Communism does not require equal distribution. In fact Marx argued communism explicitly requires
unequal distribution.
In Critique of the Gotha Program he outright ridiculed what is now the German SDP for demanding that "the proceeds of labor belong undiminished with equal right to all members of society".
He went on to write: "Further, one worker is married, another is not; one has more children than another, and so on and so forth. Thus, with an equal performance of labor, and hence an equal in the social consumption fund, one will in fact receive more than another, one will be richer than another, and so on. To avoid all these defects, right, instead of being equal, would have to be unequal."
Later in the same text he then reiterated the traditional socialist slogan, that explicitly also rejects equal distribution: "From each according to his ability, to each according to his needs!"