Using command line split, and quick hack to glue a new array out of @F:

echo 'aaabbccccdd eee' | perl -aF'(.)(?!\1)' -lne 'while(@F){push@M,sh
+ift(@F).shift(@F)}print for @M'
[download]

Producing:

aaa
bb
cccc
dd

eee
[download]

Update:

Shorter :

echo 'aaabbccccdd eee'|perl -aF'(.)(?!\1)' -lne 'for(@F){$M[$c].=$_;$c+=$d++%2}print for @M'

Not using split, and shorter still:

echo 'aaabbccccdd eee'|perl -lne 'while($_){s/((.)\2*)//;push@F,$1}print for @F'