ISIT 2004, Chicago, USA, June 27 – July 2, 2004
Adaptive Joint Source/Channel Rate Allocation Policies
for Delay Sensitive Applications over Fading Channels
C. Thejaswi, Vinod Sharma
1
90
22
80
20
70
18
Avg. Queue length→
Abstract —
We consider a problem of optimal
source-channel coding rate pair allocation over a wireless link based on the channel state and the queue
length at the transmitter. We show that by this
scheme, one can gain substantially in performance as
compared to only source or channel rate optimization.
Avg. Queue length→
Department of Electrical Communication Engg.
Indian Institute of Science, Bangalore, INDIA.
e-mail: ct@pal.ece.iisc.ernet.in, vinod@ece.iisc.ernet.in
60
PolicyŦA
50
40
30
16
14
12
10
PolicyŦB
8
20
I. Introduction
JSCŦpolicy
We consider a slotted system with a single user communicating over a fading wireless channel. The data to be transmitted which arrives from a higher layer, is subjected to a
variable rate compression depending on queue length, power
and distortion requirements and is placed in a transmission
buffer of infinite capacity. We assume that the channel and
buffer state information is available both at the transmitter
and the receiver. There are N channel uses in a slot. The
channel fading gain remains constant during a slot. The fading
process {Gn } is assumed to be a stationary, ergodic Markov
process with a compact state space G and the average number of jumps required to move from one state to any other
state is finite. We also assume that the fading process is positively correlated and hence stochastically nondecreasing. The
symbols are transmitted over the fading channel with an additive white Gaussian noise (AWGN). The transmitter, with
the knowledge of the buffer and channel states, obtains optimum source and channel coding rates and transmission power.
These actions minimize the mean queue length subject to long
run average transmit power and distortion constraints.
Let Sn be the amount of data in the buffer at the beginning of the nth slot where Sn ∈ {0, 1, 2, .....}. The state of the
system in the nth slot is Xn := (Sn , Gn ). At time n the transmitter places An bits in the buffer and removes Un bits for
transmission. The buffer state evolves as Sn+1 = Sn −Un +An
where, Un ∈ {0, 1, ..., Sn }, An ∈ A := {0, 1, 2, ..., Ā}, Ā < ∞.
For the nth slot, the transmitter incurs a cost of distortion
D(An /J) to encode J source symbols into An bits and power
P (Un , Gn ) for transmission of Un bits when the fading gain is
Gn . D(.) is the distortion-rate function. The objective is to
minimize the mean delay with constraints on the mean distortion and power. Since the delay process is more complicated,
instead we try to minimize the mean workload process.
The above problem can be considered as a constrained
Markov Decision Problem which can be converted into an
unconstrained one via the Lagrangean approach. The corresponding Lagrangean functional is
J π (x) = lim sup
M
M −1
π
1
Ex
M
Sn + βP (Un , Gn ) + θD(An /J) ,
n=0
1 This
work was partially supported by the DRDO-IISc program
on advanced research in Mathematical Engineering.
‹,(((
10
6
0
4
8
8.5
9
9.5
10
10.5
11
11.5
12
JSCŦpolicy
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
Avg.SNR (in dB)→
Avg. SNR (in dB)→
Figure 1:
Comparison of avg.queue length of JSC with policy A
and B respectively for different avg.SNR and same avg. distortion.
where x is the initial state, π is the given policy and β and θ
are Lagrange multipliers. The aim is to find π that minimizes
J π (x). We have shown that this problem has an optimal solution which is also optimal for the constrained problem. The
optimal policy is independent of x and can be obtained as the
limit of optimal solutions corresponding to α−discount problems as α → 1. Furthermore, for the optimal solution (u, a),
u(s) − a(s) is nondecreasing in s.
Recently we have extended this work to MIMO and multiuser uplink channels which will be reported elsewhere.
II. Results
In this section, we obtain the optimal average cost solution
for an example and compare the performance of the optimal
policy (JSC) with the following two suboptimal policies.
Policy A. Source Coder (SC) has only the buffer state information and the Channel Coder (CC) has only channel state
information. This provides the well known water-filling power
control.
Policy B. SC with no state information and CC with complete state information. The SC computes the minimum
source coding rate which satisfies the distortion constraint.
The optimal CC policy for this case is studied in [1] and [2].
The source is iid N (0, 1), the fading process is Jake’s
Rayleigh process (with 8 multipath components and Doppler
BW of 5Hz) discretized into an 8-state Markov chain and the
AWGN is N (0, 1). Figure 1 gives the comparison of JSC with
policy A and with policy B. Policy B performs much better
than policy A. However JSC provides significant improvement
over policy B also (at 8.5 dB 40% and at 10dB 29%).
References
[1] R. A. Berry, R. G. Gallager, ”Communication over Fading
Channels with Delay Constraints”, IEEE Transactions on
Inf.Theory, Vol 48, no. 5, 1135-1149, 2002.
[2] M. Goyal, A. Kumar and V. Sharma, ”Power Constrained and
Delay Optimal Policies for Scheduling Transmission over a Fading Channel,” IEEE INFOCOM 2003, San Francisco, USA.