99-2 직교신호설계이론

1999학년도 2학기 본대학원 전기컴퓨터공학과,

월 1:00-2:30,  수 12:40-2:00,

담당교수: 송홍엽(http://calab.yonsei.ac.kr/~hysong)  E-mail

수업내용

1주(수) : Introduction to Signals with "good" correlation property

Hand-out: "Design of Signals with favourable correlation property "
HW#1 on Simplex bound, signal constellation, correlation, etc.

2주(월) : Simplex Bound 소개 및 증명
2주(수) : "Some new constructions for Simplex code" 앞부분 소개

3주(월) : HW#1 제출마감,

Hand-out: HW#1 solution, Some notes on constructions for Hadamard matrices.
HW#2 on various construction of hadamard matrices and
                design of binary sequences that achieves Simplex bound
Hadamard Matrix 소개
                Order must be a multiple of 4 if bigger than 2.
                Sylvester type, cyclic type, Williamson type, Paley type I and II,
                Current status.

3주(수):

Hadamard matrix construction
        Kronecker product (Sylvester type), Quadratic residue/nonresidue, Autocorrelation

4주(월):

Decimation preserves autocorrelation,
More constructions for hadamard Matrices
         Paley type I and II,
        Twin-prime construction

4주(수): Williamson type construction

5주(월) :

HW#2 제출 마감
HW#3 on review problems of Number Theory
division, congruence, gcd, Euler-phi function

5주(수) :

Discussions on HW#2
definition of the order of a mod n

6주(월) :

mu function, order, primitive root mod n, When n has a primitive root ?
Hand-out: "Existence of cyclic Hadamard difference sets" MTNS 자료.

6주(수) : Quadratic reciprocity law + Difference Sets

7주(월) :

HW#3 제출마감, HW#3 solution Hand-out
HW#4 on cyclic difference sets and Finite Field
Cyclic Difference Sets, Cyclic hadamard Difference Sets

7주(수) :

More on Cyclic Difference Sets
Multiplier and constructive test for existence

8주 (중간시험기간 - 수업 없음)

9주 (월) : Comments on HW#3 + Typo, CDS 완료, 2-dimensional patterns

9주 (수) : Barker Sequences, Rulers, Costas Arrays, Sonar Arrays -- Broad introduction

10주(11/1-)
(월)

Fibonacci configuration of LFSR,
Generating function approach of LFSR,
State diagram, possible period
Fibonacci sequences, characteristic polynomial, irreducible polynomials, primitive polynomials

(수)

sieve methods of finding irreducible polynomials,
Randomness properties of m-sequences: span-n property, balance property, run property 

11주(11/8-) :
(월)

HW#4 마감,
Randomness properties of m-sequences:
                autocorrelation property, cycle-and-add property, constant-on-the-coset property
Characteristic phase of m-sequences
Relation with cyclic Hadamard difference sets
Classification of balanced binary sequences of period 2^n -1 (Hand-out: Cheng & Golomb)
Open problem: Does span and optimal autocorrelation imply m-sequences ?

(수)

Handout-HW#5 (10주 + 11주 내용)
Introduction to Finite Fields
    1. additive structure
    2. vector space
    3. primitive element
    4. minimal polynomials

12주(11/15-) :
(월)

Properties of minimal polynomials
    5. conjugates and cyclotomic cosets
    6. lots of examples
    7. factorization of x^N+1
    8. period of LFSR seqences

(수)

HW#5 마감
HW#6 on Finite Fields
Properties of minimal polynomials and irreducible polynomials
Cubic transformations,
Trace functions and m-sequences
    1. subfield and extension
    2. ADDONE table
    3. definition of trace
    4. properties of trace function

13주(11/22-) : Trace functions, m-sequences, randomness properties revisited
(월)

Handout - Solutions to HW#4 and HW#5
handout - HW#7 (Gold and Kasami sequences - programming and checking)
properties of trace function
m-sequence as a trace
Galois-configuration of LFSR

(수)

randomness properties of m-sequences as trace map  
balance, run, span, constant-on-the-coset, optimal autocorrelation, cycle-and-add
q-ary m-sequences

14주(11/29-) : Binary GMW sequences and Crosscorrelation of m-sequences
(월)

Randomness properties of q-ary m-sequences
             balance, span, run, constant-on-the-coset, optimal autocorrelation when q=prime, cycle-and-add
Binary GMW sequences: balance property and optimal autocorrelation property

(수)

optimal autocorrelation property of binary GMW sequences - revisited
crosscorrelation of m-sequence and its r-decimation
Linear Design of set of binary sequences

15주(12/6-) : Gold sequences and small set of Kasami sequences
(월)

Definition of Gold sequences
crosscorrelation property
autocorrelation property
weight distribution property
span property
Sidelnikov bound and optimality

(수)

Welch Bound and Proof
Definition of small set of Kasami sequences
crosscorrelation property
autocorrelation property
Welch bound and optimality

16주(12/13, 월) : 종강일
        (월) HW#7 마감
기말시험 - 12월 13일 (월) 1시-3시