A new method is described which builds on Mitzenmacher’s idea of adding a different pseudo-random number to each packet to help in verification-based decoding low density codes with packet deletions or errors, or out-of-order receptions, and no sequence numbers. The new method has less decoding complexity and is applicable to any parity check code structure, not just low density codes. Performa...

This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations of repeat-accumulate codes). The transmission of the code ensembles is assumed to take place over a binary erasure channel, and the bounds refer to the asymp...

Fountain codes have demonstrated great results for the binary erasure channel and have already been incorporated into several international standards to recover lost packets at the application layer. These include multimedia broadcast/multicast sessions and digital video broadcasting on global internet-protocol. The rateless property of Fountain codes holds great promise for noisy channels. The...

<p>Erasure code has been used by more and researchers to solve the problem of efficient, reliable, fault-tolerant data storage. However, existing libraries based on erase can only run Linux platform, some them need GPU support. This paper implements a cross-platform storage library RS erasure code, PyRS, which is running CPU without support developed in Python. PyRS uses Vandermonde matri...

An instance of the framework for cryptographic security enhancement symmetric-key encryption employing a dedicated error correction encoding is addressed. The main components proposal are: (i) coding and (ii) use simulator noisy channel. proposed designed binary erasure channel where at most one bit erased in each codeword byte. has been evaluated traditional scenario we consider advantage an a...

In this paper, we introduce a new family of linear block codes, which we refer to as Partial Reed Solomon (PRS) Codes. These codes are specifically designed and optimized for real-time multimedia communication over packet-based erasure channels. Based on the constraints and flexibilities of real time applications, we define a performance measure, message throughput ( m τ ), which is suitable fo...

The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and number of decoding iterations to achieve a certain residual erasure probability for complexity metric. We first propose a quite accurate approximation of the numb...

We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits which is the minimal number for the present task (see reference [1]). The encoding and error recovery operat...

When a data ow contains information of di erent priority levels, it is natural to try to o er an unequal protection where the high priority data bene ts from a higher protection than the rest of data. In this work we focus on the erasure channel", for instance the Internet where the UDP/IP datagram integrity is guaranteed by the physical layer FCS (or CRC) and the UDP checksum. In this context ...

We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete-time random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully...