Message
I started my academic life in
the theory of algebraic error-correcting codes and its applications,
and have recently been interested also in information theory.
For the past 15 years I have been studying on the asymptotic
capability of algebraic error-correcting codes, which are
able to prove Shannon's fundamental theorem for noisy channel
not by random coding technique but by constructive coding.
Now I would like to study on Shannon's channel coding theorem
from the viewpoints of both the reliability function in
information theory and the asymptotic distance ratio in
coding theory. As the final purpose (dream) in my academic
life, I will try to challenge the fundamental problems to
determine the reliability function for low rates and to
clarify relationship between the reliability function and
the asymptotic distance ratio.
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Publications(January 2001 - December 2001)
- T. Nishijima, "The distance ratio for the ensemble
of binary expanded generalized Reed-Solomon codes asymptotically
meets Varshamov -Gilbert bound," Proceedings of The
35th Annual Conference on Information Science and Systems
Vol. I, p. 141, The Johns Hopkins University, Baltimore,
Maryland USA, March 2001.
Abstract - We get an
upper bound on the average probability of undetected error
for the ensemble of binary expanded generalized Reed-Solomon
codes. From this bound, we simultaneously show that the
asymptotic distance ratio for this ensemble meets the
Varshamov-Gilbert bound and this ensemble satisfies the
expurgated bound.
- T. Nishijima, "An upper bound on the average probability
of an undetected error for the ensemble of binary expansions
of concatenated codes with generalized Reed-Solomon outer
codes," IEICE Technical Report, IT-2001-35,
pp.1-6, September 2001.
Abstract - We derive
an upper bound on the average probability of an undetected
error for the ensemble of binary expansions of concatenated
codes with generalized Reed-Solomon outer codes by applying
the technique of proof to get an upper bound on the average
probability of an undetected error for the ensemble of
all binary linear systematic codes. It is shown in this
paper that the average capacity for the ensemble of binary
expansions of concatenated codes with generalized Reed-Solomon
outer codes is poorer than that for all systematic binary
linear block codes.
- T. Nishijima, "An upper bound on the average probability
of an undetected error for the ensemble of binary expansions
of concatenated codes with generalized Reed-Solomon outer
codes," Proceedings of The 7th International Conference
on Distributed Multimedia Systems, pp. 526-529, Tamkang
University, Taipei, Taiwan, September 2001.
Abstract - We derive
an upper bound on the average probability of an undetected
error for the ensemble of binary expansions of concatenated
codes with generalized Reed-Solomon outer codes by applying
the technique of proof to get an upper bound on the average
probability of an undetected error for the ensemble of
all binary linear systematic codes.
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