Spring 2006

Schedule

Day | Topics | Preparation |
---|---|---|

Thurs. 1/19 | Introduction. Major developments in 50 years of coding theory. | . |

Tues. 1/24 | Review of number theory. Intro to commutative rings and ideals. |
Sec 1.1-2. |

Thurs. 1/26 | Polynomial rings over a field. | Sec. 1.2-3. |

Tues. 1/31 | Quotient rings. Quotients of polynomial rings. Cyclic codes. |
Sec. 1.3. |

Thurs. 2/2 | Finite fields: Existence and uniqueness. | Sec. 1.4 |

Tues. 2/7 | Finite field examples. Reed-Solomon codes, 3 definitions. |
Sec 1.4 Sec. 2.1, 2. |

Thurs. 2/9 | Coding for error correction. Cyclic codes: systematic encoding, and dual codes. |
Maple 9 mw Maple 8 mws Sec. 2.1-3 |

Tues. 2/14 | Circuit diagrams for polynomial arithmetic and constant multipliers in a finite field. Decoding, and the key polynomials. |
Sec. 2.4-6. |

Tues. 2/21 | More on cyclic codes. The Peterson-Gorenstein-Zierler decoding algorithm. |
Sec. 2.4-6. |

Thurs. 2/23 | The Berlekamp-Massey algorithm and an extension. |
Sec. 2.7,8. |

Tues. 2/28 | Beyond RS codes Generalised Reed-Solomon codes, subfield subcodes. |
. |

Thurs. 3/2 | Convolutional codes | Hankerson 8.1 |

Tues. 3/7 | Convolutional code: state diagrams | Hankerson 8.2 |

Thurs. 3/9 | Convolutional codes: Trellis representation. Error free decoding. |
Hankerson 8.3 |

Tues. 3/21 | Viterbi algorithm. | Hankerson 8.4 |

Thurs. 3/23 | Suggestions for research topics: Generalized RS codes, Sudan's algorithm, bounds on codes, AG codes, ring-linear codes, quasi-cyclic codes | . |

Tues. 3/28 | Suggestions for research topics: Quadratic residue codes, trellis representations, convolutional codes, LDPC codes. | . |

Thurs. 3/30 | Probability, Bayes' theorem and decoding | Sec. 3.1,2 |

Tues. 4/4 | The generalized distributive law. A decoding example | Sec. 3.3 |

Thurs. 4/6 | The sum-product algorithm and the max-product algorithm |
Sec. 3.6 |

Tues. 4/11 | An alternate version of the SPA. Exactness of the algorithm on trees |
Sec. 3.4,5 |

Thurs. 4/13 | Signal to noise ratio and performance curves |
. |

Tues. 4/18 | Shannon's noisy coding theorem: preparation. | . |

Thurs. 4/20 | Shannon's noisy coding theorem: proof. | . |

Tues. 4/25 | Discuss your project with me. | . |

Thurs. 4/27 | Discuss your project with me. | . |

Tues. 5/2 | Project presentations. | . |

Thurs. 5/4 | Project presentations. | . |

Tues. 5/9 | Project presentations. | . |