  We study achievable rates of reliable communication in a power-constrained
two-way additive interference channel over the real alphabet where
communication is disrupted by a power-constrained jammer. This models the
wireless communication scenario where two users Alice and Bob, operating in the
full duplex mode, wish to exchange messages with each other in the presence of
a jammer, James. Alice and Bob simultaneously transmit their encodings $
\underline{x}_A $ and $\underline{x}_B $ over $ n $ channel uses. It is assumed
that James can choose his jamming signal $ \underline{s} $ as a noncausal
randomized function of $ \underline{x}_A $ and $ \underline{x}_B $, and the
codebooks used by Alice and Bob. Alice and Bob observe $
\underline{x}_A+\underline{x}_B +\underline{s}$, and must recover each others'
messages reliably. In this article, we provide upper and lower bounds on the
capacity of this channel which match each other and equal $
\frac{1}{2}\log\left(\frac{1}{2} + \mathsf{SNR}\right) $ in the
high-$\mathsf{SNR}$ regime (where $\mathsf{SNR}$, signal to noise ratios, is
defined as the ratio of the power constraints of the users to the power
constraint of the jammer). We give a code construction based on lattice codes,
and derive achievable rates for large $\mathsf{SNR}$. We also present upper
bounds based on two specific attack strategies for James. Along the way, sumset
property of lattices for the achievability and general properties of
capacity-achieving codes for memoryless channels for the converse are proved,
which might be of independent interest.
