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