Punctured Bent Function Sequences for Watermarked DS-CDMA

Abstract

In this letter, we investigate the effect of inserting some randomly generated watermarking chips into known spreading sequences in terms of periodic correlations; moreover, we give two design criteria for good watermarked sequences in the sense of: 1) reducing the average correlation value and 2) minimizing the variance of correlations. For $n=2m$ with even $m$ , we propose a set of $2^{m-1}$ punctured bent function sequences of length $2^{n}-1$ punctured by the Singer difference set. The maximum non-trivial correlation magnitude of the proposed set turns out to be $2^{m}+1$ , which is asymptotically two times the Welch bound.