Parallelizing a Coarse Grain Graph Search Problem Based upon LDPC Codes on a Supercomputer

Codes on graphs have become the most important way to reach channel capacity. A new problem for High Performance Computing has been constructed with this work. The graph search problem as posed in this work is the coarsest version of the problem which corresponds to the exhaustive search case. The coarse grain graph search (CGGS) problem chooses an optimal parity-check matrix, based on minimum value of BER objective function. Based upon the specified range of parity-check matrices and range of signal to noise ratio (SNR), the CGGS generates the parity-check matrices using the Modified PEG algorithm, performs LDPC encoding, adds noise to the encoder output, performs LDPC decoding, computes Bi terror rate (BER), and thus the BER objective function. The CGGS problem in its current implementation runs in an MPI implementation on the T2K supercomputer at The University Of Tokyo. Two scheduling strategies have been proposed, Generalized Max-Min pairing (GMMP) and random pairing(RP) scheduling algorithms have been proposed, and good parallel performance of CGGS over an MPI implementation on T2K has been achieved.