Sequential Soft Decision Decoding of Reed Solomon Codes - PowerPoint PPT Presentation

1 / 19
About This Presentation
Title:

Sequential Soft Decision Decoding of Reed Solomon Codes

Description:

Title: Sequential Soft Decision Decoding of Reed Solomon Codes Author: Hari Palaiyanur Last modified by: hrp3 Created Date: 7/19/2003 9:06:24 PM Document presentation ... – PowerPoint PPT presentation

Number of Views:260
Avg rating:3.0/5.0
Slides: 20
Provided by: HariPal2
Category:

less

Transcript and Presenter's Notes

Title: Sequential Soft Decision Decoding of Reed Solomon Codes


1
Sequential Soft Decision Decoding of Reed Solomon
Codes
  • Hari Palaiyanur
  • Cornell University
  • Prof. John Komo
  • Clemson University
  • 2003 SURE Program

2
Outline
  • Background
  • System Model
  • Stack and Bucket Algorithms
  • Results
  • Conclusions

3
Background
  • Error Control Coding adding redundancy to
    improve reliability over noisy channel
  • Reed Solomon Codes (n,k) cyclic block codes
    over GF(qm), n qm 1
  • (n1)k possible code words
  • Erasure if symbol is unreliable, denote it as
    an erasure

4
Background
  • Soft Decision Decoding takes advantage of side
    information, i.e. quality of received signal
  • Sequential decoding searches through tree of
    possible code words

5
Motivation and History
  • Soft decision decoding more reliable
  • Soft decision decoding more decoding time
  • Good, efficient errors only and errors and
    erasures decoders available
  • Still need good, efficient soft decision decoders
  • Stack/Bucket Algorithm - 1969

6
System Model
  • MFSK over AWGN channel
  • For each symbol, detector outputs
  • mi As ni (i sent)
  • mi ni (i not sent)
  • ni indep. G. R. V.

RS Encoder
MFSK Modulator
Data
AWGN Channel
Coherent MFSK Detector
Sequential RS Decoder
7
Stack Algorithm
Start and Load stack with 2m initial nodes
P is Head of Stack
Len P k-1?
No
Yes
Remove P Search 2m forward nodes Update
Metrics Push onto Stack
Remove P Search 2m forward nodes and
encode Update Metrics Push onto Stack
Len P n?
No
Yes
Done. Decoded code word is P
8
Metrics and RS (7,3) Example
  • Metrics provide information about quality of
    symbol
  • Forward metric is sum of previous metric and
    metric for added symbol
  • Good metric
  • mi max(mj)

Symbol 0 1 2 3 4 5 6
7
Mi 3.3 0.2 1.5 0.1 1.1 0.7 2.0
0.8
Node 0 0.0
Node 1 -3.1
Node 2 -4.8
Node 3 -3.4
Start
Node 4 -2.2
Node 5 -2.6
Node 6 -5.3
Node 7 -2.5
9
Stack Algorithm
  • Algorithm goes through many unnecessary code
    words
  • Perform quick erasure decoding
  • Let threshold be this code words metric
  • Only push nodes onto stack if their metric is at
    least threshold

10
Bucket Algorithm
  • Instead of one sorted stack, use many buckets
  • Buckets have certain metric gradations
  • No need to keep code words sorted, if gradations
    are fine enough
  • Sacrifice memory for speed

Metrics 0.0 to -5.0
Metrics -5.0 to -10.0
Metrics -10.0 to -15.0
Metrics Below -15.0
11
Results RS (15,9)
12
Results Number of Searches
13
Results RS (31,21)
14
Conclusions
  • Soft decision decoding gives better reliability
    over hard decision decoding
  • Stack algorithm adapted to RS codes for
    sequential soft decision decoding

15
Future Work
  • Other transmissions schemes including
    non-coherent MFSK
  • Other channel models
  • Quantize metrics to a limited number of bits

16
Acknowledgements
  • Prof. Komo for the project ideas and guidance
  • Prof. Russell and Fred Block
  • Profs. Noneaker and Xu for the program overall

17
Questions?
  • ?

18
References
  • 1 S.B. Wicker, Error Control Systems for
    Digital Communication and Storage, Englewood
    Cliffs, NJ Prentice Hall, 1995.
  • 2 Komo, J.J. and L.L. Joiner, "Fast Error
    Magnitude Evaluations for Reed-Solomon Codes,"
    Proc. 1995 IEEE International Symposium on
    Information Theory, p. 416, Sep. 1995.
  • 3 F. Jelinek, A Fast Sequential Decoding
    Algorithm Using a Stack, IBM Journal of
    Research and Development, Vol. 13, pp. 675-685,
    Nov. 1969

19
Stack Algorithm RS(7,3) Code
Write a Comment
User Comments (0)
About PowerShow.com