Matrix-Vector Multiplication via Erasure Decoding

The problem of fast evaluation of a matrix-vector product over GF (2) is considered. The problem is reduced to erasure decoding of a linear error-correcting code. A large set of redundant parity check equations for this code is generated. The multiplication algorithm is derived by tracking the execution of the message-passing algorithm on the obtained set of parity check equations. The obtained algorithms outperform the classical ones.