Systems and methods for probabilistic quadrature amplitude modulation (QAM)

1 . An apparatus comprising:

a transmitter and one or more processors, wherein

the one or more processors are configured to:

identify a code rate of a low-density parity-check (LDPC) code;

receive, by an LDPC encoder, a set of information bits;

encode, 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;

generate, from the set of encoded bits, a matrix of bit arrays;

discard 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;

generate 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

modulate, by a modulator, the bit array to generate modulated data for transmission by the transmitter.

2 . The apparatus of claim 1 , wherein the transmitter is configured to transmit the modulated data.

3 . The apparatus of claim 1 , wherein

the set of information bits includes a first set of bits and a second set of bits;

the one or more processors are configured to:

identify, by a shaping encoder, a shaping code;

encode, by the shaping encoder using the shaping code, data to generate the first set of information bits; and

receive, by the LDPC encoder from an output of the shaping encoder, the first set of information bits.

4 . The apparatus of claim 1 , wherein

in modulating the bit array, the one or more processors are configured to perform a quadrature amplitude modulation with a number of bits per symbol on the bit array to generate the modulated data; and

in generating the matrix of bit arrays, the one or more processors are configured to:

determine, based at least on the number of bits per symbol and a size of the set of encoded bits, the number of columns of the matrix of bit arrays; and

determine, based at least on the number of bits per symbol, a number of rows of the matrix of bit arrays.

5 . The apparatus of claim 4 , wherein the bit array has a size equal to the number of bits per symbol.

6 . The apparatus of claim 1 , wherein in generating the bit array, the one or more processors are configured to:

select a first column and a second column from the matrix of bit arrays; and

select, from the parity bit array, a first bit and a second bit corresponding to the first column and the second column of the matrix of bit arrays, respectively; and

concatenate the first column, the second column, the first bit, and the second bit to generate the bit array.

7 . The apparatus of claim 6 , wherein the generated bit array includes the first column, the first bit, the second column, and the second bit in this order.

8 . The apparatus of claim 6 , wherein the first column and the second column are randomly selected from columns of the matrix of bit arrays.

9 . The apparatus of claim 6 , wherein the first column and the second column are sequentially selected from columns of the matrix of bit arrays in an order of the columns of the matrix of bit arrays.

10 . 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.

11 . The method of claim 10 , further comprising:

transmitting, by a transmitter, the modulated data.

12 . The method of claim 10 , wherein

the set of information bits includes a first set of bits and a second set of bits;

the method comprises:

identifying, by a shaping encoder, a shaping code;

encoding, by the shaping encoder using the shaping code, data to generate the first set of information bits; and

receiving, by the LDPC encoder from an output of the shaping encoder, the first set of information bits.

13 . The method of claim 10 , wherein

modulating the bit array comprises performing, by the modulator, a quadrature amplitude modulation with a number of bits per symbol on the bit array to generate the modulated data;

generating the matrix of bit arrays comprises:

determining, based at least on the number of bits per symbol and a size of the set of encoded bits, the number of columns of the matrix of bit arrays; and

determining, based at least on the number of bits per symbol, a number of rows of the matrix of bit arrays.

14 . The method of claim 13 , wherein the bit array has a size equal to the number of bits per symbol.

15 . The method of claim 10 , wherein generating the bit array comprises:

selecting a first column and a second column from the matrix of bit arrays; and

selecting, from the parity bit array, a first bit and a second bit corresponding to the first column and the second column of the matrix of bit arrays, respectively; and

concatenating the first column, the second column, the first bit, and the second bit to generate the bit array.

16 . The method of claim 15 , wherein the generated bit array includes the first column, the first bit, the second column, and the second bit in this order.

17 . The method of claim 15 , wherein the first column and the second column are randomly selected from columns of the matrix of bit arrays.

18 . The method of claim 15 , wherein the first column and the second column are sequentially selected from columns of the matrix of bit arrays in an order of the columns of the matrix of bit arrays.

19 . 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.

20 . The apparatus of claim 19 , wherein in determining the code rate, the one or more processors are configured to:

identify one or more code rates to encode the data at the target rate;

determine, for each of the one or more code rates, a number of parity bits discarded before the modulation; and

select, from among the one or more code rates, a code rate corresponding to a least number parity bits discarded before the modulation.