Non-binary polar codes for probabilistic amplitude shaping
Various aspects of the present disclosure generally relate to wireless communication. Some aspects more specifically provide procedures and configurations used to perform, at a transmitter, probabilistic amplitude shaping (PAS) of quadrature amplitude modulation (QAM) communications using non-binary polar coding (NBPC). NBPC differs from binary polar coding (BPC) in that BPC uses a binary-input channel whereas NBPC uses a non-binary input channel. For example, while BPC uses a log likelihood ratio (LLR) with a single value corresponding to a given bit to be shaped, NBPC may use a probability mass function (PMF) to define or represent amplitude shaping target values. As another example, aspects use non-binary transformations, which reduce the number of passes to shape q bits from q passes (for BPC) to 1 pass (for NBPC).
1 . A wireless communication device, comprising:
a processing system that includes one or more processors and one or more memories coupled with the one or more processors, the processing system configured to cause the wireless communication device to:
perform a first non-binary polar transformation encoding operation on a first symbol vector, including a set of data symbols, that generates a second symbol vector including a set of transformed data symbols, the set of data symbols being associated with first locations associated with the first non-binary polar transformation encoding operation;
perform a non-binary polar transformation decoding operation on the second symbol vector, in accordance with a set of probability values associated with a set of amplitude shaping target values, that generates a third symbol vector including a first set of shaping symbols;
perform a second non-binary polar transformation encoding operation on the third symbol vector that generates a fourth symbol vector including a second set of shaping symbols, the second set of shaping symbols being associated with second locations associated with the second non-binary polar transformation encoding operation; and
transmit a signal that is modulated in accordance with a fifth symbol vector including a set of shaped symbols associated with a combination of the second symbol vector and the fourth symbol vector.
2 . The wireless communication device of claim 1 , wherein the first locations comprise lower-reliability bit locations associated with the first non-binary polar transformation encoding operation and the second locations comprise higher-reliability bit locations associated with the second non-binary polar transformation encoding operation.
3 . The wireless communication device of claim 1 , wherein the first symbol vector is associated with a uniform probability distribution with regard to values of the set of data symbols, and wherein the fifth symbol vector is associated with a non-uniform probability distribution with regard to values of the set of shaped symbols.
4 . The wireless communication device of claim 1 , wherein the processing system is configured to cause the wireless communication device to:
combine, prior to transmitting the signal, the second symbol vector and the fourth symbol vector to generate the fifth symbol vector comprising the set of shaped symbols.
5 . The wireless communication device of claim 1 , wherein the processing system is configured to cause the wireless communication device to:
obtain, prior to performing the first non-binary polar transformation encoding operation, a bit vector including a quantity of bits; and
convert the bit vector to the first symbol vector including the set of data symbols.
6 . The wireless communication device of claim 1 , wherein the processing system is configured to cause the wireless communication device to compute the set of probability values for the second symbol vector according to the set of amplitude shaping target values.
7 . The wireless communication device of claim 6 , wherein:
each symbol of the set of data symbols has q possible values;
the set of probability values includes q values; and
q is a positive integer.
8 . The wireless communication device of claim 6 , wherein;
each symbol of the set of data symbols has q possible values; and
the set of probability values includes fewer than q values.
9 . The wireless communication device of claim 8 , wherein the set of probability values includes fewer than q values in accordance with a normalization operation.
10 . The wireless communication device of claim 6 , wherein, to cause the wireless communication device to compute the set of probability values, the processing system is configured to cause the wireless communication device to generate a log probability mass function using the second symbol vector and the set of amplitude shaping target values.
11 . The wireless communication device of claim 1 , wherein the set of probability values are defined by a log probability mass function.
12 . The wireless communication device of claim 1 , wherein the non-binary polar transformation decoding operation is associated with at least one of:
a successive cancellation decoder,
a successive cancellation list decoder, or
a belief propagation decoder.
13 . The wireless communication device of claim 1 , wherein, to cause the wireless communication device to perform the non-binary polar transformation decoding operation, the processing system is configured to cause the wireless communication device to perform the non-binary polar transformation decoding operation on one or more transformed data symbols of the set of transformed data symbols.
14 . The wireless communication device of claim 13 , wherein the one or more transformed data symbols are on information locations associated with the non-binary polar transformation decoding operation.
15 . A method of wireless communication by a wireless communication device, comprising:
performing a first non-binary polar transformation encoding operation on a first symbol vector, including a set of data symbols, that generates a second symbol vector including a set of transformed data symbols, the set of data symbols being associated with first locations associated with the first non-binary polar transformation encoding operation;
performing a non-binary polar transformation decoding operation on the second symbol vector, in accordance with a set of probability values associated with a set of amplitude shaping target values, that generates a third symbol vector including a first set of shaping symbols;
performing a second non-binary polar transformation encoding operation on the third symbol vector that generates a fourth symbol vector including a second set of shaping symbols, the second set of shaping symbols being associated with second locations associated with the second non-binary polar transformation encoding operation; and
transmitting a signal that is modulated in accordance with a fifth symbol vector including a set of shaped symbols associated with a combination of the second symbol vector and the fourth symbol vector.
16 . The method of claim 15 , wherein the first locations comprise lower-reliability bit locations associated with the first non-binary polar transformation encoding operation and the second locations comprise higher-reliability bit locations associated with the second non-binary polar transformation encoding operation.
17 . The method of claim 15 , wherein:
the first symbol vector is associated with a uniform probability distribution with regard to values of the set of data symbols; and
the fifth symbol vector is associated with a non-uniform probability distribution with regard to values of the set of shaped symbols.
18 . The method of claim 15 , further comprising:
combining, prior to transmitting the signal, the second symbol vector and the fourth symbol vector to generate the fifth symbol vector comprising the set of shaped symbols.
19 . The method of claim 15 , further comprising:
obtaining, prior to performing the first non-binary polar transformation encoding operation, a bit vector including a quantity of bits; and
converting the bit vector to the first symbol vector including the set of data symbols.
20 . The method of claim 15 , further comprising:
computing the set of probability values for the second symbol vector according to the set of amplitude shaping target values.
21 . The method of claim 20 , wherein;
each symbol of the set of data symbols has q possible values;
the set of probability values includes q values; and
q is a positive integer.
22 . The method of claim 20 , wherein:
each symbol of the set of data symbols has q possible values; and
the set of probability values includes fewer than q values.
23 . The method of claim 22 , wherein the set of probability values includes fewer than q values in accordance with a normalization operation.
24 . The method of claim 20 , wherein computing the set of probability values comprises generating a log probability mass function using the second symbol vector and the set of amplitude shaping target values.
25 . The method of claim 15 , wherein the set of probability values are defined by a log probability mass function.
26 . The method of claim 15 , wherein the non-binary polar transformation decoding operation is associated with at least one of:
a successive cancellation decoder,
a successive cancellation list decoder, or
a belief propagation decoder.
27 . The method of claim 15 , wherein performing the non-binary polar transformation decoding operation comprises performing the non-binary polar transformation decoding operation on one or more transformed data symbols of the set of transformed data symbols.
28 . The method of claim 27 , wherein the one or more transformed data symbols are on information locations associated with the non-binary polar transformation decoding operation.
29 . A non-transitory computer-readable medium storing a set of instructions for wireless communication, the set of instructions comprising:
one or more instructions that, when executed by one or more processors of a wireless communication device, cause the wireless communication device to:
perform a first non-binary polar transformation encoding operation on a first symbol vector, including a set of data symbols, that generates a second symbol vector including a set of transformed data symbols, the set of data symbols being associated with first locations associated with the first non-binary polar transformation encoding operation;
perform a non-binary polar transformation decoding operation on the second symbol vector, in accordance with a set of probability values associated with a set of amplitude shaping target values, that generates a third symbol vector including a first set of shaping symbols;
perform a second non-binary polar transformation encoding operation on the third symbol vector that generates a fourth symbol vector including a second set of shaping symbols, the second set of shaping symbols being associated with second locations associated with the second non-binary polar transformation encoding operation; and
transmit a signal that is modulated in accordance with a fifth symbol vector including a set of shaped symbols associated with a combination of the second symbol vector and the fourth symbol vector.
30 . An apparatus for wireless communication, comprising:
means for performing a first non-binary polar transformation encoding operation on a first symbol vector, including a set of data symbols, that generates a second symbol vector including a set of transformed data symbols, the set of data symbols being associated with first locations associated with the first non-binary polar transformation encoding operation;
means for performing a non-binary polar transformation decoding operation on the second symbol vector, in accordance with a set of probability values associated with a set of amplitude shaping target values, that generates a third symbol vector including a first set of shaping symbols;
means for performing a second non-binary polar transformation encoding operation on the third symbol vector that generates a fourth symbol vector including a second set of shaping symbols, the second set of shaping symbols being associated with second locations associated with the second non-binary polar transformation encoding operation; and
means for transmitting a signal that is modulated in accordance with a fifth symbol vector including a set of shaped symbols associated with a combination of the second symbol vector and the fourth symbol vector.