A General Formula for the Mismatch Capacity

作者：Somekh Baruch Anelia^*

来源：IEEE Transactions on Information Theory, 2015, 61(9): 4554-4568.

DOI：10.1109/TIT.2015.2449856

• Channel coding
• mismatch capacity
• mismatched decoding
• threshold decoding

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 Verdu-Han general channel capacity formula, and the mismatch capacity formula applied to maximum likelihood decoding metric. Furthermore, 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. In addition, necessary and sufficient conditions are stated for a channel to have a strong converse.

• 出版日期2015-9