A parallel adaptive version of the block-based Gauss-Jordan algorithm

Abstract

Abstract

Fast Parallel Implementation for Random Network Coding on Embedded Sensor Nodes

“…Note that, however, the original data only can be recovered and decoding process can be finished at the arrival of the last data even though such progressive decoding is used. Conventional parallelized Gauss-Jordan elimination algorithms such as parallel adaptive Gauss-Jordan algorithm [18] and other related algorithms such as parallel matrix inversion [19] and parallel LU decomposition [20] require the entire data before starting the decoding process and thus will incur additional decoding latency on the receiver compared to the progressive decoding. Park et al also have proposed efficient parallelized progressive network coding algorithm with dynamic partitioning algorithms for multicore CPUs [5].…”

Benefits of using parallelized non-progressive network coding

“…The evaluation of the result is performed on dual core processors or single core using SMT. Melab et al (2000) have proposed another method, a blockwise implementation of parallel Gauss-Jordan elimination. Basically blockwise algorithm implies loop transformations, which results in deeper loops.…”

“…In this section we present parallel blockwise Gauss-Jordan elimination (Melab et al, 2000;Petiton and Aouad, 2004;Vancea and Vancea, 2008), which is utilized in order to achieve parallelism of the non-progressive decoder in Fig. 3(a).…”

“…We adopt blockwise and tiling methods in order to improve data locality. Blockwise Gauss-Jordan elimination is used for the pure Gauss-Jordan decoding method and also for the matrix inversion (Melab et al, 2000;Petiton and Aouad, 2004;Vancea and Vancea, 2008), and tiling scheme is adopted by matrix multiplication (Hunold et al, 2004;Park et al, 2003). These methods modify the general data access pattern in a matrix into a more efficient manner.…”

A Matrix Inversion Method with YML/OmniRPC on a Large Scale Platform

“…It is very important to notice that the OmniRPC program with out-of-core is not a version of Gauss-Jordan with out-of-core. The program only reads and writes data at each step of the Gauss-Jordan method, like [7]. This evaluation is firstly done with the same condition than the first experiment: one cluster, with heteregenous nodes and networks.…”