We develop a low-complexity coding scheme to achieve covert communications over binary-input discrete memoryless channels (BI-DMCs). We circumvent the impossibility of covert communication with linear codes by introducing non-linearity through the use of pulse position modulation (PPM) and multilevel coding (MLC). We show that the MLC-PPM scheme exhibits many appealing properties; in particular, the channel at a given index level remains stationary as the number of level increases, which allows one to use families of channel capacity- and channel resolvability-achieving codes to concretely instantiate the covert communication scheme.
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