Recently, several methods that divide the original bitstream of an image/video progressive wavelet based source coders into multiple correlated substreams have been proposed. The principle behind transmitting independent multiple substream is to generate multiple descriptions of the source such that the graceful degradation is
achieved when transmitted over severe fading channels and lossy packet networks since some of the streams may be recovered. Noting that multiple substream can benefit from multiple independent channel paths, we naturally consider Multi-Input Multi-Output communication systems where we obtain multiple independent fading channels. Depending on several factors including: the number of antennas employed, the transmission energy, the Doppler shift (due to the motion between the transmitter antenna and receiver antennas), the
total transmission rate and the distortion-rate (D-R) of the source-there exists an optimal number of balanced substreams and an optimal joint source-channel coding policy such that the expected distortion at the receiver is minimized. In this paper we derive an expected distortion function at the receiver based on all of these parameters and provide a fast real-time numerical technique to find the optimal or near optimal number of balanced substreams to be transmitted. This expected distortion is based on our derivation of the probabilistic loss patterns of a balanced multiple substream progressive source coder. The accuracy of the derived expected distortion estimator is confirmed by Monte-Carlo simulation employing Dent's modification of Jakes' model. By accurately estimating the optimal number of balanced substreams to be transmitted, a substantial gain in visual quality at low and intermediate signal-to-noise ratio (SNR) is obtained over severely fading channels. At high SNR, the single stream source coder's source efficiency makes it slightly better than the multiple substream source coder. Overall, using our analytic development, we provide a systematic real-time non-adhoc method that achieves high quality image and video at low and moderate signal-to-noise ratios in severe fading channels for single and multiple antenna systems.
In this paper we consider the problem of robust image coding and packetization for the purpose of communications over slow fading frequency selective channels and channels with a shaped spectrum like those of digital subscribe lines (DSL). Towards this end, a novel and analytically based joint source channel coding (JSCC) algorithm to assign unequal error protection is presented. Under a block budget constraint, the image bitstream is de-multiplexed into two classes with different error responses. The algorithm assigns unequal error protection (UEP) in a way to minimize the expected mean square error (MSE) at the receiver while minimizing the probability of catastrophic failure. In order to minimize the expected mean square error at the receiver, the algorithm assigns unequal protection to the value bit class (VBC) stream. In order to minimizes the probability of catastrophic error which is a characteristic of progressive image coders, the algorithm assigns more protection to the location bit class (LBC) stream than the VBC stream. Besides having the advantage of being analytical and also numerically solvable, the algorithm is based on a new formula developed to estimate the distortion rate (D-R) curve for the VBC portion of SPIHT. The major advantage of our technique is that the worst case instantaneous minimum peak signal to noise ratio (PSNR) does not differ greatly from the averge MSE while this is not the case for the
optimal single stream (UEP) system. Although both average PSNR of our method and the optimal single stream UEP are about the same, our scheme does not suffer erratic behavior because we have made the probability of catastrophic error arbitarily small. The coded image is sent via orthogonal frequency division multiplexing (OFDM) which is a known and increasing popular modulation scheme to combat ISI (Inter Symbol Interference) and impulsive noise. Using dual adaptive
energy OFDM, we use the minimum energy necessary to send each bit stream at a particular probability of bit error. An added benefit of OFDM over serial transmission schemes is that some degree of progressiveness of SPIHT is preserved by transmitting both the VBC and LBC streams in parallel.