On Soft Decoding and Robust Vector Quantization

Doctoral thesis, 1997

This thesis considers vector quantization for noisy channels. Vector quantization (VQ) is an important technique for block-based source coding, with applications in, e.g., speech and image coding. Commercial systems already employ VQ as a basic tool, and it is expected that VQ will play an increasingly important role in future systems. Throughout, we emphasize the use of combined source-channel coding with the motivation that, under a practical delay constraint, separate source and channel coding is not optimal since perfect error correction requires infinite delay. Consequently, the VQ should be made robust for noisy transmission, using robust VQ (RVQ) and index assignment (IA) design, or the source-channel codes should be combined into one overall code, using the approach of channel optimized VQ (COVQ). In the thesis we investigate general models for noisy channel VQ transmission using RVQ, IA and COVQ. The work is divided into four parts. The first three consider soft decoding in VQ transmission. In soft decoding all received analog information is utilized and no decisions are taken. In part one we report work on the basics of soft decoding, treating VQ over memoryless Gaussian and Rayleigh fading channels, and general channels with memory. The emphasis is on decoding based on a Hadamard transform representation of the VQ. New techniques for RVQ and COVQ design are presented, and theoretical analysis of the distortion introduced by the channel is provided. The performance is compared with traditional decision-based decoding. Part two of the thesis treats the application of soft decoding to image coding and LPC-based speech coding. This part provides subjective performance results, and it is illustrated that much can be gained by relatively small modifications in existing systems. Part three investigates soft decoding for VQ in multiuser communications, using code-division multiple access (CDMA). Here, methods for combined multiuser and source-channel decoding are investigated. The main conclusion of the work on optimal soft decoding is that there is a significant performance gain compared to traditional decision-based decoding. The price, however, is increased complexity. For some channels, e.g., memoryless Gaussian channels, the complexity increase is acceptable, whereas in other cases, e.g., for channels with memory and CDMA channels, the complexity is substantial. In parts of the work we have therefore addressed the complexity issue and presented sub-optimal decoders of lower complexity. Part four of the thesis, concerns theory for VQ transmission over discrete channels. Here, we present analytical results in VQ transmission. An important tool in this work is the Hadamard transform. The obtained results can be applied to analysis and synthesis of robust VQ systems. Part four also contains a thorough general treatment of VQ transmission for noisy channels and Hadamard-based methods. A main conclusion is that many of the existing techniques for noisy channel VQ can now be theoretically motivated and analyzed