Bit mapping for variable-size higher-order digital modulations
Mapping of m input bits to 2 m modulation symbols of a two-dimensional symbol constellation. A quarter-quadrant constellation of 2 m-4 modulation symbols that are located in a first quadrant of the two-dimensional signal plane is formed with each modulation symbol associated with a respective m-4 bit label. A quarter constellation of the two-dimensional symbol constellation is formed by adding to the quarter-quadrant constellation three copies of the quarter-quadrant constellation rotated by −90 degrees, 180 degrees, and −270 degrees, respectively, and then displacing the quarter constellation by a shift value Δ, with each modulation symbol associated with a respective m-2 bit label. The two-dimensional symbol constellation is then formed by adding to the quarter constellation three copies of the quarter constellation rotated by +90 degrees, 180 degrees, and +270 degrees, respectively. Each symbol of the two dimensional constellation is associated with a respective m bit label of the m input bits.
1. A method for forming and transmitting a communication including mapping m input bits to 2 m modulation symbols of a two-dimensional symbol constellation, where m is a positive integer greater than or equal to four, the method comprising:
forming a quarter-quadrant constellation of 2 m-4 modulation symbols that are located in a first quadrant of the two-dimensional signal plane, the quarter-quadrant constellation having one-sixteenth the size of the two-dimensional symbol constellation;
uniquely associating each modulation symbol of the quarter-quadrant constellation with a respective m-4 bit label of the m input bits;
forming a quarter constellation of the two-dimensional symbol constellation by adding to the quarter-quadrant constellation three copies of the quarter-quadrant constellation rotated by −90 degrees, 180 degrees, and −270 degrees, respectively, and then displacing the quarter constellation by a shift value Δ such that the symbols coincide with symbols of the two-dimensional symbol constellation, wherein the quarter constellation has one-fourth the size of the two-dimensional symbol constellation;
uniquely associating each symbol of the quarter constellation with a respective m-2 bit label of the m input bits, wherein m-4 bits of the m-2 bit label are inherited from the quarter-quadrant constellation and two further bits of the m-2 bit label are used to distinguish quarter-quadrants of the quarter constellation;
forming the two-dimensional symbol constellation by adding to the quarter constellation three copies of the quarter constellation rotated by +90 degrees, 180 degrees, and +270 degrees, respectively;
uniquely associating each symbol of the two-dimensional symbol constellation with an m-bit label, wherein m-2 bits of the m-bit label are inherited from the quarter constellation and two further bits of the m input bits are used to distinguish quarters of the two-dimensional symbol constellation; and
for each of a plurality of groups of m input bits:
mapping each group of m input bits to the two-dimensional symbol constellation to form a communication symbol; and
transmitting the communication symbol.
2. The method of claim 1 , wherein of the two further bits of the m-2 bit label used to distinguish quarter-quadrants of the quarter constellation:
a value of [00] corresponds to a first quarter-quadrant of the quarter constellation having the quarter-quadrant constellation;
a value of [01] corresponds to a second quarter-quadrant of the quarter constellation having a quarter-quadrant constellation that has been rotated by −90 degrees;
a value of [11] corresponds to a third quarter-quadrant of the quarter constellation having a quarter-quadrant constellation that has been rotated by 180 degrees; and
a value of [10] corresponds to a fourth quarter-quadrant of the quarter constellation having a quarter-quadrant constellation that has been rotated by −270 degrees.
3. The method of claim 1 , wherein of the two further bits of the m input bits used to distinguish quadrants of the two-dimensional symbol constellation:
a value of [00] corresponds to a first quadrant of the two-dimensional symbol constellation having the quarter constellation;
a value of [01] corresponds to a second quadrant of the two-dimensional symbol constellation having a quarter constellation that has been rotated by −90 degrees;
a value of [11] corresponds to a third quadrant of the two-dimensional symbol constellation having a quarter constellation that has been rotated by 180 degrees; and
a value of [10] corresponds to a fourth quadrant of the two-dimensional symbol constellation having a quarter constellation that has been rotated by −270 degrees.
4. The method of claim 1 , wherein:
the two-dimensional symbol constellation is a 256-QAM constellation;
the m input bits comprise eight bits [y 7 , y 6 , y 5 , y 4 , y 3 , y 2 , y 1 , y 0 ];
the 2 m-4 bits are bits [y 7 , y 6 , y 4 , y 3 ];
the two further bits of the m-2 bit label are bits [y 5 , y 2 ]; and
the two further bits of the m input bits are bits [y 1 , y 0 ].
5. The method of claim 1 , wherein:
the two-dimensional symbol constellation is a 1024-QAM constellation;
the m input bits comprise ten bits [y 9 , y 8 , y 7 , y 6 , y 5 , y 4 , y 3 , y 2 , y 1 , y 0 ];
the 2 m-4 bits are bits [y 9 , y 8 , y 7 , y 5 , y 4 , y 3 ];
the two further bits of the m-2 bit label are bits [y 6 , y 2 ]; and
the two further bits of the m input bits are bits [y 1 , y 0 ].
6. The method of claim 1 , wherein forming the quarter constellation further comprises repositioning a plurality of quarter constellation symbol positions.
7. The method of claim 6 , wherein:
the two-dimensional symbol constellation is a 128 QAM constellation;
the m input bits comprise seven bits [y 6 , y 5 , y 4 , y 3 , y 2 , y 1 , y 0 ];
the 2 m-4 bits are bits [y 6 , y 4 , y 3 ];
the two further bits of the m-2 bit label are bits [y 5 , y 2 ]; and
the two further bits of the m input bits are bits [y 1 , y 0 ].
8. The method of claim 6 , wherein:
the two-dimensional symbol constellation is a 512-QAM constellation;
the m input bits comprise eight bits [y 8 , y 7 , y 6 , y 5 , y 4 , y 3 , y 2 , y 1 , y 0 ];
the 2 m-4 bits are bits [y 8 , y 7 , y 5 , y 4 , y 3 ];
the two further bits of the m-2 bit label are bits [y 6 , y 2 ]; and
the two further bits of the m input bits are bits [y 1 , y 0 ].
9. The method of claim 1 , further comprising forming the m input bits from a plurality of information bits by operating upon the plurality of information bits to form a Forward Error Correction (FEC) frame.
10. The method of claim 9 , wherein the FEC frame includes an integer number of trellis groups.
11. The method of claim 9 , wherein Reed-Solomon encoding is employed to form the FEC frame.
12. The method of claim 1 , further comprising forming the m input bits from a plurality of information bits by:
Forward Error Correction (FEC) coding the plurality of information bits to produce a plurality of FEC blocks;
interleaving and randomizing the plurality of FEC blocks; and
appending a frame synch trailer to the plurality of interleaved and randomized FEC blocks to form a FEC frame.
13. The method of claim 9 , wherein the FEC frame includes an integer number of trellis groups.
14. A method for forming and transmitting a communication including mapping m input bits to a two-dimensional symbol constellation, where m is a positive integer greater than or equal to four, the method comprising:
forming a quarter-quadrant constellation of 2 m-4 modulation symbols;
forming a quarter constellation of the two-dimensional symbol constellation by adding to the quarter-quadrant constellation three copies of the quarter-quadrant constellation rotated by −90 degrees, 180 degrees, and −270 degrees, respectively, and then displacing the constellation by a shift value Δ such that the symbols coincide with symbols of the two-dimensional symbol constellation, wherein the quarter constellation has one-fourth the size of the two-dimensional symbol constellation;
forming the two-dimensional symbol constellation by adding to the quarter constellation three copies of the quarter constellation rotated by +90 degrees, 180 degrees, and +270 degrees, respectively; and
for each of a plurality of groups of m input bits:
mapping each group of m input bits to the two-dimensional symbol constellation to form a communication symbol; and
transmitting the communication symbol.
15. The method of claim 14 , wherein forming the quarter-quadrant constellation further comprises uniquely associating each symbol of the quarter-quadrant constellation with a respective m-4 bit label of the m input bits.
16. The method of claim 14 , wherein forming the quarter constellation further comprises uniquely associating each symbol of the quarter constellation with a respective m-2 bit label of the m input bits, wherein m-4 bits of the m-2 bit label are inherited from the symbols of the quarter-quadrant constellation and two further bits of the m-2 bit label are used to distinguish quarter-quadrants of the quarter constellation.
17. The method of claim 16 , wherein of the two further bits of the m-2 bit label used to distinguish quarter-quadrants of the quarter constellation:
a value of [00] corresponds to a quarter-quadrant of the quarter constellation having an unrotated quarter-quadrant constellation;
a value of [01] corresponds to a second quarter-quadrant of the quarter constellation having a quarter-quadrant constellation that has been rotated by −90 degrees;
a value of [11] corresponds to a third quarter-quadrant of the quarter constellation having a quarter-quadrant constellation that has been rotated by 180 degrees; and
a value of [10] corresponds to a fourth quarter-quadrant of the quarter constellation having a quarter-quadrant constellation that has been rotated by −270 degrees.
18. The method of claim 14 , wherein forming the two-dimensional symbol constellation further comprises uniquely associating each symbol of the two-dimensional symbol constellation with an m-bit label, wherein m-2 bits of the m-bit label are inherited from the quarter constellation and two further bits of the m input bits are used to distinguish quadrants of the two-dimensional symbol constellation.
19. The method of claim 18 , wherein of the two further bits of the m input bits used to distinguish quadrants of the two-dimensional symbol constellation:
a value of [00] corresponds to a first quadrant of the two-dimensional symbol constellation having the quarter constellation;
a value of [01] corresponds to a second quadrant of the two-dimensional symbol constellation having a quarter constellation that has been rotated by −90 degrees;
a value of [11] corresponds to a third quadrant of the two-dimensional symbol constellation having a quarter constellation that has been rotated by 180 degrees; and
a value of [10] corresponds to a fourth quadrant of the two-dimensional symbol constellation having a quarter constellation that has been rotated by −270 degrees.
20. The method of claim 14 , further comprising forming the m input bits from a plurality of information bits by operating upon the plurality of information bits to form a Forward Error Correction (FEC) frame.
21. The method of claim 20 , wherein the FEC frame includes an integer number of trellis groups.
22. The method of claim 20 , wherein Reed-Solomon encoding is employed to form the FEC frame.
23. The method of claim 14 , further comprising forming the m input bits from a plurality of information bits by:
Forward Error Correction (FEC) coding the plurality of information bits to produce a plurality of FEC blocks;
interleaving and randomizing the plurality of FEC blocks; and
appending a frame synch trailer to the plurality of interleaved and randomized FEC blocks to form a FEC frame.
24. The method of claim 23 , wherein the FEC frame includes an integer number of trellis groups.
25. A transmitter comprising:
Forward Error Correction block that receives a plurality of information bits and that produces a plurality of FEC blocks;
an interleaver that interleaves the plurality of FEC blocks;
a randomizer that randomizes the plurality of FEC blocks;
a frame synch trailer block that appends a frame synch trailer block to the plurality of interleaved and randomized FEC blocks to form an FEC frame having a plurality of input bits; and
an encoder that maps m input bits of the plurality of input bits to a two-dimensional symbol constellation that that was constructed by:
forming a quarter-quadrant constellation of 2 m-4 modulation symbols, where m is a positive integer greater than or equal to four;
forming a quarter constellation of the two-dimensional symbol constellation by adding to the quarter-quadrant constellation three copies of the quarter-quadrant constellation rotated by −90 degrees, 180 degrees, and −270 degrees, respectively, and then displacing the constellation by a shift value Δ such that the symbols coincide with symbols of the two-dimensional symbol constellation, wherein the quarter constellation has one-fourth the size of the two-dimensional symbol constellation; and
forming the two-dimensional symbol constellation by adding to the quarter constellation three copies of the quarter constellation rotated by +90 degrees, 180 degrees, and +270 degrees, respectively.
26. An apparatus for mapping m input bits to 2 m modulation symbols of a two-dimensional symbol constellation, where m is a positive integer greater than or equal to four, the apparatus comprising:
means for forming a quarter-quadrant constellation of 2 m-4 modulation symbols that are located in a first quadrant of the two-dimensional signal plane, the quarter-quadrant constellation having one-sixteenth the size of the two-dimensional symbol constellation;
means for uniquely associating each modulation symbol of the quarter-quadrant constellation with a respective m-4 bit label of the m input bits;
means for forming a quarter constellation of the two-dimensional symbol constellation by adding to the quarter-quadrant constellation three copies of the quarter-quadrant constellation rotated by −90 degrees, 180 degrees, and −270 degrees, respectively, and then displacing the constellation by a shift value Δ such that the symbols coincide with symbols of the two-dimensional symbol constellation, wherein the quarter constellation has one-fourth the size of the two-dimensional symbol constellation;
means for uniquely associating each symbol of the quarter constellation with a respective m-2 bit label of the m input bits, wherein m-4 bits of the m-2 bit label are inherited from the quarter-quadrant constellation and two further bits of the m-2 bit label are used to distinguish quarter-quadrants of the quarter constellation;
means for forming the two-dimensional symbol constellation by adding to the quarter constellation three copies of the quarter constellation rotated by +90 degrees, 180 degrees, and +270 degrees, respectively; and
means for uniquely associating each symbol of the two-dimensional symbol constellation with an m-bit label, wherein m-2 bits of the m-bit label are inherited from the quarter constellation and two further bits of the m input bits are used to distinguish quarters of the two-dimensional symbol constellation.