  In this paper, we propose a new polar coding scheme for the unsourced,
uncoordinated Gaussian random access channel. Our scheme is based on sparse
spreading, treat interference as noise and successive interference cancellation
(SIC). On the transmitters side, each user randomly picks a code-length and a
transmit power from multiple choices according to some probability distribution
to encode its message, and an interleaver to spread its encoded codeword bits
across the entire transmission block. The encoding configuration of each user
is transmitted by compressive sensing, similar to some previous works. On the
receiver side, after recovering the encoding configurations of all users, it
applies single-user polar decoding and SIC to recover the message list.
Numerical results show that our scheme outperforms all previous schemes for
active user number $K_a\geq 250$, and provides competitive performance for
$K_a\leq 225$. Moreover, our scheme has much lower complexity compared to other
schemes as we only use single-user polar coding.
