Two$-$sender two$-$receiver channel. Consider the DM $-$sender $-$receiver channel

depicted in Figure $.$ with message pair $($M$1,$ M$2)$ uniformly distributed over

$[1$:$2$nR$1]\backslash$times $[1$:$2$nR$2].$ Sender j $=1,2$ encodes the message Mj$.$ Each receiver

wishes to recover both messages $($how is this channel related to the multiple access

channel?$).$ The average probability of error is defined as P$($n$)$

e $=$ P$\{($M$11,$ M$21)=$

$($M$1,$ M$2)$ or $($M$12,$ M$22)=($M$1,$ M$2)\}.$ Achievability and the capacity region are

defined as for the DM$-$MAC. Find a single$-$lette