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Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title Communications Theory
Module Code MS414
School School of Mathematics
Online Module Resources

Module TeacherNiamh O'Sullivan
NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
Description
In this module students are introduced to coding and cryptography. This module builds on the students knowledge of linear algebra, rings and fields. The approach taken will encourage students to develop critical thinking and apply logical reasoning to mathemtical problems. Students will participate in the following learning activities: Lectures: Students will attend three one-hour lectures per week. These lectures are designed to introduce learners to the mathematical principles and problem solving techniques that underpin this module. Tutorials: Each student will attend one one-hour tutorial per week. Problem sheets based on lecture content are distributed to the students and they are strongly advised to attempt all tutorial questions in advance of the tutorial.Reading: Students are expected to fully utilise the textbooks recommended.

Learning Outcomes
1. Define error-detecting and error-correcting codes, explain their significance and construct simple examples.
2. Construct decoding processes and compute error probabilities.
3. Define and identify the advantages of linear codes.
4. Define, construct and manipulate generator matrices and parity-check matrices.
5. Define basic cryptographic concepts.
6. Compare and contrast some public key cryptosystems, the hard problems onwhich their security relies and certain attacks on them.



Workload Full-time hours per semester
Type Hours Description
Lecture363 Lectures per week
Tutorial121 tutorial per week
Independent learning140Study over 15 weks including exam period
Total Workload: 188

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities
Error-correcting codes.
Basic concepts: codes, minimum distance, equivalence of codes. Bounds on codes.Noisy channels and nearest-neighbour decoding. Shannon's Noisy Coding Theorem.Linear codes. Generator matrices and parity-check matrices. Syndrome decoding.Cyclic codes. Linear Shift-Register sequences, Reed-Muller, Hamming and Golay codes..

Cryptosystems.
History and basic concepts: substitution and other traditional ciphers; plaintext, ciphertext, key; statistical attack on ciphers..

Public-key Cryptography.
Trpadoor functions. RSA system. Primality testing. Knapsack based systems. Discrete Logarithms. Diffie-Hellman key exchange. El-Gamal system. McEliece cryptosystem..

Assessment Breakdown
Continuous Assessment30% Examination Weight70%
Course Work Breakdown
TypeDescription% of totalAssessment Date
AssignmentFour assignments will be set during the semester.30%As required
Reassessment Requirement
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
This module is category 3
Indicative Reading List
  • Dominic Welsh: 1988, Codes and cryptography, Clarendon Press, Oxford, 0198532873
  • F. J. MacWilliams, N. J. A. Sloane: 1983, The theory of error-correcting codes, North Holland, 0444851933
  • Douglas R. Stinson,: 2005, Cryptography, Chapman and Hall, 1584885084
  • Simon Singh,: 2003, The Code Book, Delacorte Press, 0385730624
Other Resources
None
Array
Programme or List of Programmes
APMB.Sc. Applicable Mathematics
Timetable this semester: Timetable for MS414
Date of Last Revision26-JAN-12
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