Title: Exponential Source/Channel Duality,
Abstract: We propose a source/channel duality in the exponential regime, where
success/failure in source coding parallels error/correctness in channel coding,
and a distortion constraint becomes a log-likelihood ratio (LLR) threshold. We
establish this duality by first deriving exact exponents for lossy coding of a
memoryless source P, at distortion D, for a general i.i.d. codebook
distribution Q, for both encoding success (R < R(P,Q,D)) and failure (R >
R(P,Q,D)). We then turn to maximum likelihood (ML) decoding over a memoryless
channel P with an i.i.d. input Q, and show that if we substitute P=QP, Q=Q, and
D=0 under the LLR distortion measure, then the exact exponents for
decoding-error (R < I(Q, P)) and strict correct-decoding (R > I(Q, P)) follow
as special cases of the exponents for source encoding success/failure,
respectively. Moreover, by letting the threshold D take general values, the
exact random-coding exponents for erasure (D > 0) and list decoding (D < 0)
under the simplified Forney decoder are obtained. Finally, we derive the exact
random-coding exponent for Forney's optimum tradeoff erasure/list decoder, and
show that at the erasure regime it coincides with Forney's lower bound and with
the simplified decoder exponent.