For an [n, k, d] (r, δ)-locally repairable codes ((r, δ)-LRCs) , its minimum distance d satisfies the Singleton-like bound. The construction of optimal δ)-LRC, attaining this bound, is important research problem in recent years for thier applications distributed storage systems. In letter, we use Reed-Solomon to construct two classes δ)-LRCs. LRCs are given by evaluations multiple polynomials d...

We present Kovalenko’s full-rank limit as a tight lower bound for decoding error probability of LDPC codes and LT codes over BEC. From the limit, we derive a full-rank overhead as a lower bound for stable overheads for successful maximum-likelihood decoding of the codes.

Diversity is a powerful means to increase the transmission performance of wireless communications. For the case of fountain codes relaying, it has been shown previously that introducing diversity is also beneficial since it counteracts transmission losses on the channel. Instead of simply hop-by-hop forwarding information, each sensor node diversifies the information flow using XOR combinations...

A new approach for estimating the Decoding ErrorProbability (DEP) of LT codes with dense rows is derived by using the conditional Kovalenko’s rank distribution. The estimate by the proposed approach is very close to the DEP approximated by Gaussian Elimination, and is significantly less complex. As a key application, we utilize the estimates for obtaining optimal LT codes with dense rows, whose...

LDPC codes and digital fountain techniques have received significant attention from both academics and industry in the past few years. There have also been extensive interests in applying LDPC code techniques to distributed storage systems such as cloud data storage in recent years. This paper carries out the theoretical analysis on the feasibility and performance issues for applying LT codes t...

We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to each submatrix. For this scheme, we prove that up to a given number of partitions the communication load and the computational delay (not including the encoding...

We consider the use of extrinsic information transfer charts for the design of Luby Transform (LT) codes over the binary erasure channel (BEC). In particular, we formulate an optimization problem to determine asymptotically good checknode degree distributions in terms of decoder overhead. We further propose a modified encoding scheme that maximizes the minimum variable-node degree, thus optimiz...

Following fast growth of cellular networks, more users have drawn attention to the contradiction between dynamic user data traffic and static data plans. To address this important but largely unexplored issue, in this paper, we design a new data plan sharing system named Prometheus, which is based on the scenario that some smartphone users have surplus data traffic and are willing to help other...

A Digital Fountain is an approach used to provide reliability in multicast networks without the use of receiver initiated packet retransmissions. Prior work to Digital Fountain has shown that use of receiver initiated retransmissions to recover lost data is unscalable in multicast networks and the impact is significant in lossy networks. Instead, like many other techniques that transmit redunda...