# The strong converse for the MAC, part 2

The last time we saw that a packing lemma, together with a good choice of reference output distribution $r$ (the Fano-* distribution) could give a converse for nonstationary DMC:

$\log M \le \sum_{t=1}^{n} I(X_t ; Z_t) + (\frac{ 2 }{1 - \lambda} 3 |\mathcal{X}| n)^{1/2} + \log \frac{2}{1 - \lambda}$

where the distribution on $(X^n,Z^n)$ is given by the Fano distribution on the codebook, i.e. uniform input distribution on codewords followed by applying the channel. The next step in the argument is to apply this result to the MAC with inputs $X$ and $Y$.

I think it’s true, but I’m sure there’s some special property of $\mathbb{F}_p$ that I have forgotten. I guess further generalizations would include whether or not it’s possible for arbitrary $p$ (not necessarily prime), how many elements of an arbitrary field you would need, and so on. I’d ask this on MathOverflow but… meh. It’s probably a homework problem.