수업일지 -- 직교신호설계이론 (본대학원, 2001-2)
여러분이 이 페이지를 읽는 날짜를
기준으로 하여 이전의 기록은 이미 수업시간에
다루었던 내용을 간추린 것이고 이후의 기록은 대략적인 계획입니다.자주 들러서 예습/복습에 도움이
되기를 바라며, 열심히 공부하기 바랍니다.
담당교수: 송홍엽
FIRST QUARTER
(GO
TO 1st 2nd 3rd 4th quarter; top today bottom )
1주
(9월 6일) Introduction and Some Bounds
- Goal:
Find a set of n (normalized) signals which are as mutually uncorrelated
as possible.
- Basis:
Such a set of signals is the best in the communication system over AWGN
channel and correlation detection.
- Various
Correlation Measures:
- over
reals
- over
binary
- over
compex
- over
square-integrable functions
- Simplex
Bound
- Welch
Bound
- Some
Mechanics
- HW#1.
마감: 다음주 목요일 오전 10시(A4 용지사용, staple once at the top-left corner)
- Hand-out:
Tutorial Paper by S.W.Golomb
- Hand-out:
Sequences with Low Correlation by Helleseth and Kumar, Chapter 24 of Handbook
of Coding Theory, edited by V. Pless.
2주
(9월 13일) Review
of Elementary Number Theory
- congruence
- Integers
mod n -- When is it cyclic ?
- Integers
mod n is a field if and only if n is a prime.
- mobius
inversion
- quadratic
residues and quadratic reciprocity
- Some
Mechanics
- Hand-out: Fairly
Comprehensive
Introduction to Finite Fields
- Hand-out:
Simple Introduction to Finite Fields (by Hong-Yeop Song)
- Some
Other References
- McEliece,
Finite fields for Computer Scientists and Engineers, Kluwer, --
VERY GOOD introduction to Finite Fields
- Wicker,
Error Control Systems for Digital Communication and Storage, Chaters
2 and 3, Prentice Hall, -- VERY GOOD and SHORT (but pretty comprehensive)
introduction to Finite Fields
- This
course depends heavily on the Theory of Finite Fields. So, you had
better review one of the above materials unless you took the course
"Theory and application of Finite Fields" in the spring
of 2001 from me.
- HW#2.
마감: 다음주 목요일 오전 10시(A4 용지사용, staple once at the top-left corner)
3주
(9월 20일) Introduction to Hadamard Matrices
- Definition
and Some Necessary Conditions on the Existence
- Hadamard
Matrics and Signal Designs
- Some
Types of Hadamard Matrices
- Circulent
Hadamard Matrices and Barker Sequences
- Sylvester
Type using Kronecker Product
- Williamson
Type and some Variations
- Payley
Type - II when p=1 mod 4
- Payley
Type - I when p=3 mod 4 (this is a cyclic type using Quadratic Residues
mod p)
- Cyclic
type Hadamard matrices are equivalent to balanced binary sequences with
ideal autocorrelation of period 3 mod 4.
- Some
Mechanics
4주
(9월 27일) Cyclic Difference Sets
- Introduction
to Cyclic Difference Sets
- Definition
and Some Necessary Conditions
- Two
Extreme Cases: Planar and Hadamard
- Current
Status of Research
- Cyclic
Hadamard Difference Sets
- Definition
and Existence
- Various
Known Constructions
- Quadratic
Residue Construction (Payley Type - I)
- Hall's
Sextic Residue Construction
- Twin
Prime Construction
- m-sequence
Construction (LFSR Construction) -- next time
- GMW
Construction -- next time
- Some
Mechanics
SECOND QUARTER (GO
TO 1st 2nd 3rd 4th quarter; top today bottom )
5주
(10월 4일) m-sequences and GMW sequences
- Proof
of Payley type Constructions
- Introduction
- Some
Mechanics
6주
(10월 11일)
- Binary
m-sequences
- Non-binary
m-sequences
- Trace
Representation and Properties
- GMW
sequences and more
7주
(10월 18일 take-home midterm is due
today) Code Designs for FH-CDMA
8주
(중간시험기간)
THIRD QUARTER (GO
TO 1st 2nd 3rd 4th quarter; top today bottom )
9주
take-home midterm is due
today (연기)
10주
11주
12주
FOURTH QUARTER (GO
TO 1st 2nd 3rd 4th quarter; top today bottom )
13주
14주
15주
16주(기말시험기간)
(GO
TO 1st 2nd 3rd 4th quarter; top today bottom )
최종성적처리결과