ECE 550
Channel Coding
Fundamental Limits of Performance
Shannons Channel Capacity Theorem
C = B log2cfw_1 + [S/(NoB)]
Noise density, W/Hz (const)
Received signal power, W
Bandwidth, Hz
Capacity (data rate), bit/s
Information Transmission
The Shannons cha
Chapter2
SignalandSystemsandFourierSeriesand
Transformation
Supplements
I.
The Properties of Delta Function
g (t )d (t  t0 ) = g (t0 )d (t  t0 )
1.
g (t )d (t  t )dt =g (t )
0
0

g
d
(t )d (t  t )dt =g (t ) (t  t )dt
Verify:
0
0
0

0

x =  t0
t
Chapter7
RandomSignalsandNoise
1Page
1. Probability and Random Variable
Random phenomena: outcomes are random but demonstrate statistically properties.
Sample space is the union of all possible events or outcomes. For example, cfw_TH is the sample
space
Chapter4
PulseModulation
1. Sampling Theorem
1) FourierTransformationofaperiodicsignal
As we know from Fourier series: a periodic signal can be expressed by a set of complex
exponentials.
n=
gT0 (t ) = cn e j 2p nf0t
n=
T0
2
T
 0
2
1
cn =
T0
gT0 (t )e 
Chapter5
BasebandDataTransmission
1. Baseband Transmission of Digital Data
cfw_ak
y (t )
x(t )
s (t )
Tx filter
G(f)
Channel
H(f)
Rx filter
Q(f)
Tx
Channel
Rx
Demodulation
Figure 1 The diagram of baseband transmission
s (t ) = ak g (t  kTb )
k =
cfw_
Chapter6
DigitalBandpassModulationTechniques
1. BandPass Assumption
2
b(t ) cos(2p f ct )
Tb
s (t ) =b(t )c(t ) =
where f c ?
1
. It is easy to have,
Tb
Eb
1
Tb
Tb
0
2
b(t ) dt
2. BASK: Binary AmplitudeShift Keying
2 Eb
cos(2p f c t ) if b(t ) =1
s (t
Digital Communications
Chapter 4. Optimum Receivers for AWGN Channels
PoNing Chen, Professor
Institute of Communications Engineering
National ChiaoTung University, Taiwan
Digital Communications. Chap 04
Ver. 2012.11.05
PoNing Chen
1 / 226
4.1 Waveform
ECE 550
Source Coding
Fundamental Limits of Performance
Preliminaries
Source
Examples
Symbols
Examples
Coding symbols
Examples
Transmitting symbols
Bitrate
Information
Definition
Entropy
Definition
Calculation
Maximum value
Source Coding
Sh
1
Digital Transmission
of Analog Data:
PCM and Delta Modulation
Required reading:
Garcia 3.3.2 and 3.3.3
CSE 3213, Fall 2010
Instructor: N. Vlajic
Digital Transmission of Analog Data
Digitization process of converting analog data into digital signal
examp
Digital Communications
Chapter 3: Digital Modulation Schemes
PoNing Chen, Professor
Institute of Communications Engineering
National ChiaoTung University, Taiwan
Digital Communications: Chapter 3
Ver. 2012.10.15
PoNing Chen
1 / 160
3.1 Representation o
336
TRANSACTIONS IRE
ON COMMtJNICATIONS SYSTEMS
,
December
On the Optimum Detection of Digital Signals in the Presence o White Gaussian Noisef A Geometric Interpretation and a Study of ThreeLBasicIData
Transmission Systems*
AND
H. DYMZ,
MEMBER, IRE
Summar
Part I
Signal Processing and Detection
1
Contents
I
Signal Processing and Detection
1
1 Fundamentals of Discrete Data Transmission
1.1 Data Modulation and Demodulation . . . . . . . . . . . . . . . . . . . . .
1.1.1 Waveform Representation by Vectors . .
ECE 550
Channel Coding
Fundamental Limits of Performance
Source Coding: Loose Ends
Prefix coding:
Instantaneous decoding
Huffman codes
Preliminaries
Channel:
Physical transmission layer that is used to convey
information from sender (transmitter) to
Chapter2
SignalandSystemsandFourierSeriesand
Transformation
1. Basics of Signals and Systems
1) Definition
In communications, a signal represents a physical variable, such as electric voltage, electric
current or electromagnetic field, which is used to be