A study of iterative capacity-approaching codes and their optimal decoding algorithms.

Abstract

Since the invention of turbo codes in 1993 and the rediscovery of Gallager’s LDPC codes in 1999, Shannon’s determination of the capacity of memoryless channels has become touchable and achievable by adopting these codes iterative decoding scheme. Theoretically, turbo codes and LDPC codes have essentially revolutionised the coding field and become the most focused research topic in recent years. Although these remarkable codes have demonstrated an asymptotic performance close to the Shannon limit, there exists a fact that the practice still lags behind the theory by some margins, for instance the code constructional difficulty, decoding complexity and the hardware or other implementation issues. In terms of the near optimum decoding performance, it still seems infeasible in practice. This research work endeavours to fill some of these gaps concerning the design, analysis, application and algorithm optimisation of the simple but good codes, which aims to provide a near optimum decoding performance with much less computational complexity.