Tài liệu Format (Channel coding ) ppt

1 Facuty of Electronics & Telecommunications, HCMUNS

BÀI 3:

Format

(Channel coding)

Facuty of Electronics & Telecommunications, HCMUNS

Đặng Lê Khoa

Email:[email protected]

[email protected]

2 Facuty of Electronics & Telecommunications, HCMUNS

Facuty of Electronics & Telecommunications, HCMUNS

Digital Communications I:

Modulation and Coding Course

Period 3 - 2007

Catharina Logothetis

Lecture 9

2006-02-16 Lecture 9 4 Facuty of Electronics & Telecommunications, HCMUNS

Last time we talked about:

„ Evaluating the average probability of

symbol error for different bandpass

modulation schemes

„ Comparing different modulation schemes

based on their error performances.

2006-02-16 Lecture 9 5 Facuty of Electronics & Telecommunications, HCMUNS

Today, we are going to talk about:

• Channel coding

• Linear block codes

– The error detection and correction capability

– Encoding and decoding

– Hamming codes

– Cyclic codes

2006-02-16 Lecture 9 6 Facuty of Electronics & Telecommunications, HCMUNS

Block diagram of a DCS

Format

Source

encode

Format

Source

decode

Channel

encode

Pulse

modulat

e

Bandpass

modulate

Channel

decode

Demod.

Sample Detect

Channel Digital modulation Digital demodulation

2006-02-16 Lecture 9 7 Facuty of Electronics & Telecommunications, HCMUNS

• Channel coding:

Transforming signals to improve communications

performance by increasing the robustness against

channel impairments (noise, interference, fading, ..)

• Waveform coding: Transforming waveforms to

better waveforms

• Structured sequences: Transforming data

sequences into better sequences, having

structured redundancy.

-“Better” in the sense of making the decision process less

subject to errors.

What is channel coding?

2006-02-16 Lecture 9 8 Facuty of Electronics & Telecommunications, HCMUNS

• Automatic Repeat reQuest (ARQ) Error control techniques

– Full-duplex connection, error detection codes

– The receiver sends a feedback to the transmitter, saying that

if any error is detected in the received packet or not (Not￾Acknowledgement (NACK) and Acknowledgement (ACK),

respectively).

– The transmitter retransmits the previously sent packet if it

receives NACK.

• Forward Error Correction (FEC)

– Simplex connection, error correction codes

– The receiver tries to correct some errors

• Hybrid ARQ (ARQ+FEC)

– Full-duplex, error detection and correction codes

2006-02-16 Lecture 9 9 Facuty of Electronics & Telecommunications, HCMUNS

Why using error correction coding? – Error performance vs. bandwidth

– Power vs. bandwidth

– Data rate vs. bandwidth

– Capacity vs. bandwidth

(dB) / b NE 0

PB

A

F

B

D

C

E Uncoded

Coded

Coding gain:

For a given bit-error probability,

the reduction in the Eb/N0 that can be

realized through the use of code:

[dB] [dB] [dB]

0

u

0

c

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

=

N

E

N

E

G

b

b

2006-02-16 Lecture 9 10 Facuty of Electronics & Telecommunications, HCMUNS

Channel models

• Discrete memory-less channels

– Discrete input, discrete output

• Binary Symmetric channels

– Binary input, binary output

• Gaussian channels

– Discrete input, continuous output

2006-02-16 Lecture 9 11 Facuty of Electronics & Telecommunications, HCMUNS

Linear block codes

• Let us review some basic definitions first which are

useful in understanding Linear block codes.

2006-02-16 Lecture 9 12 Facuty of Electronics & Telecommunications, HCMUNS

Some definitions

• Binary field :

– The set {0,1}, under modulo 2 binary addition and

multiplication forms a field.

– Binary field is also called Galois field, GF(2).

011

101

110

000

=⊕

=⊕

=⊕

⊕

=

111

001

010

000

=⋅

=⋅

=⋅

⋅ =

Addition Multiplication