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The theory and technology of error correcting codes have been
developed in the last fifty years for error free transmission of
messages or strings of symbols over electronic media which
introduces disturbances or errors into the message. Thus it is of
interest of note that several millennia ago error correcting
code-like procedures were developed for chanting the Rig Veda
Samhita, the Sacred Sanskrit text of the Hindus so that the
complete text even after oral transmission over several millennia
has not been corrupted at all except for one syllable in a single
verse out of about ten thousand verses [1]. The key idea behind the special chanting methods called as
Vikratis and modern error
correcting codes is same namely the use of encoder and decoder.
The modern error correcting methods are based on the advanced
mathematical concepts such as group theory. The sages seem to have
arrived at similar results purely by intuition. Specifically
consider the correct preservation of the chanting of one verse M
consisting of m words. The Vikrati
will generate another verse M' based on the words of M having many
more words, typically 4 m or more.
Let the verse O be the corrupted version of M', the version
recited by a chanter who makes unconscious errors. Applying
mentally the decoder idea - reverse of the encoder idea - to the
corrupted output of O yields the correct verse M under appropriate
conditions. Alternatively another person who is familiar with the
decoder and hears the output O can suggest the correction. The
sages were very much aware of the trade off between the redundancy
in the code quantified by the length of M' versus the error.
Since there are many different types of errors, the sages realized
that only one encoder or vikrati
is not enough. There are eight families of
Vikratis each having many members. Using all these
methods in totality results in the almost zero error
feature quoted earlier. We focus in
this paper on one particular procedure namely
Krama-maala Vikrati.
We also mention the error detection schemes - not error correcting
- applicable to ordinary chanting of the verses without involving
the elaborate vikrati.
The appendix has the original description of the two
vikratis in ancient texts in
Sanskrit with English transliteration and their translations. |
