Bits-to-symbol mapping method for 4+12+16 APSK modulation

1. A computer-implemented bits-to-symbol mapping method of 4+12+16 APSK modulation, the method comprising executing computer program code instructions to cause one or more computer processor to:

represent 32 symbols of the 4+12+16 APSK modulation by a polar coordinate and arranging the 32 symbols by a size of θ while giving priority to a symbol having a small signal size when the size of θ of two or more symbols are same;

group the arranged 32 symbols into 4 groups according to quadrant regions where the symbols are located; and

allocate bits so that a same bit is allocated to symbols belonging to the same quadrant region for each region with respect to each of first to fifth bits of the symbols grouped into four regions; wherein bits are allocated so that the bits-to-symbol mapping of the third to the fifth bits of each symbol are symmetrical to Quadrature axis and In-phase axis.

2. The method of claim 1 , wherein the allocating the bits allocates bits so that the bit difference between all the adjacent symbols forming a decision boundary is 1 bit or 2 bits.

3. The method of claim 1 , wherein the allocating the bits allocates bits so that a Hamming distance between all the adjacent symbols becomes a minimum value.

4. The method of claim 1 , wherein the allocating the bits allocates bits according to following Equations 10 to 14 for the first to fifth bits, respectively

b i,h =0, if s i ∈ {R 1 ∪R 2 }, i= 1, 2, . . . , 32

b i,h =1, if s i ∈ {R 3 ∪R 4 }, i= 1, 2, . . . , 32  [Equation 10]

b i,h =0, if s i ∈{R 1 ∪R 4 }, i= 1, 2, . . . , 32

b i,h =1, if s i ∈{R 2 ∪R 3 }, i= 1, 2, . . . , 32  [Equation 11]

A =sort ( r i |r i ∈R 1 )=[α 1 α 2 . . . α 8 ]

b i,h =0, if r i ∈{α 1 . . . α 4 }, i =1, 2, . . . , 32

b i,h =1, otherwise  [Equation 12]

B =sort(r i — Q |r i ∈ R 1 )=[b 1 b 2 . . . b 8 ].

b i,h =0, if r i — Q ∈ { b 5 . . . b 8 }, i= 1, 2, . . . , 32

b i,h =1, otherwise  [Equation 13]

C =sort ( r i — I |r i ∈R 1 )=[ c 1 c 2 . . . c 8 ]

b i,h =0, if r i — I ∈ {c 4 . . . c 7 }, i= 1, 2, . . . , 32

b i,h =1, otherwise  [Equation 14]

(where s, represents an i-th symbol, b i , h represents an h-th symbol of the i-th symbol, and R k is defined by following Equation 15,

R k =[s 8k-7 s 8k-6 s 8k-5 s 8k-4 s 8k-3 s 8k-3 s 8k-1 s 8k ], k= 1, . . . , 4  [Equation 15]

r i , r i — Q , r i — 1 represent a size of the i-th signal, a Quadrature axis size of the i-th signal, and an In-phase axis size of the i-th signal, respectively, and

A=[a 1 , a 2 . . . a 8 ], B=[b 1 b 2 . . . b 8 ], C=[c 1 c 2 . . . c 8 ]

represent a set rearranged by a size r, of signals belonging to R 1 , a Quadrature axis size r i — Q , and an In-phase axis size r i I , respectively, in an ascending order).

5. A non-transitory computer-readable storage medium having stored thereon computer-executable instructions for a bits-to-symbol mapping method of 4+12+16 APSK modulation method that, in response to being executed by a computing device, cause the computing device to perform operations comprising:

representing 32 symbols of the 4+12+16 APSK modulation by a polar coordinate and arranging the 32 symbols by a size of θ while giving priority to a symbol having a small signal size when the size of θ of two or more symbols are same;

grouping the arranged 32 symbols into 4 groups according to quadrant regions where the symbols are located; and

allocating bits so that a same bits is allocated to the symbols belonging to the same quadrant region for each region with respect to each of the first to fifth bits of the symbols grouped into four regions; wherein bits are allocated so that the bits-to-symbol mapping of the third to the fifth bits of each symbol are symmetrical to Quadrature axis and In-phase axis.

6. The storage medium of claim 5 , wherein the allocating the bits allocates bits so that the bit difference between all the adjacent symbols forming a decision boundary is 1 bit or 2 bits.

7. The storage medium of claim 5 , wherein the allocating the bits allocates bits so that a Hamming distance between all the adjacent symbols becomes a minimum value.

8. The storage medium of claim 5 , wherein the allocating the bits allocates bits according to following Equations 10 to 14 for the first to fifth bits, respectively.

b i,h =0, if s i ∈ {R 1 ∪R 2 }, i= 1, 2, . . . , 32

b i,h =1, if s i ∈ {R 3 ∪R 4 }, i= 1, 2, . . . , 32  [Equation 10]

b i,h =0, if s i ∈{R 1 ∪R 4 }, i= 1, 2, . . . , 32

b i,h =1, if s i ∈{R 2 ∪R 3 }, i= 1, 2, . . . , 32  [Equation 11]

A =sort ( r i |r i ∈R 1 )=[α 1 α 2 . . . α 8 ]

b i,h =0, if r i ∈{α 1 . . . α 4 }, i =1, 2, . . . , 32

b i,h =1, otherwise  [Equation 12]

B =sort(r i — Q |r i ∈ R 1 )=[b 1 b 2 . . . b 8 ].

b i,h =0, if r i — Q ∈ { b 5 . . . b 8 }, i= 1, 2, . . . , 32

b i,h =1, otherwise  [Equation 13]

C =sort ( r i — I |r i ∈R 1 )=[ c 1 c 2 . . . c 8 ]

b i,h =0, if r i — I ∈ {c 4 . . . c 7 }, i= 1, 2, . . . , 32

b i,h =1, otherwise  [Equation 14]

(where s i represents an i-th symbol, b i , h represents an h-th symbol of the i-th symbol, and R k is defined by following Equation 15,

R k =[s 8k-7 s 8k-6 s 8k-5 s 8k-4 s 8k-3 s 8k-3 s 8k-1 s 8k ], k= 1, . . . , 4  [Equation 15]

r i , r i — Q , r i — 1 represent a size of the i-th signal, a Quadrature axis size of the i-th signal, and an In-phase axis size of the i-th signal, respectively, and

A=[a 1 a 2 . . . a 8 ], B=[b 1 b 2 . . . b 8 ], C=[c 1 c 2 . . . c 8 ]

represent a set rearranged by a size r, of signals belonging to R 1 , a Quadrature axis size r i — Q , and an In-phase axis size r i I , respectively, in an ascending order).