  A new algorithm for efficient exact maximum likelihood decoding of polar
codes (which may be CRC augmented), transmitted over the binary erasure
channel, is presented. The algorithm applies a matrix triangulation process on
a sparse polar code parity check matrix, followed by solving a small size
linear system over GF(2). To implement the matrix triangulation, we apply
belief propagation decoding type operations. We also indicate how this decoder
can be implemented in parallel for low latency decoding. Numerical simulations
are used to evaluate the performance and computational complexity of the new
algorithm.
