We introduce LT codes, the first rateless erasure codes that are very efficient as the data length grows.

This paper introduces a new scheme of LT codes, named multiple configurations. In multiple configurations LT codes (MC-LT codes), multiple sets of output symbols are simultaneously provided to receivers for recovering the source data. Each receiver, without the need to send information back to the sender, is capable of receiving the output symbols generated by some configuration chosen accordin...

LT codes, the first universal erasure-correcting codes, have near-optimal performance over binary erasure channels for any erasure probability, but exhibit high bit error rate and error floor over the noisy channels. This paper investigated the performance of LT codes over the additive white Gaussian noise channels. We designed the systematic LT codes through reconstructing the bipartite graph ...

Erasure codes are a type of encoding of data, generally for transmission over a lossy medium, that survive deletions (erasures) of parts of the message.1 They are especially useful for transmission of data across a medium or network that can drop packets of data, when it is impractical for the receiver to be in constant communication with the sender. Given a file with K blocks, the sender gener...

Luby Transform (LT) codes are more important in communication applications due to the characteristics of fast encoding/decoding process, and low complexity. However, LT codes are optimal only when the number of input symbols is close to infinity. Some researches modified the degree distribution of LT codes to make LT codes suitable for short symbol length. In this article, we propose an optimal...

Fountain codes were introduced to provide higher reliability, lower complexities, and more scalability for networks such as the Internet. In this thesis, we study LubyTransform (LT) codes which are the first realization of Fountain codes. In the LT codes, a sparse random factor graph is dynamically generated on both the encoder and decoder sides of the communications channel. The graph is gener...

In this paper, we introduce Falcon codes, a class of authenticated error correcting codes that are based on LT codes [23] and achieve the following properties, for the first time simultaneously: (1) with high probability, they can correct adversarial symbol corruptions in the encoding of a message, and (2) they allow for very efficient encoding and decoding times, even linear in the message len...

Rateless codes over a binary erasure channel (BEC) provide successful transmission independent of the erasure probability. Luby Transform (LT) codes and raptor codes are examples of rateless codes over a BEC. For successful decoding, LT codes require either a large overhead at linear complexity, or capacity-approaching overheads with nonlinear complexity. When overhead is low at linear complexi...

This paper concerns application of feedback in LT codes. The considered type of feedback is acknowledgments, where information on which symbols have been decoded is given to the transmitter. We identify an important adaptive mechanism in standard LT codes, which is crucial to their ability to perform well under any channel conditions. We show how precipitate application of acknowledgments can i...

Faculty of Electrical Engineering, Mathematics and Computer Science CAS-MS-2006-02 The concept of Network-on-Chip (NoC) is becoming a main trend in the area of System-on-Chip (SoC) design. In NoC communications the transmission data may have errors raised by noises or technologies. Forward-Error-Correction (FEC) schemes can be used to improve the systems’ reliability by detecting and correcting...