We present a linear time probabilistic erasure code with the following properties. The encoding algorithm produces cn letters from an n letter message. The decoding algorithm is able with high probability to reconstruct the message from any set of (1+ ǫ)n letters. Alon and Luby [5, 6] simultaneously developed a deterministic version but their running time is O(ǫ−4n) instead of our O(ǫ−1 ln(ǫ)n)...

We propose an adaptive redundancy control method for erasure-code-based real-time data transmission over the Internet. The loss rate is an important quality of service (QoS) parameter for real-time data transmission. However, real-time data transmission over best-effort networks, such as the Internet, suffers from a frequent packet loss due to traffic congestion. Erasure-code-based loss recover...

Given two versions of a file, a current version located on one machine and an outdated version known only to another machine, the remote file synchronization problem is how to update the outdated version over a network with a minimal amount of communication. In particular, when the versions are very similar, the total data transmitted should be significantly smaller than the file size. In this ...

We consider a decoder with an erasure option and a variable size list decoder for channels with non-casual side information at the transmitter. First, universally achievable error exponents are offered for decoding with an erasure option using a parameterized decoder in the spirit of Csiszár and Körner’s decoder. Then, the proposed decoding rule is generalized by extending the range of its para...

It is well known that erasure coding can be used in storage systems to efficiently store data while protecting against failures. Conventionally, the design of erasure codes has focused on the tradeoff between redundancy and reliability; under this criterion, an Maximum Distance Separable (MDS) code is optimal. However, practical storage systems call for additional considerations. In particular,...

The dune-functions Dune module introduces a new programmer interface for discrete and non-discrete functions. Unlike the previous interfaces considered in the existing Dune modules, it is based on overloading operator(), and returning values by-value. This makes user code much more readable, and allows the incorporation of newer C++ features such as lambda expressions. Run-time polymorphism is ...

An (n, c, `, r)-erasure code consists of an encoding algorithm and a decoding algorithm with the following properties. The encoding algorithm produces a set of `-bit packets of total length cn from an n-bit message. The decoding algorithm is able to recover the message from any set of packets whose total length is r, i.e., from any set of r/` packets. We describe erasure codes where both the en...

C++ is a multi-paradigm language. The two main paradigms in C++ are object-oriented programming and generic programming. Many real-world C++ software projects use these two paradigms side by side. This creates considerable tension due to the fact that object-oriented programming is largely based on the judicious choice of types and hierarchies, while generic programming tends to cause an abunda...

This letter considers an iterative decoding algorithm for non-binary linear block codes in which erasure and error decoding is performed for input words given by the sums of a hard-decision received sequence and given test patterns. We have proposed a new selection method of test patterns for the iterative decoding algorithm. Simulation results have shown that the decoding algorithm with test p...

To reduce storage overhead, cloud file systems are transitioning from replication to erasure codes. This process has revealed new dimensions on which to evaluate the performance of different coding schemes: the amount of data used in recovery and when performing degraded reads. We present an algorithm that finds the optimal number of codeword symbols needed for recovery for any XOR-based erasur...