A communication system transmits an input block of bits over a communication channel using a prefix tree that maps a dyadic distribution of compositions of output symbols to prefixes of variable lengths. A path to each leaf of the prefix tree is defined by a prefix formed by a unique sequence of binary values of a length equal to a depth of the leaf. Each leaf is associated with a composition that has at least a number of unique permutations equals to two in a power of a length of a suffix of the block of input bits. The system selects a composition identified in the prefix tree by a prefix in the input block of bits, permutes the selected composition according to a suffix in the input block of bits, and transmits the permuted composition over a communication channel.