Publications(January 2002 - December 2002)
- T. Nishijima, "An Upper Bound on the Average Probability
of an Undetected Error for the Ensemble of Binary Expansions
of Generalized Reed-Solomon Codes," IEICE Transactions
on Fundamentals of Electronics, Communications and
Computer Sciences, Vol. J85-A No. 1, pp. 137-140, January
2002.
Abstract - We derive
an upper bound on the average probability of an undetected
error for the ensemble of binary expansions of generalized
Reed-Solomon codes and, from this bound, conclude that
the ensemble satisfies, in average, the Varshamov - Gilbert
bound as well as the expurgated bound asymptotically for
large block lengths.
- T. Nishijima, "On the Probability of an Undetected
Error for Binary Expansions of Concatenated Codes with
Generalized Reed-Solomon Outer Codes," IEICE Technical
Report, IT-2002-1, pp.1-6, May 2002.
Abstract - Concatenated
codes given by G. D. Forney, Jr. are very important codes
from practical and theoretical viewpoint. It can be shown
that binary concatenated codes exist in this class which
asymptotically meet the Varshamov - Gilbert bound. The
constructive concatenated codes are the first asymptotically
good codes. However the probability of an undetected error
for binary expansion of concatenated codes is not discussed
in the literature from both practical and theoretical
viewpoints. As the first step, by utilizing the characteristic
structure of concatenated codes, an approximately good
computation method of the probability of an undetected
error without knowing weight distributions of concatenated
codes is proposed in this paper. Since the computational
complexity of the method is at the most O(n), it
is an efficient method when investigating the capability
of error detection for a code from practical and theoretical
viewpoint. By comparing exact values with approximate
value in some examples of the codes, which are small enough
for their weight distributions to be found by computer
search, we show the efficiency of the approximate values
by the proposed method. Their values also is compared
with a upper bound on the average probability of an undetected
error for the ensemble of those codes.
>PAGE TOP
|
|
|
