This book presents new methods for the analysis, design and decoding of low-density parity-check (LDPC) codes. First, we propose an efficient method for analyzing finite-length LDPC codes on symmetric channels. This method is based on the threhold behavior of LDPC codes and studying the atypical behavior of the channel when observed during a final block length. Different channel parameters can be used to model the channel behavior and predict the performance. We investigate and compare the results obtained by considering different channel parameters for predicting the performance. Second, we consider iterative decoding on uncorrelated fading channels where the channel fading and/or the noise power is not known at the receiver. We propose a linear LLR approximation method which is optimum in the sense of maximum achievablle transmission rate on the channel. This method is also applicable to other iteratively decoded codes.