| Paper ID | D3-S3-T1.1 |
| Paper Title |
Robust multicasting and an upper bound on the mismatch capacity of the DMC |
| Authors |
Anelia Somekh-Baruch, Bar-Ilan University, Israel; , |
| Session |
D3-S3-T1: Mismatched Decoding |
| Chaired Session: |
Wednesday, 14 July, 22:40 - 23:00 |
| Engagement Session: |
Wednesday, 14 July, 23:00 - 23:20 |
| Abstract |
We revisit the multicasting approach to the analysis of converse bounds that we recently introduced, and present a refined proof technique for upper bounding the mismatch capacity of the DMC $P_{Y|X}$ with decoding metric $q$. To this end, we present an algorithm, which given a $2$-user broadcast channel $P_{YZ|X}$, decoding metrics $(q,\rho)$, and rate-$R$ codebook, produces a sub-codebook of possibly lower rate $R'$, which has the property that the intersecting event of erroneous $\rho$-decoding by the $Z$ receiver and correct $q$-decoding of the $Y$ receiver has a vanishing probability. This results in a bound on the mismatch capacity of the channel to the $Y$-receiver that is given in terms of the sum of an achievable rate for a $Z$ receiver of {\it any} broadcast channel having marginal $P_{Y|X}$ plus the corresponding rate reduction $R-R'$. We further detect the $\rho^*$ metric which yields the tightest bound out of all the type-dependent metrics, and focusing on the case of zero rate reduction, we show that the resulting bound is at least as tight as our previous best known upper bound [1]. We conclude by presenting sufficient conditions for the tightness of our bound and equivalence classes of code composition-channel-metric triplets.
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