Abstract

Random-like codes with iterative decoding, also referred to as turbo-like codes, have been shown to provide near optimal performance for error control over noisy channels. Low-density parity check (LDPC) codes and parallel concatenated convolutional (turbo) codes are by far the two most well-known turbo-like coding schemes. This dissertation is dedicated to a new code family, Low Density Generator Matrix codes (LDGM codes), investigating its applications in source, channel, and joint-source-channel coding of single and multiple users.

The first problem that naturally arises is the use of LDGM codes for error control coding of single users. This dissertation shows that it is possible to design LDGM codes with performance comparable to that of state-of-the-art LDPC and turbo codes with lower computational complexity. A typical engineering approach is followed in this study: first a practical solution is proposed, and then it is analyzed and optimized. Specifically, the density evolution technique is adopted for the analysis and optimization of two types of designs in order to drive the performance.

This work then focuses on the use of LDGM codes for distributed coding of multiple correlated users, considering the cases of source and joint source-channel coding. This problem is far from resolved, and plays a critical role in many important applications, such as sensor networks and emerging techniques in video compression. In the case of pure source coding (data compression), hidden Markov models (HMM's) are utilized to define the correlation between sources, which provides a good approximation for the real-world data. The HMM has to be exploited at the decoder site in order to optimize performance. When channel noise is present, two types of scenarios are considered: separated channels between each source and the common receiver and multi-access schemes. In the former case, where separation between source and channel coding is optimum, the resulting performance is close to that limit. For the case of multiple-access channels, separation between source and channel coding does not lead to the optimum performance, since the correlation between the users should not be destroyed in the coding procedure. However, no practical schemes have been able to outperform this bound until now; the proposed scheme is shown to provide reliable communications even with signal-to-noise-ratios below the separation limit. The use of LDGM in this context is critical, since thanks to them the codewords of the different users keep a high degree of correlation. (Abstract shortened by UMI.)