The author reports on the performance of a new class of constrained co
des, called weakly constrained codes. These codes do not strictly guar
antee the imposed channel constraints, but rather generate codewords t
hat violate, with a given (small) probability, the prescribed constrai
nt. Weakly constrained codes are specifically of interest when it is d
esirable that the code rate R = p/q is very high, requiring codewords
of length q > 100.