Eindhoven University of Technology MASTER Shannon strategieen voor het and-channel van Dorsselaer, E.L.M.E. Award date: 1982 Link to publication Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain
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Eindhoven University of Technology
MASTER
Shannon strategieen voor het and-channel
van Dorsselaer, E.L.M.E.
Award date:1982
Link to publication
DisclaimerThis document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Studenttheses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the documentas presented in the repository. The required complexity or quality of research of student theses may vary by program, and the requiredminimum study period may vary in duration.
General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain
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X 1= O. 6705838240 00 X 1'"' O. 669Tt:',J17'71.l 00
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drempels uit fig.5.18 drempels uit fig.5.19
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X 7= 0.6648389280 00 X 7= O. 5438284740 00
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X 9= 0.150693117D 00 X 9"'- O. 1679181550 00
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X 11= 0.9736898500 00 X 11= O. 9948362990 00
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X 13= 0.8718926090 00 X 13= O. 9541461850 00
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X 17= 0.8358444520 00 X 17"- 0.8910358830 00
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X 24= O. 1668412850-09 X 24= 0.4180754500-11
X 25= 0.3420347000 00 X 25= O. 1679181. 550 00
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drempels uit figS.20 drempels uit fig.S. 21
89
X 1.. O. 6905053850 00X 1'" 0.6925268170 00
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X 3= O. 3614227690 00X 3= O. 5351540970 00
X 4= O. 9998080650 00X 4 .. 0.9875710280 00
X 5= 0.8624989730 00X 5= 0.8915187570 00
X 6= 0.9283244170 00X 6= 0.831917739D 00
X 7= O. 5959385540 00X 7= O. 5876543890 00
X 8= O. 5047768290-01X 8= 0.2183011660 00
X 9.. O. 1402043350 00X 9= 0.3764928720 00
X 10= O. 1000000000 01X 10=- O. 1000000000 01
X 11= O. 9849827280 00X 11=- O. 9503482920 00
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X 13=- 0.9240216720 00X 13= 0.8915189480 00
X 14= 0.8123933960 00X 14= O. 8548878040 00
X 15= 0.8201924030 00X 15= O. 8915187560 00
X 16= 0.9501078080 00X 16= O. 8738478150 00
X 17= 0.8555571940 00X 17= O. 7899882210 00
X 18... 0.9283244170 00X 18= O. 7899898470 00
X 19= 0.663759469D 00X 19=- 0.6499243850 00
X 20= O. 5267273870 00X 20= 0.5351540990 00
X 21= 0.5327781730 00X 21= 0.5351540970 00
X 22= O. 2696693740 00X 22= 0.4712381850 00
X 23= 0.4080471110-09X 23=- O. 4339467651>-09
X 24= O. 5047768280-01X 24= O. 367776~300-08
X 25= O. 2920315710 00X 25= 0.4881125230 00
X 26= 0.3459106780-09X 26= O. 2648660900 00
X 27= 0.4000000000-12X 27= O. 264865765D 00
uit fig.5.22 drempels uit fig.5.23drempels
90
'..
91
"
X 1-= O. 6905393600 00 X 1= O. 693115;></70 00
X 2= 0.9378141710 00 X 2"" 0.9469842710 00
X 3= 0.3878659390 00 X 3= O. 375~/830600 00
X 4= O. 9673113170 00 X 4'" O. 977208~200 00
X 5= 0.8771320310 00 X 5= O. 87652b2240 00
X 6= 0.9224772260 00 X 6= O. 9274724720 00
X 7"" 0.6130194480 00 X 7'" O. 5999308510 00
X 8 .. 0.3878659370 00 X 8= 0.3759827020 00
X 9= 0.1421142780 00 X 9,.- O. 1426877670 00
X 10= O. 1000000000 01 X 10.. O. 9921065570 00
X 11= 0.9673113170 00 X 11= 0.9469842790 00
X 12= 0.9585651370 00 X 12= 0.9682464620 00
X 13- 0.898077631D 00 X 13= 0.9290479380 00
X 14= 0.8771320310 00 X 14= 0.8366292080 00
X 15= 0.8218088500 00 X 15= 0.8221463380 00
X 16= 0.9319062540 00 X 16= 0.9469842710 00
X 17= 0.8546960990 00 X 17= 0.8550053270 00
X 18= 0.922477226D 00 X 18= O. 927472472D 00
X 19- 0.6460483690 00 X 19= 0.6685483550 00
X 20= 0.6130194480 00 X 20= O. 5452842130 00
' ..........., X 21= O. 5462636070 00" X 21= O. 5335319870 00
X 22= 0.3878659380 00 X 22= 0.3759830600 00
X 23= O. 5737724080-08 X 23= 0.2796439990 00
X 24= 0.2728711860 00 X 24= 0.2645142400 00
X 25= 0.3158871840 00 X 25= 0.3037720310 00
X 26= O. 127279999D 00 X 26= O. 1442450360-09
X 27'" 0.6391825860-11 X 21'= O. 4000000000-12
drempels uit fig. 5.26 drempe-ls uit fig.5.27
92
.I 1
01 1 1I
I 0000 I 0100I
I I0001.. i"'- - - - - - - ... -.
I
_. - --Jr ----- I
II
0101 I 01 10I 0010 0000 1
I ---_ .. _---.,I
I, I,
I I l
rnl nm-- ~1-n-r - - J I,I - -- ---
l • I rO-O~~- I 0000 I, 001 1 00 t 1I I II I •~---_.
I
I I1I1
~----L\_- ------ .-I
II
III I
I II I
t--- K3
1-- --
1
fig.5.28 beste opdeling voo.r K4
R = 0.6208791
1
o
SLOTBESCHOUWING.
Dit verslag geeft een overzicht van verschillende
methoden welke gebruikt kunnen worden am het
capaciteitsgebied van het and-channel nader te bepalen.
De methode van de Shannon-strategieen is hierbij de
minst geschikte voor numerieke berekeningen.
De methode van het and-chgnnel als beslissingsprobleem
of het opdelen van een vierkant, levert resultaten op
welke buiten het inner-bound gebied liggen.
Vanwege de vele maxima die optreden wordt oak deze
methode voor hog ere orden van het afgeleide kanaal
minder gsschikt. Het ziet er niet naar uit dat er op deze
manier rate-pairs gevonden kunnen worden die de rate van
het Schalkwijk coding-schema benaderen.
WeI kunnen de verkregen opdelingen van het vierkant
nader geanalyseerd worden.
Het blijft echter de vraag of de inzichten die hier-mee
verkregen worden representatief zijn voor hog ere orden
van het afgeleide kanaal.
Een andere mogelijkheid is am coding-schema's te zoeken
in de vorm van Markov-chains. Dit is zeker geen eenvoudige
opgave. In het coding-schema van hoofdstuk 4 kunnen
echter nag weI een paar extra vrijheidsgraden worden
,verwerkt, door minder aannamen te doen.
REFERENCES
[1] C~E. Shannon, "TwoTway communication channels",
Proc. 4th Berkeley Symp. Math. Statist. and Prob,
vol. 1, pp. 611-644, 1961.
~1 J.P.M. Schalkwijk, "The Binary Multiplying Channel
A Coding Schema that Operates Beyond Shannon's
Innerbound Region", IEEE TraQs. Inform. Theory,
vol. IT-2B, pp 107-110, jan 1982.
~] J.P.M. Schalkwijk, "On a Nontrivial Extension of an
Achievable Rate Region for the Binary Multiplying
Channel", to be pUblished in IEEE Trans. Inform.
Theory.
~] G. Dueck,"The Capacity Region of the Two-way Channel
can Exceed the Inner Bound", Inform. Contr., vol 40
pp. 258-266, Ma~ 1979.
~] Do Slepian and J.K.Wolf," ~oiseless Coding of
Correlated Information Sources", IEEE Trans. Inform.
Theory, vol. I~-19, ·pp.471-480, July 1973.
~] R.E. Blahut," Computation of Channel Capacity and
Rate-Distortion Functions", IEEE Trans. Inform.
Theory, vol. IT-18, pp.460-473, July 1972.
~].M. Horstein," Sequential Transmission using Noiseless
Feedback", IEEE Trans. Inform. Theory, vol. IT-9,
pp.136-143, July 1963.
~J J.P.M. Schalkwijk," A Class of Simple and Opti~al
Strategies for Block Coding on the Binary Symmetric
Channel with Noiseless Feedback", IEEE Trans. Inform.
Theory, vol. IT-17,pp.283-287, May 1971.
DANKWOORD
Het is hier op z1Jn plaats am een dankwoord te richten
aan aIle leden van de vakgroep informatie-theorie.
Dit vanwege de collegiale omgang en het feit dat men
op elk moment be reid is am tijd ter beschikking te stellen