Pearson Codes

The Pearson distance has been advocated for improving the error performance of noisy channels with unknown gain and offset. The Pearson distance can only fruitfully be used for sets of $q$-ary codewords, called Pearson codes, that satisfy specific properties. We will analyze constructions and properties of optimal Pearson codes. We will compare the redundancy of optimal Pearson codes with the redundancy of prior art $T$-constrained codes, which consist of $q$-ary sequences in which $T$ pre-determined reference symbols appear at least once. In particular, it will be shown that for $q\le 3$ the $2$-constrained codes are optimal Pearson codes, while for $q\ge 4$ these codes are not optimal.Comment: 17 pages. Minor revisions and corrections since previous version. Author biographies added. To appear in IEEE Trans. Inform. Theor

Polarity-Balanced Codes

Abstract—Balanced bipolar codes consist of sequences in which the symbols ‘−1 ’ and ‘+1 ’ appear equally often. Several generalizations to larger alphabets have been considered in literature. For example, for the q-ary alphabet {−q + 1, −q + 3,..., q − 1}, known concepts are symbol balancing, i.e., all alphabet symbols appear equally often in each codeword, and charge balancing, i.e., the symbol sum in each codeword equals zero. These notions are equivalent for the bipolar case, but not for q> 2. In this paper, a third perspective is introduced, called polarity balancing, where the number of positive symbols equals the number of negative symbols in each codeword. The minimum redundancy of such codes is determined and a generalization of Knuth’s celebrated bipolar balancing algorithm is proposed. I

On the Number of Encoder States of a Type of RLL Codes

[6] J. I. Fujii, “A trace inequality arising from quantum informatio

Constructions and Properties of Block Codes for Partial-Response Channels

game-theoretic aspect of the competitively optimal coding, and Prof