiplexer , and the . packet interarrival
times are i.i.d. with arbitrary probability density
function . Since the packet service times are assumed
i.i.d. and exponentially distributed, the single-
multiplexer can be modeled as a standard queueing
system. Let be the number of packets in the buffer
just before the th packet arrives at the system.
Because of the memoryless property of the
exponential service time, is a discrete-time Markov
chain (DTMC) [16, pg. 249], illustrated in Fig. 5,
with the state space and state-transition matrix
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where , , is the probability that packets are served out
of the system during an arbitrary interarrival time,
provided that there are at least packets in the system
at the beginning of that interarrival time. It can be
shown [16, pg. 248]n that (12) subject to a
normalization constraint. Let be the stationary
distribution of the DTMC, which can be obtained as
the solution to (13) Define , , , , to be the probability
of losses in a block of packets, given that there are
packets in the system just before the first packet of
the block arrives to the system. So we have (14)
where is determined from (13).
B. FEC With Block Interleaving
FEC performance is often limited by the bursty
nature of typical packet-loss processes, and block
interleaving techniques are frequently used to reduce
the burstiness of the packet-loss processes in
networks [4], thereby improving FEC performance.
In this section, we analyze the efficacy of
interleaving in reducing the burstiness of network
packet-loss processes and in improving the FEC
performance.
1) Interleaving Operation: The operation of block
interleaving is illustrated in Figs. 12 and 13. Before
being transmitted into the network, packets are filled
into an matrix row-wise and then read-out from the
matrix column wise. Therefore, the originally
consecutive packets will be packets apart from each
other after interleaving. is called the interleaving
depth (ILDP). At the receiver the packets will be
reordered in the deinterleaver before decoding. In
what follows we analyze the corresponding block-
error distribution incorporating the interleaving
operation.
2) Analysis of Block-Error Distribution: As shown
in Fig. 12, we again assume the packet arrival process
at the single multiplexer (after interleaving) is a
renewal process, i.e., the packet interarrival time at
the multiplexer is i.i.d. with some common
probability density function . Let denote the number
of packets in the buffer just before the th packet
arrives at the multiplexer (Point in Fig. 12). Again,
we assume the packet service times are i.i.d. with an
exponential distribution and the average service rate
is . Therefore, the random sequence is a discrete-time
Markov chain with the state space , transition-
probability matrix and stationary probability as
expressed in (11) and (13), respectively. Define
another random sequence , where is the number of
packets in the buffer just before the th packet, seen by
the interleaver (Point in Fig. 12), arrives at the single-
multiplexer. Since after interleaving the originally
consecutive packets will be packets apart from each
other, is formed by selecting every th element of .
Therefore,is also a discrete-time Markov chain with
the state space , and the corresponding transition-
probability matrix , is the –step transition matrix of ,
(19) Let be the stationary distribution of , which can
be obtained as the solution to (20) subject to a
normalization constraint. Then, proceeding with the
same procedure as in Section III-A1, we can obtain
recursive expressions for computing . If an ideal
interleaver is applied, then the packet-loss process is
independent. Suppose the average packet-loss rate is ,
then the packet-loss statistics with ideal interleaving
are given by the binomial distribution (21) Once we
obtain the block-error distribution incorporating the
interleaving operation, the effective packet-loss rate
after FEC decoding can be obtained from (8). In
Appendix A, we determine the autocorrelation
function for packet-loss processes associated with the
single-multiplexer model (modeled as a queue) with
interleaving. Next we show some numerical
examples.
3) Numerical Examples: Fig. 14 illustrates the
efficacy of interleaving in reducing packet-loss
correlation associated with the single-multiplexer
model. In particular, we illustrate the packet-loss
autocorrelation function as a functionof lag for the
case in which the arrivals are Poisson with the
average loadand the buffer size is . It shows, as
expected,that interleaving can effectively reduce the
correlation of the packet-lo ss process, which means
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that interleaving can make the packet losses more
independent and isolated.
POTENTIAL OF FEC AND AN INFORMATION-
THEORETIC BOUND
In Fig. 17, we demonstrated that, with the same
packet-loss rate requirement, FEC coding with a
larger block size can support increased source traffic.
However, the source traffic that can be supported is
not unlimited because of the channel capacity
limitation imposed by the single-multiplexer
transport channel model. In what follows we develop
an information-theoretic upper bound on the FEC
performance based on the single-multiplexer network
model. In this section, we only consider the case of a
single source , although the approach can be extended
to arbitrary .
A. Channel Model for Packet Transmission Over
Networks
Consider a channel model for packet transmission
over a general packet-switched network. Assume a
packet has bits. It is either transmitted and received
by the receiver, or is lost due to network congestion
or buffer overflow. For a received packet, bit errors
may be introduced. Then packet transmission over
networks can be modeled for coding purpose in terms
of serial bit-by-bit transmission of -bit symbols either
over a binary symmetrical channel (BSC) with
crossover probability Fig. 23. Component channels of BIC
corresponding to packet delivery and loss. Fig. 24. Simplified
communication system model. (state 0) or over a binary
erasure channel (BEC) (state 1), both of which are
illustrated in Fig. 23, where is used to indicate the
erasure symbol.A lost packet corresponds to the
entire codeword symbol of bits being erased, while a
received packet means each of the bits is sequentially
transmitted over the BSC. This channel model
belongs to the class of block interference channels
(BIC), introduced by McEliece and Stark [14]. Let
represent the state space of the BIC. If the state
transitions are independent, then the Shannon
capacity of the BIC is given as [14], (26) where is the
capacity of the component channel , and the
expectation is over the state space . It follows
that(27) where is the probability of being in the loss
state and isthe binary entropy function, (28)
B. Information-Theoretic Bound on FEC
Performance
Referring to Fig. 12, suppose the interleaving is ideal,
and consequently the packet-loss process seen by the
channel decoder is independent. If we consider the
interleaver and the deinterleaver as components of
the coding channel, then the channel, consisting of
the interleaver, the single-multiplexer and the
deinterleaver, can be modeled as a BICwith
independent state transitions, as ill ustrated in Fig. 24.
Here we consider only the packet losses caused by
the buffer overflows, and assume no bit errors, i.e.,
the BSC crossover probability . Let be the packetloss
rate of thesingle-multiplexer, so . Then, from (27),
the capacity of the BIC is given by (29) Assume the
source creates packets at rate and the packetservice
rate is . Then the normalized system load before
coding is . The channel encoder applies channel
coding (notnecessarily RS codes) with coding rate to
thesource traffic.
CONCLUSIONS AND FUTURE WORK
We have analyzed the efficacy of FEC in combating
network packet losses based on a single-multiplexer
network model and demonstrated that FEC has great
potential in recovering the packet losses caused by
congestion at a bottleneck node of a packet-switched
network, provided that the coding rate and other
coding parameters are appropriately chosen. We
developed a discrete-time Markov chain model to
analyze the efficacy of interleaving in improving the
FEC performance and determined how much
interleaving depth is required for FEC to approach
the optimum performance. We derived an upper
bound on the end-to-end performance using FEC
based
on an information-theoretic methodology, which is
useful in predicting source rates that can be supported
with arbitrarily high reliability. Despite the great
potential of FEC coding in recovering network packet
losses, the implementation complexity of FEC coding
and the corresponding coding/decoding delay also
need
to be considered, which is an issue particularly
important for real-time applications. One objective
for future work is the analysis of the additional delay
caused by the FEC coding, perhaps combined with
interleaving/deinterleaving. Likewise, the application
of FEC for network transport is limited by the time-
varying and often uncertain error characteristics of
the channel, which makes the appropriate choice of
FEC coding rate difficult to determine. In real world
applications, FEC cod ers are required which can
adapt the channel code rate to the time-varying
channel conditions. This issue is also a topic for
future work.
REFERENCES
[1] O. J. Boxma, ―Sojourn times in cyclic queues—
The influence of the slowest server,‖ in Proc. 2nd Int.
MCPR Workshop on Computer Performanceand
Reliability, Rome, Italy, May 1988. YU et al.: A
MODEL-BASED APPROACH TO EVALUATION
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OF THE EFFICACY OF FEC CODING IN
COMBATING NETWORK PACKET LOSSES 641
[2] D. Y. Eun and N. B. Shroff, ―Network
decomposition: Theory and practice,‖ IEEE/ACM
Trans. Networking, vol. 13, no. 3, pp. 526–539, Jun.
2005.
[3] J. Bolot, ―End-to-end delay and loss behavior in
the Internet,‖ in Proc. ACM SIGCOMM 1993, San
Francisco, CA, Sep. 1993, pp. 289–298.
[4] N. Shacham and P. Mckenney, ―Packet recovery
in high-speed networks using coding and buffer
management,‖ in Proc. IEEE INFOCOM 1990, San
Francisco, CA, Jun. 1990, vol. 1, pp. 124–131.
[5] I. Cidon, A. Khamisy, and M. Sidi, ―Analysis of
packet loss processes in high-speed networks,‖ IEEE
Trans. Inf. Theory, vol. 39, no. 1, pp.
98–108, Jan. 1993.
[6] R. Kurceren, ―Joint source-channel coding
approach to transport of digital video on lossy
networks,‖ Ph.D. dissertation, Rensselaer Polytechnic
Inst., Troy, NY, May 2001.
[7] R. Kurceren and J. W. Modestino, ―Optimum
FEC coding rate allocation for video transport over
ATM networks,‖ in Proc. IEEE Int. Symp.
Information Theory (ISIT 1998), Cambridge, MA,
Aug. 1998, p. 251.
[8] R. Kurceren and J. W. Modestino, ―A joint
source-channel coding approach to scalable delivery
of digital video over ATM networks,‖ in Proc. Int.
Conf. Image Processing (ICIP 2000), Vancouver,
Canada, Sep. 2000, vol. 1, pp. 371–374.
[9] E. Altman and A. Jean-Marie, ―Loss probabilities
for messages with redundant packets feeding a finite
buffer,‖ IEEE J. Sel. Areas Commun., vol. 5, no. 6,
pp. 778–787, Jun. 1998.
[10] O. Ait-Hellal, E. Altman, A. Jean-Marie, and I.
A. Kurkova, ―On loss probabilities in presence of
redundant packets and several traffic
sources,‖ Perform. Eval., vol. 36–37, pp. 485–518,
1999.
[11] P. Dube, O. Ait-Hellal, and E. Altman, ―On loss
probabilities in presence of redundant packets with
random drop,‖ Perform. Eval., vol. 53,
pp. 147–167, 2003.
12] A. Jean-Marie, P. Dube, D. Artiges, and E.
Altman, ―Decreasing lossprobabilities by redundancy
and interleaving: A queueing analysis,‖ in Proc. ITC
18, Berlin, Germany, Sep. 2003.
[13] Y. Shen, P. C. Cosman, and L. B. Milstein,
―Error resilient video communications over
CDMAnetworks with a bandwidth constraint,‖ IEEE
Trans. Image Process., vol. 15, no. 11, pp. 3241–
3252, Nov. 2006.
[14] R. McEliece and W. Stark, ―Channels with
block interference,‖ IEEETrans. Inf. Theory, vol. 30,
pp. 44–53, Jan. 1984.
[15] V. Parthasarathy, J. W. Modestino, and K. S.
Vasto la, ―Reliable transmissions of high-quality
video over ATM networks,‖ IEEE Trans. Image
Process., vol. 8, no. 3, pp. 361–374, Mar. 1999.
[16] D. Gross and C. M. Harris, Fundamentals of
Queueing Theory, 3
rd
ed. New York: Wiley, 1998.
[17] M. Mushkin and I. Bar-David, ―Capacity and
coding for the Gilbert-Elliott channels,‖ IEEE Trans.
Inf. Theory, vol. 35, no. 6, pp. 1277–1290, Nov.
1989.
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