Authenticated partial correction over AV-MACs: toward characterization and coding
Duncan Koepke, Michaela Schnell, Madelyn St. Pierre, Allison Beemer
TL;DR
This work studies $\gamma$ partial correction over a $t$-user AV-MAC, defining the problem so that at least a $\gamma$ fraction of users' messages are decoded correctly in each transmission. It develops necessary channel conditions—extensions of symmetrizability and overwritability—that determine when the $\gamma$-partial-correction authentication capacity region $\mathscr{C}_{auth,\gamma}$ has nonempty interior, and proposes a block-length extension scheme that preserves positive rates from short zero-error codes by concatenating an inner $\gamma$-correcting code with outer erasure codes. A concrete channel, $W^{+}_{t,\ell}$, is analyzed to verify the necessary conditions and to characterize zero-error $\gamma$-partial-correction codes, including a two-user example with Sperner-type bounds and a discussion for three or more users. The results advance understanding of authentication and partial correction in adversarial multi-user settings and suggest practical coding strategies for maintaining reliable portions of messages under adversarial erasures, with future work on sufficiency proofs, refined extension schemes, and inner bounds for the $\mathscr{C}_{auth,\gamma}$ region.
Abstract
In this paper we study $γ$ partial correction over a $t$-user arbitrarily varying multiple-access channel (AV-MAC). We first present necessary channel conditions for the $γ$ partially correcting authentication capacity region to have nonempty interior. We then give a block length extension scheme which preserves positive rate tuples from a short code with zero probability of $γ$ partial correction error, noting that the flexibility of $γ$ partial correction prevents pure codeword concatenation from being successful. Finally, we offer a case study of a particular AV-MAC satisfying the necessary conditions for partial correction.