Abstract
A symbol permutation invariant balanced (SPI-balanced) code over the alphabet ℤ m ={0,1,…, m–1} is a block code over ℤ 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 a SPI-balanced code into a 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. The 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≃[(m–1)/2] log m n–(1/2)[1–(1/log2π m)]m–(1/log2π m) for SPI-balanced code with k information digits and length n=k+r. For example, the first method given in the paper encodes k information digits into a SPI-balanced code of length n=k+r, with r=(m–1) logm k+O(mlog m log m k). A second method is a recursive method, which uses the first as base code, and encodes k digits into a SPI-balanced code of length n=k+r, with r≃(m–1) log m n log m [(m–1)!].
Published Version
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