Viterbi decoder in optical comm system
-
Upload
boni-anissuzzaman -
Category
Engineering
-
view
290 -
download
4
description
Transcript of Viterbi decoder in optical comm system
Optical Communication Systems 1
Viterbi-Decoder in Optical
Communication Systems
Prepared By : Anisuzzaman Boni
Mat No : 33109062
Date : 27th May 2014
Optical Communication Systems 2
Table of Contents
Introduction
Electronics Circuits for Conversion
Convolutional Encoder
• Operation
• Trellis Diagram
Optimum Decoding-Viterbi Algorithm
• Computing the Correlation Metrics
• Metrics Selection criteria
• Observation
Decoding Received Sequence
Complexity of Viterbi Algorithm
Recent Advancement
Reference
Summary
Optical Communication Systems 3
Modulator
Light Source
Transmitted
Circuit
Demodulator Decoder
Fiber Optic
Cable
Encoder
Digital
Bits
01101100
00101001
Figure: Generic Model of Optical Communication System
Introduction
Electronic
Circuits
Trans. Rate In Gb/s
Optical Communication Systems 4
Figure : Block diagram of MLSE based receiver of OC-192 fiber links
Electronic Circuits for Conversion
9.9Gbps
Viterbi Decoding
Ref [3]
Optical Communication Systems 5
Convolutional Encoder
Features
• Code generated by passing the information into finite state shift register
• Code word-Entire data stream
• Denoted by (n,k,L) code
• Code perfectly describe by
Trellis diagram-Key concept for Viterbi algorithm
State diagram
• Better code to reach Theoretical Shannon limit
Optical Communication Systems 6
Convolutional Encoder
mj-2mj-1mj X1 X2
Shift RegisterEncoded Bits
Figure: (2,1,2)bit Convolutional Encoder
Operation
I/P P/S N/S
X1=mj
+mj-2
X2=mj+mj-1
+mj-2
O/P
0 0 0 00 0+0=0 0+0+0=0 00
1 0 0 10 1+0=1 1+0+0=1 11
0 0 1 00 0+1=1 0+0+1=1 11
1 0 1 10 1+1=0 1+0+1=0 00
0 1 0 01 0+0=0 0+1+0=1 01
1 1 0 11 1+0=1 1+1+0=0 10
0 1 1 01 0+1=1 0+1+1=0 10
1 1 1 11 1+1=0 1+1+1=1 01
P/S:Present StateN/S:New StateI/P:InputO/P:Output
1 00 0 1
0 1
[2]
Optical Communication Systems 7
Trellis Diagram
I/P P/S N/S O/P
0 0 0 00 00
1 0 0 10 11
0 0 1 00 11
1 0 1 10 00
0 1 0 01 01
1 1 0 11 10
0 1 1 01 10
1 1 1 11 01
00
01
10
11
00
01
10
11
I/P: 0 1
00
1111
00
0110
10
01
Figure: Trellis diagram for (2,1,2) convolutional code
[2]
Optimum Decoding- Viterbi Algorithm
Optical Communication Systems 8
Computing the Correlation Metrics
• Searching through trellis for probable sequence /path
• Hamming Metrics Computation based on Hamming Distance
• Hamming Distance - the weight difference between two code words
- the no of position where two code words differ
Transmitted
Code word : 010100110
Hamming Weight
4
Received
Code word: 100100010 3
Hamming Distance : 3
Optical Communication Systems 9
Metrics Selection criteria
• Select the path having higher path metrics
• Correlation path metrics CM(0),CM(1),CM(2)
Compare the metrics and if CM(0) > CM(1) >CM(2)
Select CM(0) as Survivor path and discard else path from consideration
• Same procedure repeat at each stages of trellis when new bits are
received
Observation
• Survivor paths minimize the probability of error for the received
information
Optimum Decoding-Viterbi Algorithm
Optical Communication Systems 10
Decoding Received Sequence
Transmitted Sequence : 11 10 10 00 01 11
Received sequence : 11 10 11 00 11 11 (2 bit error)
00
01
10
11
2
0
2
0
1
1
2
0
1
1
0
2
1
11
1
11 10 10 00 01 11Decoded bits
Figure:(2,1,2)
Convolutional
Encoder
Figure: Decoding through Viterbi Algorithm
Optical Communication Systems 11
Complexity of Viterbi Algorithm
Computational Complexity
• Any trellis has 2k(L-1) states
• 2k(L-1) surviving paths and 2k(L-1) metrics
• Only one path survive (most Probable path)
• Needed large memory
• Complexity increases exponentially with k and L
Recent Advancement
Optical Communication Systems 12
Lazy Viterbi Algorithm
• Applicable for both block and convolutional code
• Much faster compare to original one
• Running time does not depend on the constraint length
• Algorithms work by not expanding any nodes until
it really needs to
Practically found:
Code with constraint length 6,the Lazy algorithm is about 50% faster
than normal Viterbi Algorithm when SNR > 6 dB
Ref [4]
Optical Communication Systems 13
Summary
• Most Optimum although having some drawbacks
• Very efficient to decode a large no of data
• Algorithm very easy to understand and implementing
in software is also easy
• Algorithm universally used in CDMA,GSM technology, satellite,
Wireless LAN
Optical Communication Systems 14
Reference
2. Enrico Forestieri Optical Communication Theory and Techniques .3rd
edition. 2005
4. Jhon,ibrahim. A Fast Maximum-Likelihood Decoder forConvolutional Codes.Available at:http://people.csail.mit.edu/jonfeld/pubs/lazyviterbi.pdf
3. Hyeon,jonathan,jinki.An MSLE Receiver for Electronic Dispersion Compensation of OC-192 Fiber Links,IEEE Journal of Solid State Circuits.Vol.41,No.11,November2006
1. Arunlal,Hariprasad.An efficient viterbi decoder. International Journal Advanced Information Technology (IJAIT) Vol. 2, No.1, February 2012