arXiv subjects

Siyi Yang

Publications and source records attributed to Siyi Yang.

21 records · Page 2Linked to original sources

arXiv2020

Theoretical Bounds and Constructions of Codes in the Generalized Cayley Metric

Permutation codes have recently garnered substantial research interest due to their potential in various applications including cloud storage systems, genome resequencing and flash memories. In this paper, we study the theoretical bounds and constructions of permutation codes in the generalized Cayley metric. The generalized Cayley metric captures the number of generalized transposition errors in a permutation, and subsumes previously studied error types, including transpositions and translocations, without imposing restrictions on the lengths and positions of the translocated segments. Relying on the breakpoint analysis proposed by Chee and Vu, we first propose a coding scheme that is order-optimal albeit not constructive based on this method. We then develop another construction of permutation codes in the generalized Cayley distance. This scheme is both explicit and systematic. We also prove the existence of order-optimal systematic codes and offer a concrete construction based on this method. For the generalized Cayley metric, we prove that our coding schemes have less redundancy than the existing codes based on interleaving when the codelength is sufficiently large and the number of errors is relatively small.

cs.IT↗

arXiv2019

Hierarchical Coding to Enable Scalability and Flexibility in Heterogeneous Cloud Storage

In order to accommodate the ever-growing data from various, possibly independent, sources and the dynamic nature of data usage rates in practical applications, modern cloud data storage systems are required to be scalable, flexible, and heterogeneous. Codes with hierarchical locality have been intensively studied due to their effectiveness in reducing the average reading time in cloud storage. In this paper, we present the first codes with hierarchical locality that achieve scalability and flexibility in heterogeneous cloud storage using small field size. We propose a double-level construction utilizing so-called Cauchy Reed-Solomon codes. We then develop a triple-level construction based on this double-level code; this construction can be easily generalized into any hierarchical structure with a greater number of layers since it naturally achieves scalability in the cloud storage systems.

cs.IT↗

arXiv2017

On the Polynomial Parity Argument Complexity of the Combinatorial Nullstellensatz

The complexity class PPA consists of NP-search problems which are reducible to the parity principle in undirected graphs. It contains a wide variety of interesting problems from graph theory, combinatorics, algebra and number theory, but only a few of these are known to be complete in the class. Before this work, the known complete problems were all discretizations or combinatorial analogues of topological fixed point theorems. Here we prove the PPA-completeness of two problems of radically different style. They are PPA-Circuit CNSS and PPA-Circuit Chevalley, related respectively to the Combinatorial Nullstellensatz and to the Chevalley-Warning Theorem over the two elements field GF(2). The input of these problems contain PPA-circuits which are arithmetic circuits with special symmetric properties that assure that the polynomials computed by them have always an even number of zeros. In the proof of the result we relate the multilinear degree of the polynomials to the parity of the maximal parse subcircuits that compute monomials with maximal multilinear degree, and we show that the maximal parse subcircuits of a PPA-circuit can be paired in polynomial time.

cs.CC↗