IEEE
Signal Processing Society 1997 Workshop on Multimedia Signal Processing
June 23 --- 25, 1997, Princeton, New Jersey, USA
Electronic Proceedings
This paper proposes an adaptive source-channel subband coding scheme for the transmission of video over fading wireless channels. A three-dimensional subband decomposition followed by vector quantization of the subband coefficients forms the source coding strategy. For transmission over the channel, the individual subbands are offered different amounts of protection depending on their importance in reconstruction at the receiver. For each subband, the source coding rate as well as the level of protection (quantified by the channel coding rate) are jointly chosen to minimize the total mean-squared distortion suffered by the video coder. The choice of source and channel coding rates depends on the state of the physical channel. We use a finite state model for the fading channel, where every state corresponds to an AWGN channel. This results in a joint source-channel coding scheme that adapts in an optimal way to the current state of a fading channel.
One of the biggest challenges in multimedia communications is reliable videoconferencing over wireless channels. Wireless channels exhibit fading effects caused by the multipath phenomenon. A video compression scheme designed for these channels must degrade gracefully in performance when channel fading occurs. This requirement favours a coding method that adapts itself to the channel condition. In this paper, we consider a three-dimensional subband coding scheme, motivated by its inherent multiresolution character which lends itself to unequal error protection.
Shannon's separation principle establishes the optimality of separate design of source and channel coders, and states that total distortion is essentially limited to the source coding distortion as long as the rate of the source coder is less than channel capacity. This however, is an asymptotic result, and real-world systems benefit through joint design of the source and channel coders, given knowledge of the channel. The aim of a joint source-channel coding approach is to optimally allocate bits between the source and channel coders to minimize total distortion, while satisfying a constraint on the total rate.
Several approaches for joint source-channel coding have been proposed in the literature. Modestino et al. illustrate the advantages of source-channel coding using the DCT in [1]. Burlina, Alajaji and Chellappa [2] use a joint source-channel decoding approach in the form of MAP decoding for exploiting residual redundancy in images transmitted over channels with memory. Ruf and Modestino [3] use bit-sensitivity analysis to compute operational rate-distortion curves and also provide information-theoretic bounds on performance. Cheung and Zakhor [4] consider the problem in the context of three-dimensional subband coding using multi-rate quantization also using a bit-sensitivity approach. We approach this problem along the lines of [5] in which Srinivasan and Chellappa have developed a joint-source channel subband coding strategy based on unequal error protection (UEP) for the subbands.
The data in the subbands is corrupted during transmission over the channel. UEP can be accomplished easily in this context by protecting the subbands differently depending on their importance in reconstruction at the receiver. This is done by allocating different channel coding rates to the different subbands. The problem of joint selection of the source and channel coding rates for the different subbands to minimize the overall distortion now constitutes the joint source-channel coding approach.
Figure 1 : Joint Source-Channel Coding System
The joint source-channel scheme is outlined in Figure 1. The source coder is based on a three-dimensional subband coding scheme outlined in [6] and illustrated in Figure 2. In [6], the authors use a combination of unbalanced tree-structured vector quantizers and geometric VQ to code the subband coefficients. We however use full-search vector quantizers for all the subbands except for subband zero which uses scalar quantizers for reasons of complexity. This approach enables a uniform approach for computation of distortion in all the subbands. The spatio-temporal subband decomposition used here localizes channel induced distortions, and makes it possible to analyze and compute them which is not the case with motion compensated coding schemes.
Figure 2 : Spatio-Temporal Subband Decomposition
Performing a simple subband decomposition in the temporal domain ensures
that VQ can efficiently exploit the remaining redundancy. Temporal filtering
is carried out using the Haar basis functions, which results in 
and 
being the sum and difference of neighbouring frames respectively. Separable
subband filters are used to decompose
and
in the spatial dimensions, producing the decomposition of Figure 2.
The quantizer indices are protected for transmission over the channel,
by using different channel codes for different subbands. Channel coding
is carried out using Rate Compatible Punctured Convolutional (RCPC) codes
[7]. These codes make it practical to
achieve a wide range of channel coding rates using a single encoder and
viterbi decoder by simply pucturing the coded bitstream according to the
level of protection desired.
The receiver, based on signal to noise ratio (SNR) measurements, relays the channel state information (CSI) back to the adaptation unit of the encoder. This unit then chooses the optimal joint source-channel coding strategy for this channel state.
Consider a source that is decomposed into M subbands. The problem
is to choose 
= { 
} (the set of source coding rates) and 
= { 
} (the set of channel coding rates) in order to minimize the overall distortion
in the source, subject to an overall rate constraint. The formulation of
this problem and a solution methodology are outlined in [5].
Under the assumptions detailed there,
where 
is the source rate-distortion curve for subband i, and
represents a channel rate-distortion curve reflecting channel distortion
in subband i as a function of the channel coding rate (which also
depends on the VQ codebook and hence on 
). The objective is to choose 
such that
where 
is the fraction of pixels in subband i.
The operational source rate-distortion curve for subband i,
,is computed during optimization of the source quantizers using training
data. The distortion in the 
subband due to the channel is
where 
is the cardinality of the codebook and d(u,v) is the
per sample distortion between the source samples corresponding to code
vectors with indices u and v. The probability p(u)
may be computed from the source statistics. The transition probability
p(v/u) is a function of the channel state, the channel
coding rate 
and the convolutional code itself. In practice, we derive estimates for
channel-induced distortion using simulation.
Using
and
, we derive an (operational) rate-distortion curve for the
subband that takes both source and channel distortions into consideration.
We denote this curve by 
. This curve determines the best allocation for source and channel coding
rates for the
subband, under the constraint that the total rate for the
subband is 
.
In order to optimally allocate the source and channel coding rates for
the subbands, we consider the ensemble of composite source/channel (operational)
rate-distortion curves of all the subbands, and choose an operating point
that results in minimum 
. This is a conventional rate allocation problem, performed however on
the composite rate-distortion curves. This optimal solution has to be derived
from the operational rate-distortion curves, which may not necessarily
be convex or even monotone decreasing. The algorithm presented in [8]
may be used under these conditions. The optimal solution naturally depends
on the state of the physical channel. The CSI is estimated by the receiver
and is relayed to the transmitter. The transmitter only has to choose the
appropriate allocation (which is pre-computed for every channel state)
based on the CSI.
In this section, we demonstrate the advantages of an adaptive source-channel
coding approach. The range of channel SNRs considered is 1 dB through 8
dB. The channel-induced distortion is negligible for higher channel SNRs.
The lowest subband is quantized using Lloyd-Max quantizers and the other
subbands are vector-quantized with full-search VQs trained using the LBG
algorithm [9]. A class of RCPC codes described
in [7] with a basic coding rate of 
is used. Higher coding rates are obtained by puncturing the coded bitstream.
We use a set of three codes with rates {0.33 0.571 0.80}. The modulation
scheme used is uncoded BPSK and soft-decision decoding is assumed. The
receiver consists of a Viterbi decoder with knowledge of the puncturing
mode, followed by a source decoder.
Table 1
Table 1 lists the source and channel coding rates allocated using our scheme for three different states of the channel. It may be observed that the more important subbands are protected using channel codes with lower rate (i.e, those that offer more protection). Also, as the channel SNR decreases, the algorithm offers more protection for the more important subbands at the cost of the higher frequency subbands.
Figure 3 : Performance of the Adaptive Source-Channel Subband Coding Scheme
Figure 3 plots received image quality as a
function of the channel state. The received image PSNR is averaged over
10 frames of the video sequence. The adaptive scheme is compared with two
fixed schemes, one optimized for a poor channel (1dB channel SNR) and the
other optimized for higher channel SNR (8dB). In all three schemes, the
coding rate is 1.0 bpp (source and channel coding combined). A scheme optimized
for poor channels has a large proportion of the rate allocated to channel
coding, and hence has too little rate for source coding when the channel
SNR improves. A scheme optimized for channels with high SNR on the other
hand performs poorly in low SNR channels since the channel coding rate
is insufficient to protect against channel errors. Since the SNR in a wireless
channel can vary over a large range, an adaptive scheme has a natural advantage.
This paper demonstrates the advantage of an adaptive source-channel coding approach for robust video transmission over noisy channels. The scheme outlined delivers reasonable quality video over channels with very low SNR, using just 1.0 bits per pixel for source as well as channel coding.
