This paper investigates the use of redundancy and self repairing against node failures indistributed storage systems using a novel non-MDS erasure code. In replication method, accessto one replication node is adequate to reconstruct a lost node, while in MDS erasure codedsystems which are optimal in terms of redundancy-reliability tradeoff, a single node failure isrepaired after recovering the ...

This application note focuses on the design of an erasure codec using the Xilinx® Vivado® High-Level Synthesis (HLS) tool, which takes the source code in C programming language and generates highly efficient synthesizable Verilog or VHDL code for a Kintex® UltraScaleTM FPGA. When there is a need to change erasure code parameters, for example, the generator matrix definition or erasure code rate...

Classical unequal erasure protection schemes split the data to be protected into classes which are encoded independently. The unequal protection scheme presented in this document is based on an erasure code which encodes all the data together according to the existing dependencies. A simple algorithm generates dynamically the generator matrix of the erasure code according to the structure of th...

The average bit erasure probability of a binary linear code ensemble under maximum a-posteriori probability (MAP) decoding over binary erasure channel (BEC) can be calculated with the average support weight distribution of the ensemble via the EXIT function and the shortened information function. In this paper, we formulate the relationship between the average bit erasure probability under MAP ...

In this paper we address the problem of decoding 2D convolutional codes over the erasure channel. In particular, we present a procedure to recover bursts of erasures that are distributed in a diagonal line. To this end we introduce the notion of balls around a burst of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main...

Packet erasure codes are today a real alternative to replication in fault tolerant distributed storage systems. In this paper, we propose the Mojette erasure code based on the Mojette transform, a formerly tomographic tool. The performance of coding and decoding are compared to the Reed-Solomon code implementations of the two open-source reference libraries namely ISA-L and Jerasure 2.0. Result...

We consider the following generalization of an (n, k) MDS code for application to an erasure channel with additive noise. Like an MDS code, our code is required to be decodable from any k received symbols, in the absence of noise. In addition, we require that the noise margin for every allowable erasure pattern be as large as possible and that the code satisfy a power constraint. In this paper ...

In this paper we address the problem of decoding 2D convolutional codes over the erasure channel. To this end we introduce the notion of balls around a burst of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main idea is to reduce the decoding problem of 2D convolutional codes to a problem of decoding a set of associate...

In this paper we extend previous results on distributed LT codes and focus on the frame erasure rate performance of the corresponding block codes with fixed rate. Specifically, we address modified LT (MLT) codes which resemble LT codes in both structure and performance. First, an MLT code construction scheme for four sources communicating with a single sink via a common relay is presented. Then...

Information Dispersal Algorithms (IDAs) have been widely applied to reliable and secure storage and transmission of data files in distributed systems. An IDA is a method that encodes a file F of size L = |F | into n unrecognizable pieces F1, F2, · · · , Fn, each of size L/m (m < n), so that the original file F can be reconstructed from any m pieces. The core of an IDA is the adopted non-systema...