To provide systems and methods for constellation shaping using a low rate loss bit-level distribution matcher.SOLUTION: Methods include receiving blocks of input bits and, for each input block of predetermined size, assigning each codeword of predetermined output block size. The number of bits of a given bit value in the codeword is dependent on a predetermined target probability distribution. A one-to-one mapping exists between each possible combination of input bits and a codeword for input blocks containing the combination. Some codewords include the number of bits having the given bit value that is different from predetermined target probability distribution, but an average number of bits having the given bit value in the available codewords meets the predetermined target probability distribution. The methods result in more available codewords and a lower rate loss than in a bit-level distribution matcher with a low modulus, while achieving similar shaping.SELECTED DRAWING: Figure 7