5 research outputs found
A General Formula for the Mismatch Capacity
The fundamental limits of channels with mismatched decoding are addressed. A
general formula is established for the mismatch capacity of a general channel,
defined as a sequence of conditional distributions with a general decoding
metrics sequence. We deduce an identity between the Verd\'{u}-Han general
channel capacity formula, and the mismatch capacity formula applied to Maximum
Likelihood decoding metric. Further, several upper bounds on the capacity are
provided, and a simpler expression for a lower bound is derived for the case of
a non-negative decoding metric. The general formula is specialized to the case
of finite input and output alphabet channels with a type-dependent metric. The
closely related problem of threshold mismatched decoding is also studied, and a
general expression for the threshold mismatch capacity is obtained. As an
example of threshold mismatch capacity, we state a general expression for the
erasures-only capacity of the finite input and output alphabet channel. We
observe that for every channel there exists a (matched) threshold decoder which
is capacity achieving. Additionally, necessary and sufficient conditions are
stated for a channel to have a strong converse. Csisz\'{a}r and Narayan's
conjecture is proved for bounded metrics, providing a positive answer to the
open problem introduced in [1], i.e., that the "product-space" improvement of
the lower random coding bound, , is indeed the mismatch
capacity of the discrete memoryless channel . We conclude by presenting an
identity between the threshold capacity and in the DMC
case
Superposition codes for mismatched decoding
An achievable rate is given for discrete memoryless channels with a given (possibly suboptimal) decoding rule. The result is obtained using a refinement of the superposition coding ensemble. The rate is tight with respect to the ensemble average, and can be weakened to the LM rate of Hui and Csiszár-Körner, and to Lapidoth's rate based on parallel codebooks. © 2013 IEEE