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This paper considers the problem of coding over a discrete memoryless channel (DMC) with noiseless feedback. The paper provides a stochastic control view of a variable-length version of the posterior matching scheme which is analyzed via a recently proposed symmetrized divergence, termed Extrinsic Jensen–Shannon (EJS) divergence. In particular, under the variable-length posterior matching scheme, the EJS divergence can be lower bounded by the Shannon capacity of the DMC, which can be used for a relatively simple proof that the variablelength posterior matching scheme achieves capacity.

An Alternative Coding Theorem for Posterior Matching via Extrinsic Jensen–Shannon Divergence