相关论文: A High-Rate MSR Code With Polynomial Sub-Packetiza…
We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature that employ trace polynomials. The Reed-Solomon codes are over $\mathbb{F}_{q^\ell}$ and have…
The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer…
In this paper, we propose two new constructions of exact-repair minimum storage regenerating (exact-MBR) codes. Both constructions obtain the encoded symbols by first treating the message vector over GF(q) as a linearized polynomial and…
We achieve new results on skew polynomial rings and their quotients, including the first explicit example of a skew polynomial ring where the ratio of the degree of a skew polynomial to the degree of its bound is not extremal. These methods…
An erasure code is said to be a code with sequential recovery with parameters $r$ and $t$, if for any $s \leq t$ erased code symbols, there is an $s$-step recovery process in which at each step we recover exactly one erased code symbol by…
We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the…
In this paper, a new repair scheme for a modified construction of MDS codes is studied. The obtained repair scheme has optimal bandwidth for multiple failed nodes under the cooperative repair model. In addition, the repair scheme has…
We consider a set up where a file of size M is stored in n distributed storage nodes, using an (n,k) minimum storage regenerating (MSR) code, i.e., a maximum distance separable (MDS) code that also allows efficient exact-repair of any…
For an $(n,k,\ell)$ MDS array code over $\mathbb{F}_q$, how small can the repair bandwidth and repair I/O be under linear exact repair? We study this question in the regime where the field size $q$, the redundancy $r=n-k$, and the…
A basic problem for the constant dimension subspace coding is to determine the maximal possible size A_q (n, d, k) of a set of k-dimensional subspaces in Fnq such that the subspace distance satisfies d(U, V )> or =d for any two different…
MRD codes are maximum codes in the rank-distance metric space on $m$-by-$n$ matrices over the finite field of order $q$. They are diameter perfect and have the cardinality $q^{m(n-d+1)}$ if $m\ge n$. We define switching in MRD codes as…
We consider multiple description coding for the Gaussian source with K descriptions under the symmetric mean squared error distortion constraints, and provide an approximate characterization of the rate region. We show that the rate region…
Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure correcting codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes with local regeneration where each local code is a…
We present the construction of a family of erasure correcting codes for distributed storage that achieve low repair bandwidth and complexity at the expense of a lower fault tolerance. The construction is based on two classes of codes, where…
An $(m,n,a,b)$-tensor code consists of $m\times n$ matrices whose columns satisfy `$a$' parity checks and rows satisfy `$b$' parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in…
Maximum rank distance codes denoted MRD-codes are the equivalent in rank metric of MDS-codes. Given any integer $q$ power of a prime and any integer $n$ there is a family of MRD-codes of length $n$ over $\FF{q^n}$ having polynomial-time…
In network communication, the source often transmits messages at several different information rates within a session. How to deal with information transmission and network error correction simultaneously under different rates is introduced…
We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent "Polynomial code" constructions in recovery threshold, i.e., the required number of successful workers. When $m$-th fraction of…
In a distributed storage systems (DSS), regenerating codes are used to optimize bandwidth in the repair process of a failed node. To optimize other DSS parameters such as computation and disk I/O, Distributed Replication-based Simple…
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…