Fast decoding for raptorQ codes using matrix dimensionality reduction

A very fast decoding algorithm using matrix dimensionality reduction for RaptorQ codes is proposed. The algorithm exploits a pre-calculated inverse matrix to achieve dimensionality reduction for the received code constraint matrix. As a result, the decoding complexity is decreased significantly, whereas the failure-overhead curve is still identical to that of conventional approaches. Simulations show that the decoding speed of the proposed algorithm can be as fast as 17.5 times the state-of-the-art algorithm when the erasure probability is relatively low.