  This paper considers the achievability and converse bounds on the maximal
channel coding rate at a given blocklength and error probability over AWGN
channels. The problem stems from covert communication with Gaussian codewords.
By re-visiting [18], we first present new and more general achievability bounds
for random coding schemes under maximal or average probability of error
requirements. Such general bounds are then applied to covert communication in
AWGN channels where codewords are generated from Gaussian distribution while
meeting the maximal power constraint. Further comparison is made between the
new achievability bounds and existing one with deterministic codebooks.
