  Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes,
seek efficient ways to distribute matrix multiplication task(s) to a set of $N$
distributed servers so that the answers returned from any $R$ servers are
sufficient to recover the desired product(s). For example, to compute the
product of matrices ${\bf U, V}$, MatDot codes partition each matrix into $p>1$
sub-matrices to create smaller coded computation tasks that reduce the
upload/storage at each server by $1/p$, such that ${\bf UV}$ can be recovered
from the answers returned by any $R=2p-1$ servers. An important concern in CDMM
is to reduce the recovery threshold $R$ for a given storage/upload constraint.
Recently, Jeong et al. introduced Approximate MatDot (AMD) codes that are shown
to improve the recovery threshold by a factor of nearly $2$, from $2p-1$ to
$p$. A key observation that motivates our work is that the storage/upload
required for approximate computing depends not only on the dimensions of the
(coded) sub-matrices that are assigned to each server, but also on their
precision levels -- a critical aspect that is not explored by Jeong et al. Our
main contribution is a dimensional analysis of AMD codes inspired by the
Generalized Degrees of Freedom (GDoF) framework previously developed for
wireless networks, which indicates that for the same upload/storage, once the
precision levels of the task assignments are accounted for, AMD codes
surprisingly fall short in all aspects to even the trivial replication scheme
which assigns the full computation task to every server. Indeed, the trivial
replication scheme has a much better recovery threshold of $1$, better download
cost, better computation cost, and much better encoding/decoding (none
required) complexity than AMD codes. The dimensional analysis is supported by
simple numerical experiments.
