ECE 515
Information Theory
Error Correcting Code Applications
Digital Communication System
Data
Source Source
Encoding
Channel Source
Decoding Data Sink
Channel Encoding
Channel Decoding
Internet
Data
Source Zip
Channel Unzip
Data Sink
Add CRC
Verify CRC
CRC stands for cyclic redundancy check
In Information Theory Terms
Zip Source
Encoding
= Data Compression
Add CRC Channel
Encoding
=
Unzip Source
Decoding
=
Verify CRC Channel Decoding
=
Data Decompression
Error Protection
Error Detection
DVD
Movie MPEG
Encoder
DVD MPEG
Decoder TV
EncodingRS
DecodingRS
RS stands for Reed-Solomon
IEEE 802.11b
Data
Source Zip
Channel Unzip
DataSink
EncodingCC
DecodingCC
CC stands for Convolutional Code
Cell Phone
Speech Encoding
Channel Speech
Decoding
EncodingTC
DecodingTC
TC stands for Turbo Code
ECC Memory
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ISBN Codes
9
Deep Space Communications
10
Mars Space Communications
1965 Mariner 4
Frequency: 2.3 GHz (S Band) Data Rate: 8.33 bps
No Source Coding Repetition code (2 x)
2004 Mars Exploration Rover
Frequency: 8.4 GHz (X Band) Data Rate: 168 kbps
12:1 lossy ICER compression
RS/Convolutional Concatenated Code
2006 Mars Reconnaissance Orbiter
Frequency: 8.4 GHz (X Band) Data Rate: 12 Mbps
2:1 lossless FELICS compression (8920,1/6) Turbo Code
Distance: 2.15 x 108 km
There are many classes of practical codes
• Hamming codes
• Convolutional codes
• Reed-Muller codes
• Cyclic codes (CRC codes)
• Reed-Solomon codes
• Product codes
• BCH codes
• LDPC codes
• Turbo codes
• Repeat-accumulate codes
• …
All belong to the class of linear block codes
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