Analysis from the Maximum Likelihood Perspective:
Distance spectrum and interleaving gain:
Union bounds:
- Average ensemble bounds using the Union bounding technique for PA codes on AWGN channels (paper), non-dispersive uncorrelated Rayleigh fading channels (paper), and optical fiber communication channels like Chi-square, asymmetric Gaussian channels (paper).
Simple bounds (due to Divsalar):
Coding Analysis from the Iterative Perspective:
Existence and computation of thresholds of codes using density evolution (DE):
- Thresholds of LDPC, turbo and TPC/SPC codes on partial response (PR) channels using density evolution with Gaussian approximation (GA) (paper).
- Thresholds of PA codes on AWGN channels (paper1, paper2) and non-dispersive uncorrelated Rayleigh fading channels (paper).
- Thresholds of GPA codes on AWGN channels (paper).
Channel Capacity:
Channel capacities for various channels:
- The ultimate channel capacity (optimal channel input) and the practical channel capacity (equal probable of channel input) of Chi-square channels in optical fiber communications. Both soft- and hard- decision is considered. Several values of the system parameter $M$ are investigated (paper).
Decoding Algorithms:
Code graph (Tanner graph) and message-passing decoding algorithms.
- Message-passing decoding algorithms of TPC/SPC codes (paper).
- Sum-product (Message-passing) decoding and min-sum decoding for cycle-free convolutional codes like $1/(1+D^n)$ (paper).