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Electrical Communications Systems ECE.09.331 Spring 2007. Lecture 9a March 20, 2007. Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring07/ecomms/. Plan. Digital Communications Introduction Digital Communications Transceiver (CODEC/MODEM)

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electrical communications systems ece 09 331 spring 2007

Electrical Communications SystemsECE.09.331Spring 2007

Lecture 9aMarch 20, 2007

Shreekanth Mandayam

ECE Department

Rowan University

http://engineering.rowan.edu/~shreek/spring07/ecomms/

slide2
Plan
  • Digital Communications
    • Introduction
    • Digital Communications Transceiver (CODEC/MODEM)
    • Digital Baseband Communications
      • Source Encoding
        • Huffman Coding
    • Error Control Coding
      • Hamming Distance
      • Error Detection Coding
        • Parity Check Code
      • Error Correction Coding
        • Hamming Code
digital communications
Digital Communications
  • Some Milestones
    • Claude Shannon, 1948
    • X.25 (Telephony)
    • IEEE 802.3 (Ethernet)
    • ARPANET, 1969
    • IEEE 802.5 (FDDI)
    • ISO-OSI 7-layer Network Reference Model
    • CDMA
    • GSM
    • VOIP
      • SIP

protocols.com

digital communications rationale
Digital Communications: Rationale
  • Information Theory:
    • What is the fundamental limit on the compression and refinement of information generated by the source?
    • What is the fundamental limit on the transmission rate of information over a noisy channel?
  • How do we approach these limits?
principle
Principle

Digital message

1 1

1 0 1 0………

0 0

Digital

code

Analog

message

modulate

1 0 1 0

Sinusoidal carrier

AM

FM

PM

AM &

PM

digital communication paradigms

Message 1

Message 1

Multiplexer

2

Demultiplexer

1

2

3

1

S

2

3

S

Message 2

Message 2

Message 3

Message 3

3

H

H

1

Depacket-izing

Message 1

2

H

Message 1

3

H

H

1

Depacket-izing

Packetizing

Message 2

Message 2

2

H

3

H

Message 3

Depacket-izing

H

1

Message 3

2

H

Digital Communication Paradigms

Circuit Switching

Sync bits

Packet Switching

Header

bits

digital communications transceiver
Digital Communications Transceiver

Anti-

aliasing

Filter

Error

Control

Encoder

Data

Encryption

Encoder

Channel/

Line

Encoder

Source

Encoder

Sampling

Quantization

Modulator

MUX

ADC

Analog i/p

CODEC

MODEM

Multiple access channel

Analog o/p

Error

Control

Decoder

Data

Encryption

Decoder

Source

Decoder

Audio

Amp

Reconstruction/

DAC

Equalization /

Decision

Circuits

Demod-ulator

DEMUX

source encoding

Analog

Message

A/D

Converter

Source

Encoder

Digital

Source

Source Encoding
  • Why are we doing this?

Source

Symbols

(0/1)

Source Entropy

Encoded

Symbols

(0/1)

Source-Coded

Symbol Entropy

source encoding requirements
Source Encoding Requirements
  • Decrease Lav
  • Unique decoding
  • Instantaneous decoding
huffman coding
Huffman Coding

2-Step Process

  • Reduction
    • List symbols in descending order of probability
    • Reduce the two least probable symbols into one symbol equal to their combined probability
    • Reorder in descending order of probability at each stage
    • Repeat until only two symbols remain
  • Splitting
    • Assign 0 and 1 to the final two symbols remaining and work backwards
    • Expand code at each split by appending a 0 or 1 to each code word
  • Example

m(j) A B C D E F G H

P(j) 0.1 0.18 0.4 0.05 0.06 0.1 0.07 0.04

digital communications transceiver1
Digital Communications Transceiver

Anti-

aliasing

Filter

Error

Control

Encoder

Data

Encryption

Encoder

Channel/

Line

Encoder

Source

Encoder

Sampling

Quantization

Modulator

MUX

ADC

Analog i/p

CODEC

MODEM

Multiple access channel

Analog o/p

Error

Control

Decoder

Data

Encryption

Decoder

Source

Decoder

Audio

Amp

Reconstruction/

DAC

Equalization /

Decision

Circuits

Demod-ulator

DEMUX

error control coding
Error Control Coding

Error Detection

(ARQ Technique)

Error Correction

(FEC Technique)

  • Hamming Distance

The number of locations (bits) at which two code words differ

  • Theorem 1

A code with a Hamming distance of

d >= t+1

can detect t errors in the received code word

  • Theorem 2

A code with a Hamming distance of

2t+1 <= d <= 2t+2

can detect and correct t errors in the received code word

error control codes

Block

Coder

n

encoded

bits

k

information

bits

k

n-k

Information bits

Parity bits

Add

Redundancy!!

n-bit codeword

Error Control Codes

Block Codes

(memoryless)

Convolutional Codes

(with memory)

Principle

Will not discuss!

(n, k) systematic block code

parity check codes

I6

I4

I7

I5

I3

I2

I1

P

Parity Check Codes

P is set such that the total no. of bits in the code word is even or odd

remediation for detected errors arq

1

Rx

2

3

3

NACK

ACK

ACK

1

2

3

Tx

Error detected!!!

Remediation for Detected Errors: ARQ
7 4 hamming code

I3

I1

I4

I2

P3

P2

P1

(7, 4) Hamming Code
  • Single error detection and correction code
  • Hamming distance, d = 3
  • Fits into a general category of coding techniques called BCH codes
  • Employs a
    • Code Generator Matrix
    • Syndrome Decoding Technique
7 4 hamming code1

I3

I3

I1

I1

I4

I4

I2

I2

P3

s3

s2

P2

P1

s1

R6

C6

R4

C4

C7

R7

C5

R5

C3

R3

C2

R2

R1

C1

(7, 4) Hamming Code

Encoding

Parity bits

Code

Generator

=

Info bits

Code word

Decoding

Parity

Check

Received code word

Error position

indicator

7 4 hamming code2
(7, 4) Hamming Code

Code Generator Matrix

hamming encoder

I3

I1

I4

I2

P3

P2

P1

+

+

+

Hamming Encoder

Info bits

Parity bits

P3 = I4 I2 I1

P2 = I4 I3 I1

P1 = I4 I3 I2

syndrome decoding
Syndrome Decoding

Parity Check Matrix

hamming decoder

s3

s2

s1

R6

R4

R7

R5

R3

R2

R1

Hamming Decoder

Received code word

Error Position Indicator

+

+

+

s3 = R7 R5 R4  R3

s2 = R7 R6 R4  R2

s1 = R7 R6 R5  R1

hamming decoder1
Hamming Decoder

Error position indicator

(syndrome)

s

Error Position, e

No error