Coding Theory

Analysis from the Maximum Likelihood Perspective:

Distance spectrum and interleaving gain:

  • Distance spectrum and interleaving gain for PA codes (paper) and GPA codes (paper).

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):

  • Eb/No thresholds of the simple bounds for PA codes (paper) and GPA codes (paper).

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 (paper1paper2) 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).