Error-correcting codes are a critical part of almost all digital communications and data storage systems, including cell phones, the Internet, space missions, and compact disks. Error control coding, also known as channel coding, protects data against transmission errors to ensure adequate transmission quality. The emergence of graph-based codes (such as turbo codes and low-density parity-check (LDPC) codes) with iterative decoding techniques has revolutionized channel coding. It is now clear that LDPC codes will be an essential part of future communication systems. Despite their astonishingly good performance, LDPC codes suffer from important problems. This research provides improvements in understanding and practical implementation of LDPC codes using new approaches introduced by the PI.
The areas of research considered are 1. Parametric Iterative Decoding: A novel decoding method for LDPC codes, called parametric iterative decoding, is investigated. The new decoding method provides better trade-offs among reliability, bandwidth usage, and cost than the standard iterative decoding. 2. Capacity-Achieving LDPC Codes: This research studies a new approach to the analytical design of capacity-achieving LDPC codes based on zero-rate codes and puncturing. Extensions of the ideas to construct universal rate-adaptive LDPC codes are also investigated. 3. Error Floor of LDPC Codes: This project develops a rigorous framework to answer the following questions: Given an accepted level of the error floor, what is the best performance we can obtain? How can we achieve this performance?
