arXiv subjects

Jinping Fan

Publications and source records attributed to Jinping Fan.

2 recordsLinked to original sources

arXiv2020

Signature codes for weighted binary adder channel and multimedia fingerprinting

In this paper, we study the signature codes for weighted binary adder channel (WbAC) and collusion-resistant multimedia fingerprinting. Let $A(n,t)$ denote the maximum cardinality of a $t$-signature code of length $n$, and $A(n,w,t)$ denote the maximum cardinality of a $t$-signature code of length $n$ and constant weight $w$. First, we derive asymptotic and general upper bounds of $A(n,t)$ by relating signature codes to $B_t$ codes and bipartite graphs with large girth respectively, and also show the upper bounds are tight for certain cases. Second, we determine the exact values of $A(n,2,2)$ and $A(n,3,2)$ for infinitely many $n$ by connecting signature codes with $C_4$-free graphs and union-free families, respectively. Third, we provide two explicit constructions for $t$-signature codes which have efficient decoding algorithms and applications to two-level signature codes. Furthermore, we show from the geometric viewpoint that there does not exist any binary code with complete traceability for noisy WbAC and multimedia fingerprinting. A new type of signature codes with a weaker requirement than complete traceability is introduced for the noisy scenario.

cs.IT↗

arXiv2020

Strongly separable matrices for nonadaptive combinatorial group testing

In nonadaptive combinatorial group testing (CGT), it is desirable to identify a small set of up to $d$ defectives from a large population of $n$ items with as few tests (i.e. large rate) and efficient identifying algorithm as possible. In the literature, $d$-disjunct matrices ($d$-DM) and $\bar{d}$-separable matrices ($\bar{d}$-SM) are two classical combinatorial structures having been studied for several decades. It is well-known that a $d$-DM provides a more efficient identifying algorithm than a $\bar{d}$-SM, while a $\bar{d}$-SM could have a larger rate than a $d$-DM. In order to combine the advantages of these two structures, in this paper, we introduce a new notion of \emph{strongly $d$-separable matrix} ($d$-SSM) for nonadaptive CGT and show that a $d$-SSM has the same identifying ability as a $d$-DM, but much weaker requirements than a $d$-DM. Accordingly, the general bounds on the largest rate of a $d$-SSM are established. Moreover, by the random coding method with expurgation, we derive an improved lower bound on the largest rate of a $2$-SSM which is much higher than the best known result of a $2$-DM.

math.CO↗