Electrical Communications Systems 0909.331.01 Spring 2005

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Electrical Communications Systems0909.331.01
Spring 2005
Lecture 9aApril 5, 2005

• Shreekanth Mandayam
• ECE Department
• Rowan University
• http//engineering.rowan.edu/shreek/spring05/ecom
  ms/

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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

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ECOMMS Topics
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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
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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?

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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
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Digital Communication Paradigms
Circuit Switching
Sync bits
Packet Switching
Header bits
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Digital Communications Transceiver
Anti- aliasing Filter
Data Encryption Encoder
Error Control Encoder
Channel/ Line Encoder
Source Encoder
Sampling
Quantization
Modulator
MUX
ADC
Analog i/p
CODEC
MODEM
Multiple access channel
Analog o/p
Data Encryption Decoder
Error Control Decoder
Audio Amp
Source Decoder
Reconstruction/ DAC
Equalization / Decision Circuits
Demod-ulator
DEMUX
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Source Encoding
Source Symbols (0/1) Source Entropy
Encoded Symbols (0/1) Source-Coded Symbol
Entropy

• Why are we doing this?

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Source Encoding Requirements

• Decrease Lav
• Unique decoding
• Instantaneous decoding

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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

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Digital Communications Transceiver
Anti- aliasing Filter
Data Encryption Encoder
Error Control Encoder
Channel/ Line Encoder
Source Encoder
Sampling
Quantization
Modulator
MUX
ADC
Analog i/p
CODEC
MODEM
Multiple access channel
Analog o/p
Data Encryption Decoder
Error Control Decoder
Audio Amp
Source Decoder
Reconstruction/ DAC
Equalization / Decision Circuits
Demod-ulator
DEMUX
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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 gt t1
• can detect t errors in the received code word
• Theorem 2
• A code with a Hamming distance of
• 2t1 lt d lt 2t2
• can detect and correct t errors in the received
  code word

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Error Control Codes
Block Codes (memoryless)
Convolutional Codes (with memory)
Will not discuss!

• Principle

(n, k) systematic block code
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Parity Check Codes
P is set such that the total no. of bits in the
code word is even or odd
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Remediation for Detected Errors ARQ
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(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

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(7, 4) Hamming Code
Encoding
Parity bits
Code Generator

Info bits
Code word
Decoding
Parity Check
Received code word
Error position indicator
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(7, 4) Hamming Code
Code Generator Matrix
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Hamming Encoder
Info bits
Parity bits
P3 I4 ? I2 ? I1 P2 I4 ? I3 ? I1 P1 I4 ? I3
? I2
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Syndrome Decoding
Parity Check Matrix
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Hamming Decoder
Received code word
Error Position Indicator



s3 R7 ? R5 ? R4 ? R3 s2 R7 ? R6 ? R4 ? R2 s1
R7 ? R6 ? R5 ? R1
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Hamming Decoder
Error position indicator (syndrome) s
Error Position, e
No error







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Summary