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Extended bit-flipping algorithm for solving sparse linear systems of equations modulo p

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3 Author(s)
Asie Abolpour ; Faculty of Mathematics and Computer Science, Amirkabir Unversity of Technology, Hafez Ave., Tehran, Iran ; Mohammad-Reza Sadeghi ; Daniel Panario

Let p be a prime number. We propose a new method for solving sparse linear systems of equations modulo p when the coefficient matrix has column degree at most 2. This algorithm is based on a well-known decoding algorithm for Low-Density Parity-Check (LDPC) codes called bit-flipping (BF) algorithm. We modify and extend this hard-decision decoding algorithm. The complexity of this algorithm is linear in terms of the number of columns n and the number of nonzero coefficients u of the matrix. We give a detailed small example, and report on computational results for larger systems.

Published in:

Information Theory Workshop (ITW), 2011 IEEE

Date of Conference:

16-20 Oct. 2011