Information Theory

  1. Error Control Coding
    1. Fundamentals of Error Control
      1. Error Models
        1. Random Errors
          1. Burst Errors
            1. Erasure Errors
            2. Code Parameters
              1. Block Length
                1. Information Length
                  1. Code Rate
                    1. Minimum Distance
                    2. Error Detection and Correction Capabilities
                      1. Hamming Distance
                        1. Sphere-Packing Bound
                          1. Singleton Bound
                            1. Plotkin Bound
                          2. Linear Block Codes
                            1. Vector Space Structure
                              1. Generator Matrix
                                1. Parity-Check Matrix
                                  1. Dual Codes
                                  2. Encoding and Decoding
                                    1. Systematic Encoding
                                      1. Syndrome Decoding
                                        1. Standard Array Decoding
                                          1. Maximum Likelihood Decoding
                                          2. Code Families
                                            1. Hamming Codes
                                              1. Extended Hamming Codes
                                                1. Simplex Codes
                                                  1. First-Order Reed-Muller Codes
                                                2. Cyclic Codes
                                                  1. Polynomial Representation
                                                    1. Generator Polynomials
                                                      1. Check Polynomials
                                                        1. Roots and Minimal Polynomials
                                                        2. BCH Codes
                                                          1. Construction Method
                                                            1. Error Correction Capability
                                                              1. Decoding Algorithms
                                                              2. Reed-Solomon Codes
                                                                1. Construction over Finite Fields
                                                                  1. Maximum Distance Separable Property
                                                                    1. Applications in Storage and Communication
                                                                  2. Convolutional Codes
                                                                    1. Encoder Structure
                                                                      1. Shift Register Implementation
                                                                        1. Generator Polynomials
                                                                          1. State Diagrams
                                                                          2. Trellis Representation
                                                                            1. State Transitions
                                                                              1. Path Enumeration
                                                                                1. Distance Properties
                                                                                2. Decoding Algorithms
                                                                                  1. Viterbi Algorithm
                                                                                    1. BCJR Algorithm
                                                                                      1. Sequential Decoding
                                                                                    2. Modern Coding Techniques
                                                                                      1. Turbo Codes
                                                                                        1. Parallel Concatenated Structure
                                                                                          1. Iterative Decoding
                                                                                            1. Performance Near Shannon Limit
                                                                                            2. Low-Density Parity-Check Codes
                                                                                              1. Sparse Matrix Structure
                                                                                                1. Belief Propagation Decoding
                                                                                                  1. Density Evolution Analysis
                                                                                                  2. Polar Codes
                                                                                                    1. Channel Polarization Phenomenon
                                                                                                      1. Successive Cancellation Decoding
                                                                                                        1. Achieving Channel Capacity

                                                                                                    Previous

                                                                                                    4. Channel Capacity and Noisy Communication

                                                                                                    Go to top

                                                                                                    Next

                                                                                                    6. Rate-Distortion Theory