  Providing connectivity to a massive number of devices is a key challenge in
5G wireless systems. In particular, it is crucial to develop efficient methods
for active device identification and message decoding in a multi-cell network
with fading, path loss, and delay uncertainties. This paper presents such a
scheme using second-order Reed-Muller (RM) sequences and orthogonal
frequency-division multiplexing (OFDM). For given positive integer $m$, a
codebook is generated with up to $2^{m(m+3)/2}$ codewords of length $2^m$,
where each codeword is a unique RM sequence determined by a matrix-vector pair
with binary entries. This allows every device to send $m(m + 3)/2$ bits of
information where an arbitrary number of these bits can be used to represent
the identity of a node, and the remaining bits represent a message. There can
be up to $2^{m(m+3)/2}$ different identities. Using an iterative algorithm, an
access point can estimate the matrix-vector pairs of each nearby device, as
long as not too many devices transmit in the same frame. It is shown that both
the computational complexity and the error performance of the proposed
algorithm exceed another state-of-the-art algorithm. The device identification
and message decoding scheme developed in this work can serve as the basis for
grant-free massive access for billions of devices with hundreds of
simultaneously active devices in each cell.
