Efficient m-ary balanced codes which are invariant under symbol permutation

A symbol permutation invariant balanced (SPI-balanced) code over the alphabet Zopf
_m
= {0, 1, ..., m - 1} is a block code over Zopf
_m
such that each alphabet symbol occurs as many times as any other symbol in every codeword. For this reason, every permutation among the symbols of the alphabet changes an SPI-balanced code into an SPI-balanced code. This means that SPI-balanced words are "the most balanced" among all possible m-ary balanced word types and this property makes them very attractive from the application perspective. In particular, they can be used to achieve m-ary DC-free communication, to detect/correct asymmetric/unidirectional errors on the m-ary asymmetric/unidirectional channel, to achieve delay-insensitive communication, to maintain data integrity in digital optical disks, and so on. This paper gives some efficient methods to convert (encode) m-ary information sequences into m-ary SPI-balanced codes whose redundancy is equal to roughly double the minimum possible redundancy r
_min
. It is proven that r
_min
sime [(m - 1)/2]log
_m
n - (1/2)[1 - (1/log
_2pi
m)]m - (1/log
_2pi
m) for any code which converts k information digits into an SPI-balanced code of length n = k + r. For example, the first method given in the paper encodes k information digits into an SPI-balanced code of length n = k + r, with r = (m - 1) log
_m
k + O(m log
_m
log
_m
k). A second method is a recursive method, which uses the first as base code and encodes k digits into an SPI-balanced code of length n = k + r, with r sime (m - 1) log
_m
n - log
_m
[(m - 1)!]