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This paper proposes a fountain coding system which has lower space decoding complexity and lower decoding erasure rate than the Raptor coding systems. The main idea of the proposed fountain code is employing shift and exclusive OR to…
In this paper we survey the various erasure codes which had been proposed and patented recently, and along the survey we provide introductory tutorial on many of the essential concepts and readings in erasure and Fountain codes. Packet…
This paper considers rateless network error correction codes for reliable multicast in the presence of adversarial errors. Most existing network error correction codes are designed for a given network capacity and maximum number of errors…
In this letter, we provide the construction of repairable fountain codes (RFCs) for distributed storage systems that are information-theoretically secure against an eavesdropper that has access to the data stored in a subset of the storage…
This paper extends linear-complexity concatenated coding schemes to fountain communication over the discrete-time memoryless channel. Achievable fountain error exponents for one-level and multi-level concatenated fountain codes are derived.…
Fountain codes like LT or Raptor codes, also known as rateless erasure codes, allow to encode a message as some number of packets, such that any large enough subset of these packets is sufficient to fully reconstruct the message. It…
One key requirement for fountain (rateless) coding schemes is to achieve a high intermediate symbol recovery rate. Recent coding schemes have incorporated the use of a feedback channel to improve intermediate performance of traditional…
Fountain codes are becoming increasingly important for data transferring over dedicated high-speed long-distance network. However, the encoding and decoding complexity of traditional fountain codes such as LT and Raptor codes are still…
Luby Transform (LT) codes are a class of fountain codes that have proved to perform very efficiently over the erasure channel. These codes are rateless in the sense that an infinite stream of encoded symbols can be generated on the fly.…
A novel fountain coding scheme has been introduced. The scheme consists of a parallel concatenation of a MDS block code with a LRFC code, both constructed over the same field, $F_q$. The performance of the concatenated fountain coding…
In this paper, a transmission strategy of fountain codes over cooperative relay networks is proposed. When more than one relay nodes are available, we apply network coding to fountain-coded packets. By doing this, partial information is…
We introduce a new family of Fountain codes that are systematic and also have sparse parities. Given an input of $k$ symbols, our codes produce an unbounded number of output symbols, generating each parity independently by linearly…
Rateless/fountain codes are designed so that all input symbols can be recovered from a slightly larger number of coded symbols, with high probability using an iterative decoder. In this paper we investigate the number of input symbols that…
Fountain codes are erasure correcting codes realizing reliable communication systems for the multicast on the Internet. The zigzag decodable fountain (ZDF) code is one of generalization of the Raptor code, i.e, applying shift operation to…
The rateless and information additive properties of fountain codes make them attractive for use in broadcast/multicast applications, especially in radio environments where channel characteristics vary with time and bandwidth is expensive.…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
While network coding can be an efficient means of information dissemination in networks, it is highly susceptible to "pollution attacks," as the injection of even a single erroneous packet has the potential to corrupt each and every packet…
LT (Luby transform) codes are a celebrated family of rateless erasure codes (RECs). Most of existing LT codes were designed for applications in which a centralized encoder possesses all message blocks and is solely responsible for encoding…
An error correcting code ($\mathsf{ECC}$) allows a sender to send a message to a receiver such that even if a constant fraction of the communicated bits are corrupted, the receiver can still learn the message correctly. Due to their…
Large-scale machine learning and data mining applications require computer systems to perform massive matrix-vector and matrix-matrix multiplication operations that need to be parallelized across multiple nodes. The presence of straggling…