Trellis based quantization using the MAP-criterion and its application to multiple correlated sources
Stephan Hellerbrand (Utbytesstudent)
Many of the information sources of interest are of a continuous nature, e.g. speech, images and video. They can be represented without loss at discrete time according to the sampling theorem. The amplitude values can assume infinitely many values and therefore would require an infinite number of bits to be represented without loss. The method to encode a sequence of continuous amplitude samples with a finite number of bits is called quantization.
A very efficient method for quantization is based on trellises. In this type of quantization, the reproducer values of a scalar quantizer are used as the labels of transitions in a trellis. The bits that belong to the branch sequence leading to the minimum distortion path through the trellis are stored / transmitted.
Many trellis quantization schemes employ the Viterbi-algorithm for finding the minimum distortion path through the trellis. There is one main drawback that comes with using the Viterbi-algorithm for trellis source coding. Since the best initial state is unknown in the encoder and the decoder a high distortion per sample is caused during the beginning of the trellis by choosing a fixed state as initial state. This problem becomes crucial for short block lengths where the impact on overall distortion is higher.
A new trellis based quantization scheme which finds a path using the tailbiting BCJR-algorithm was proposed by Anderson and Eriksson in 2003.
According to the tailbiting-property, the beginning and ending state of this path are the same and therefore the unique path can be reconstructed in the decoder if the bit sequence and the trellis are known. This method has shown to result in improved performance over the Viterbi-algorithm. However, a problem of this method is that in some cases the path that was determined by the BCJR algorithm does not tailbite.
One working item in this thesis is to determine the reasons for this problem and to find and evaluate possible solutions. One suboptimum solution that has been found so far is to modify the paths only at the trellis start and the trellis end to achieve tailbiting while minimizing the distortion caused by this constraint.
Another potential task is to modify this variant of trellis quantization for encoding multiple correlated sources. According to Rate-Distortion theory, a system that uses the correlation between concurrent source-samples achieves higher performance than a system that separately encodes the given sources.
In addition, the maximum performance that can be achieved is known and can be used to evaluate the modified trellis quantization scheme.
Advisor: John B Anderson (EIT)