Abstract: This dissertation addresses several problems concerning error correction coding and detection over inter-symbol interference (ISI) channels with applications in magnetic recording and wireless communication systems. In the first part, iterative belief propagation (BP) algorithm is proposed for channel detection over magnetic recording systems. The parallel and iterative structure of the BP detector leads to fast and memory efficient hardware implementations. BP detector achieves a near-optimal performance over several ISI channels and presents a legitimate alternative to the typically used maximum a-posteriori (MAP) and maximum likelihood (ML) detectors. A similar line of research is followed for noise predictive channel detection over ISI channels with correlated and data dependent noise and noise predictive belief propagation (NPBP) and pattern dependent noise predictive belief propagation (PD-NPBP) detectors are developed. These detectors improve the bit error rate (BER) performance significantly and they have better convergence behavior compared to the MAP and BP detectors. For error correction coding, capacity approaching turbo and low density parity check (LDPC) codes are considered. In this context, as a novel contribution, burst error problem of these codes is addressed and several effective burst error identification methods are introduced. The second part of the dissertation addresses coding and channel detection for wireless communication systems. In particular, the use of iterative belief propagation detector is introduced over single input single output (SISO) and multi-input and multi-output (MIMO) wireless channels and MIMO system factor graph representation is presented. The proposed SISO/MIMO BP detector achieves a near optimal BER performance for both uncoiled and coded systems, employing powerful LDPC codes. Furthermore, average mutual information (AMI) analysis demonstrates that BP detector has virtually identical convergence behavior with the optimal MAP detector for majority of the channel realizations.