A data scrambling method for controlling a code density according to an exemplary embodiment of the present disclosure includes receiving a plain code which is a code to be stored in the non-volatile memory device and a storage address at which the plain code is recorded; determining a rank corresponding to the plain code, using an ET table including appearance frequency rank information corresponding to individual plain code; calculating an adjustment rank corresponding to the plain code, using the rank and a random number that is generated based on the address of storage address; determining a cipher code corresponding to the appearance frequency rank of the plain code, using the adjustment rank and an ECC table including rank information determined by an objective function for individual cipher code; and storing the cipher code in the storage address.

A communication system includes a data source to receive a block of bits, a memory to store a set of distribution matchers. Each distribution matcher is associated with a probability mass function (PMF) to match equally likely input bits to a fixed number of output bits with values distributed according to the PMF of the distribution matcher. Each distribution matcher is associated with a selection probability, such that a sum of joint probabilities of all distribution matchers equals a target PMF. A joint probability of a distribution matcher is a product of PMF of the distribution matcher with the selection probability of the distribution matcher. The communication system also includes a shaping mapper to select the distribution matcher from the set of distribution matchers with the selection probability and to map the block of bits to a block of shaped bits with a non-uniform distribution using the selected distribution matcher and a transmitter front end to transmit the block of shaped bits over a communication channel, such that bits in a sequence of the blocks of shaped bits are distributed according to the target PMF.