MAC with list codes. A $(2$nR$1,2$nR$2,2$nL$2,$ n$)$ list code for a DM$-$MAC p$($y$|$x$1,$ x$2)$

consists of two message sets $[1$:$2$nR$1]$ and $[1$:$2$nR$2],$ two encoders, and a list decoder. The message pair $($M$1,$ M$2)$ is uniformly distributed over $[1$:$2$nR$1]\backslash$times $[1$ :

$2$nR$2].$ Upon receiving yn

$,$ the decoder finds m$1$ and a list of messagesL$2[1$:$2$nR$2]$

of size $|$L$2|<=2$nL$2.$ An error occurs if M$1=$ M$1$ or if the list L$2$ does not contain the

transmitted message M$2,$ i$.$e$.,$ P$($n$)$

e $=$ P$\{$M$1=$ M$1$ or M$2$ L$2\}.$ A triple $($