Systems and methods for probabilistic quadrature amplitude modulation (QAM)

A method comprising:

• identifying, by one or more processors, a code rate of a low-density parity-check (LDPC) code;
• receiving, by an LDPC encoder, a set of information bits;
• encoding, by the LDPC encoder using the code rate, the set of information bits to generate a set of encoded bits and a set of parity bits;
• generating, from the set of encoded bits, a matrix of bit arrays;
• discarding, by the one or more processors, one or more parity bits from the set of parity bits to generate a parity bit array with a size equal to a number of column of the matrix;
• generating, by the one or more processors, a bit array by concatenating (1) one or more bit arrays selected from the matrix of bit arrays and (2) one or more bits selected from the parity bit array corresponding to the one or more bit arrays;
• and
• modulating, by a modulator, the bit array to generate modulated data for transmission by the transmitter.

An apparatus comprising:

• a transmitter;
• and
• one or more processors configured to:
• identify a target code rate for which to encode data;
• determine a code rate of a low-density parity-check (LDPC) code and a number of unshaped bits, to encode the data at the target code rate;
• receive, by an LDPC encoder, the data including shaped bits generated by a shaping encoder and a set of unshaped bits with a size equal to the number, and encode, using the code rate, the data to generate a matrix of encoded bits and a set of parity bits;
• discard, based at least on the number, one or more parity bits from the set of parity bits to generate a parity bit array;
• generate a bit array by concatenating (1) one or more bit arrays obtained from columns of the matrix and (2) one or more bits obtained from the parity bit array corresponding to the one or more bit arrays;
• and
• modulate, by the modulator, the bit array to generate modulated data for transmission by a transmitter.