My research topics in Multi-User Communications:
3.
Two-Adder with feedback
4. Optical
Orthogonal Codes
One of the papers I like very much is the paper by Cohen, Heller and Viterbi on Asynchronous Multiple Access. Together with Jeroen Keuning we calculated the capacity for an extended or M-tone signaling channel. As a hidden problem, we found that the channel capacity can not be calculated in the usual way for channels where the transition probability is a function of the input probability. This fact is not very well known in multi-user theory and leads to the incorrect assumption that Symmetric input distribution gives the optimal result for symmetric channels. We show that this is not the case.
-"On the Capacity of the Asynchronous T-User M-frequency Noiseless Multiple Access Channel," IEEE Tr. on Inf. Theory, pp. 2235-2241, November 1996, with Jeroen Keuning.
An extension can be found in the following paper. It is a result of the work together with my Ph.D. student Peter Gober.
Note on ``On the Asymptotic Capacity of a Multiple-Access
Channel'' by L. Wilhelmsson and K. Sh. Zigangirov, Probl. Peredachi Inf.,
2000, vol. 36, no. 1, pp. 21--25, Gober, P. and Han Vinck, A.J., [Probl.
Inf. Trans. (Engl. Transl.), 2000, vol. 36, no. 1, pp. 19--22.
We introduce the concept of q-ary superimposed codes.
Where do we use them?
These codes are to be used in a multi-user concept where the set of active users is small compared to the total amount of potential users.
How do we use them?
The active transmitters use signatures of length n of q-ary symbols to be transmitted over a common channel and the channel output is equal to the set of active input values.
What are the results?
- We give bounds on the cardinality of the class of
signatures as a function of the length n and the number of active users.
- Furthermore, we construct a class of codes that can
be used to uniquely determine the set of active users from the
composite signature at the channel
output.
On Superimposed Codes, in Numbers, Information and
Complexity, Ingo Althöfer, Ning
Cai, Gunter Dueck, Levon Khachatrian,Mark
S. Pinsker, Andras Sarkozy, Ingo Wegener
and Zhen Zhang (eds.), Kluwer
Academic Publishers, February 2000, pp. 325-331.
„"On
Superimposed Codes," A. J. Han. Vinck, S. Martirossian and Peter
Gober,
IEEE Information Theory
Workshop, Kruger Park, South Africa ISBN 0-7803-5268-8, pp. 118, June
1999.
3. Capacity for the
"Two-Adder" channel with feedback
After finishing my Ph.D., I visited the famous NATO school organized by
Skwirzinsky in Norwich in England. I decided to investigate some basic problems
in multi user information theory. Popular were the two-adder channel and the
network protocols. I extended and generalized the two-adder model and showed
that the total-cooperation capacity can be obtained for certain model extensions.
The switching channel was introduced by me at the Swedish-Soviet workshop as a
non-trivial two access channel. Peter vanRoose a student from Edward van der
Meulen (Leuven) wrote a Ph.D. thesis on coding for the switching channel..
-"On the capacity of the Two-User M-ary multiple access channel with feedback," IEEE Trans. on Inform. Theory, July 1985, pp. 540-543. With W. Hoeks and Karel Post.
What is an OOC?
Optical Orthogonal Codes (OOC) with low auto- and cross-correlation between code words are used to allow multi user optical communication. Code words from an OOC have constant weight w.
Why do we use OOCs?
OOCs with low correlation allow detection of transmitted code words even if more code words overlap. Furthermore, the low correlation allows easy synchronization.
Some results:
We give a construction for OOCs, with correlation 1 for any weight w. For constant weight w = 4 and correlation 2 we also give a construction. These codes have cardinality |C| = O(n**2), where n is the length of the code words.
Optical Orthogonal Code Construction with Correlation 1 and 2" Mini Workshop on Synchronization, Essen, August 2000, ISBN 90-74249-24-8, pp 8 , Samvel Martirosyan, Sosina Martirosyan and A.J. Han Vinck (IEM, Essen)
M. Stam and A.J. Han Vinck, “On Optical Orthogonal Codes,” WIC Symposium on Information Theory in the Benelux, pp. 185-191, 1998.
last modified: May 13, 1998
comments to: vinck@exp-math.uni-essen.de