Source-Channel Mappings with Applications to Compressed Sensing

Abstract

Tandem source-channel coding is proven to be optimal by Shannon given unlimited delay and complexity in the coders. Under low delay and low complexity constraints, joint source-channel coding may achieve better performance. Although digital joint source-channel coding has shown a noticeable gain in terms of reconstructed signal quality, coding delay, and complexity, it suffers from the leveling-off effect. However, analog systems do not suffer from the leveling-off effect. In this thesis, we investigate the advantage of analog systems based on the Shannon-Kotel’nikov approach and hybrid digital-analog coding systems, which combine digital and analog schemes to achieve a graceful degradation/improvement over a wide range of channel conditions. First, we propose a low delay and low complexity hybrid digital-analog coding that is able to achieve high (integer) expansion ratios ( >3). This is achieved by combining the spiral mapping with multiple stage quantizers. The system is simulated for a 1 : 3 bandwidth expansion and the behavior for a 1 : M (with M an integer >3) system is studied in the low noise level regime. Next, we propose an analog joint source-channel coding system that is able to achieve a low (fractional) expansion ratio between 1 and 2. More precisely, this is an N : M bandwidth expansion system based on combining uncoded transmission and a 1 : 2 bandwidth expansion system (with N < M < 2N).Finally, a 1 : 2 analog bandwidth expansion system using the (Shannon-Kotel’nikov) Archimedes’ spiral mapping is used in the compressed sensing context, which is inherently analog, to increase the system’s immunity against channel noise. The proposed system is compared to a conventional compressed sensing system that assumes noiseless transmission and a compressed sensing based system that account for noise during signal reconstruction.