# Course Websites

## ECE 556 - Coding Theory

### Last offered Spring 2022

#### Official Description

Coding theory with emphasis on the algebraic theory of cyclic codes using finite field arithmetic, decoding of BCH and RS codes, finite field Fourier transform and algebraic geometry codes, convolutional codes, and trellis decoding algorithms. Course Information: Prerequisite: MATH 417.

Communications

#### Description

General discussion on coding theory with emphasis on the algebraic theory of cyclic codes using finite field arithmetic, decoding of BCH and RS codes, finite field Fourier transform and algebraic geometry codes, convolutional codes and trellis decoding algorithms.

#### Notes

Same as CS 577, and MATH 579.

#### Topics

• Introduction
• Linear codes: Parity and generator matrices, decoding rules, coset leaders, and standard arrays
• Bounds on code parameters; Singleton, sphere-packing, Gilbert-Varshamov and other bounds
• Some simple codes: Hamming, Golay, Reed-Muller codes
• Finite fields: Basic theory, minimal polynomials
• Cyclic codes and BCH codes: Ring ideals, generator and parity check polynomials and matrices, the BCH bond
• Reed-Solomon codes: Reed-Solomon codes as BCH codes, general theory of MDS codes
• Error-correction procedures: The Peterson-Zierler decoder, Berlekamp-Massey decoding algorithm, Berlekamp-Welch and Sudan's decoding algorithm, Generalized Minimum Distance decoding
• Convolutional codes: Introduction, encoder circuits, state-diagrams, trellises, path enumerators and error bounds
• Decoding algorithms for convolutional codes: Viterbi, BCJR, sequential decoding

#### Detailed Description and Outline

Topics:

• Introduction
• Linear codes: Parity and generator matrices, decoding rules, coset leaders, and standard arrays
• Bounds on code parameters; Singleton, sphere-packing, Gilbert-Varshamov and other bounds
• Some simple codes: Hamming, Golay, Reed-Muller codes
• Finite fields: Basic theory, minimal polynomials
• Cyclic codes and BCH codes: Ring ideals, generator and parity check polynomials and matrices, the BCH bond
• Reed-Solomon codes: Reed-Solomon codes as BCH codes, general theory of MDS codes
• Error-correction procedures: The Peterson-Zierler decoder, Berlekamp-Massey decoding algorithm, Berlekamp-Welch and Sudan's decoding algorithm, Generalized Minimum Distance decoding
• Convolutional codes: Introduction, encoder circuits, state-diagrams, trellises, path enumerators and error bounds
• Decoding algorithms for convolutional codes: Viterbi, BCJR, sequential decoding

Same as CS 577, and MATH 579.

#### Texts

R. E. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, 2002.
TitleSectionCRNTypeHoursTimesDaysLocationInstructor
Coding TheoryL70994DIS41230 - 1350 T R  3020 Electrical & Computer Eng Bldg Olgica Milenkovic