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

Finite Blocklength Analysis of Gaussian Random Coding in AWGN Channels under Covert Constraint