Optimization of Coding of AR Sources for Transmission Across Channels with Loss

Source coding concerns the representation of information in a source signal using as few bits as possible. In the case of lossy source coding, it is the encoding of a source signal using the fewest possible bits at a given distortion or, at the lowest possible distortion given a specified bit rate. Channel coding is usually applied in combination with source coding to ensure reliable transmission of the (source coded) information at the maximal rate across a channel given the properties of this channel.
In this thesis, we consider the coding of auto-regressive (AR) sources which are sources that can be modeled as auto-regressive processes. The
coding of AR sources lends itself to linear predictive coding. We address the problem of joint source/channel coding in the setting of linear predictive coding of AR sources. We consider channels in which individual source coded signal samples can be lost during channel transmission. The optimization of linear predictive coding for such lossy channel behaviour is not well understood in the literature.
We review basics of source and channel coding, differential pulse code modulation (DPCM), state-space models, minimum mean squared error (MMSE) estimation, and quantization. On this background we propose a new algorithm for optimization of predictive coding of AR sources for transmission across channels with loss.
The optimization algorithm takes as its starting point a re-thinking of the source coding operation as an operation producing linear measurements of the source signal. The source process and source encoder are formulated as a state-space model, enabling the use of Kalman filtering for decoding the source signal.
The optimization algorithm is a greedy approach that designs the filter coefficients of a generalized DPCM encoder. The objective of the optimization problem (design of the filter coefficients) is to minimize the decoder state error covariance. This is done iteratively in a greedy sense, minimizing the trace of the state error covariance at each iteration until convergence.
Furthermore, it is proved that employing fixed-lag smoothing at the decoder is guaranteed to reduce the estimated source signal mean squared error (MSE) under mild constraints on the encoder filter coefficients.
Extensive Monte Carlo simulation studies show that the proposed algorithm improves the signal-to-noise ratio (SNR) of decoded source signals substantially compared to the case where the encoder is unaware of channel loss.
We finally provide an extensive overview of cross-layer communication issues which are important to consider due to the fact that the proposed algorithm interacts with the source coding and exploits channel-related information typically available from different layers of network protocol stacks.