[@sfrl_trans], though it is asymptotic). Using our approach, we can also greatly shorten the proof of the achievability of the dispersion in joint source-channel coding [@kostina2013joint].

4.  Our proofs only use the Poisson matching lemma introduced in this paper, which replaces both the packing and covering lemmas in proofs using typicality. The Poisson matching lemma can also be used to prove a soft covering lemma. Hence the Poisson matching lemma can be the only tool needed to prove a wide range of results in network information theory.

5.  Our analyses usually involve fewer (or no) uses of sub-codebooks and binning. As a result, we can reduce the number of error events and give sharper second-order bounds. For example:

    1.  Conventional proofs of the Gelfand-Pinsker theorem involve one sub-codebook, giving an additional error event, whereas we do not use any sub-codebook.

    2.  Conventional proofs of the Wyner-Ziv theorem and the Berger-Tung inner bound [@berger1978multiterminal; @tung1978multiterminal] (for distributed lossy source coding) use binning, giving additional error events, whereas we do not require binning.

    3.  Conventional proofs of Marton’s inner bound [@marton1979broadcast] (for broadcast channels) involve two sub-codebooks, whereas we use only one.

6.  In our approach, the encoders and decoders are characterized 