Low Density Parity Check Coding: Applications and New Challenges

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

The rapid development of a myriad of networked devices for computing and telecommunications presents challenging and exciting new issues for coding. Communication system designers always have to deal with trade-offs among reliability, efficient use of available bandwidth, data throughput and cost. Error-correction coding is one of the most powerful tools available to address these trade-offs. A small improvement in error-correction can yield large savings in the overall cost of systems. Low-Density Parity-Check (LDPC) codes promise to be the ultimate answer to the questions of coding specialists. Although a great amount of research has gone into LDPC codes, the investigators believe that the potency of LDPC codes in resolving many practically relevant coding issues such as rate-compatible coding, improved decoding and coding for error detection has yet to be discovered. Today, theoretical limits on rates at which reliable transmission or storage of data is possible are known for many telecommunications challenges. Today's and tomorrow's challenges are to employ LDPC codes in networked, distributed computing and communications applications. This work first investigates finite and infinite length punctured LDPC codes over MBIOS channels. Bounds on the performance degradation of punctured LDPC ensembles as a function of puncturing fraction are derived. Using which, the investigators plan to arrive at criteria for good puncturing patterns and degree distributions. Then, the research expands on improved decoding algorithms that outperform standard iterative decoding by orders of magnitude over MBIOS channels. The intention is to derive conditions on the choice of guessed bits and bounds (on the number of them) for the improved decoding to successfully complete decoding. Finally, the research investigates the error detection capability of LDPC codes and analyzes the tradeoff between computational complexity and average performance of ensembles.