Strategies for Changing the Redundancy of Sub-band Signals in Oversampled Filter Banks

Communication channels are always vulnerable to noise sources. Thereby, any kind of data transmitted over these channels suffer from errors that happen during transmission which degrades the quality of the signal on the receiver side. To tackle this problem, some amount of redundancy should be added to the input signal so on the receiver side, this redundancy could be exploited to remove the errors. However, most of the existing schemes for adding redundancy to the signal have two main drawbacks. First, they are designed to work decently as long as the channel quality is always above a certain threshold. But when the channel quality falls under that threshold, the system tends to break down completely and is no longer capable of correcting the errors (threshold effect). Second, most of the current error correction schemes lack the inherent adaptability and flexibility for changing the added redundancy which is necessary due to the unavoidable change in channel characteristics. In this thesis, we will explore the methods of signal representation that are naturally amenable to transmission at flexible rates and offer graceful degradation in signal quality with degrading link quality. For such applications, we will consider the insertion of soft, structured redundancy in signals to be transmitted, through the use of Oversampled Filter Banks (OFBs). These codes enable a joint compression and protection of signals through the application of a redundant transform (or frame operator) to the signal, which serves both for signal conditioning for compression and for insertion of redundancy in the signal so as to be able to combat adverse channel effects. More specifically, in this thesis, we extend the framework of redundant expansions to the case where the amount of injected redundancy can be adjusted on the fly. This will be accomplished through two main approaches.;The first method is called Adaptive Downsampling. Here, the idea is to change the downsampling rate of the OFB as a response to the changes in channel quality. We investigate the effect of such downsampling variation on filtering the input signal vectors on analysis side and propose suitable signal reconstruction method on the synthesis side of the OFB. In the second method, we introduce the notion of Instantaneous Erasures in OFBs which accounts for a situation when samples of sub-band vectors are erased arbitrarily in different time instances. We find the conditions under which the OFB maintains its perfect reconstruction property using time-domain analysis and we propose structures in order to be able to design implementable OFBs.