Encoding apparatus and communication apparatus
According to one embodiment, an encoding apparatus includes an encoding unit. The encoding unit encodes a data bit sequence to generate a codeword corresponding to a parity check matrix. The parity check matrix is based on a protograph. In the protograph, each of n check nodes of a first type is connected to n variable nodes of a first type by a total of at least one edge of a first type, and to n variable nodes of a second type by a total of at least two edges of a second type. In the protograph, each of n check nodes of a second type is connected to the n variable nodes of the second type by a total of r edges of a third type, and to n variable nodes of a third type by a total of g edges of a fourth type.
1. A communication apparatus comprising:
an encoding unit configured to encode a data bit sequence to generate a codeword corresponding to a parity check matrix;
a modulation unit configured to modulate the codeword to obtain a modulation signal;
a digital-to-analog conversion unit configured to carry out a digital-to-analog conversion on the modulation signal to obtain a baseband transmission signal; and
a frequency conversion unit configured to up-convert the baseband transmission signal to obtain an RF transmission signal,
wherein:
the parity check matrix matches a matrix obtained by performing a copy and permutation operation on a spatially-coupled matrix,
the spatially-coupled matrix comprises L first matrices arranged in a diagonal direction, where L denotes an integer of at least 2,
elements in the spatially-coupled matrix other than the first matrices are all zero,
each of the first matrices comprises (d+1) expanded matrices coupled together in a row direction, where d denotes an integer of at least 1,
each of the expanded matrices is an m p rows×n p columns matrix, where m p denotes an integer of at least 2, and n p denotes an integer of at least 2,
a first total number of non-zero elements included in any row among 1 st to m p th rows of the spatially-coupled matrix is smaller than a second total number of non-zero elements included in any row among m p d+1 th to m p L th rows of the spatially-coupled matrix,
a third total number of non-zero elements included in any row among m p (L+d−1)+1 th to m p (L+d) th rows of the spatially-coupled matrix is smaller than the second total number,
a summation of the expanded matrices is equal to a fundamental matrix,
the fundamental matrix corresponds to a protograph comprising n check nodes of a first type, n check nodes of a second type, n variable nodes of a first type, n variable nodes of a second type, n variable nodes of a third type, at least n edges of a first type, at least 2n edges of a second type, rn edges of a third type, and gn edges of a fourth type, where n denotes an integer of at least 1, r denotes an integer of at least 3, and g denotes an integer of at least 2,
in the protograph, each of the n check nodes of the first type is connected to the n variable nodes of the first type by a total of at least one edge of the first type, and to the n variable nodes of the second type by a total of at least two edges of the second type,
in the protograph, each of the n check nodes of the second type is connected to the n variable nodes of the second type by a total of r edges of the third type, and to the n variable nodes of the third type by a total of g edges of the fourth type,
in the protograph, each of the n variable nodes of the first type is connected to the n check nodes of the first type by a total of at least one edge of the first type,
in the protograph, each of the n variable nodes of the second type is connected to the n check nodes of the first type by a total of at least two edges of the second type, and to the n check nodes of the second type by a total of r edges of the third type, and
in the protograph, each of the n variable nodes of the third type is connected to the n check nodes of the second type by a total of g edges of the fourth type.
2. The apparatus according to claim 1 , wherein:
the protograph further comprises n check nodes of an i+1 th type, n variable nodes of an i+2 th type, rn edges of a 2i+1 th type, and gn edges of a 2i+2 th type, where i means all integers of at least 2 and at most k and k means any integer of at least 2,
in the protograph, each of the n check nodes of the i+1 th type is connected to the n variable nodes of the second type by a total of r edges of the 2i+1 th type, and to the n variable nodes of the i+2 th type by a total of g edges of the 2i+2 th type,
in the protograph, each of the n variable nodes of the i+2 th type is connected to the n check nodes of the i+1 th type by a total of g edges of the 2i+2 th type, and
in the protograph, each of the n variable nodes of the second type is further connected to the n check nodes of the i+1 th type by a total of r edges of the 2i+1 th type.
3. The apparatus according to claim 1 , wherein:
the protograph further comprises n variable nodes of an i+3 th type, and rn edges of an i+4 th type, where i means all integers of at least 1 and at most e, and e means any integer of at least 1,
in the protograph, each of the n variable nodes of the i+3 th type is connected to the n check nodes of the second type by a total of r edges of the i+4 th type, and
in the protograph, each of the n check nodes of the second type is further connected to the n variable nodes of the i+3 th type by a total of r edges of the i+4 th type.
4. The apparatus according to claim 1 , wherein r=3 and g=2.
5. The apparatus according to claim 1 , wherein:
in the protograph, each of the n check nodes of the first type is connected to the n variable nodes of the first type by a total of one edge of the first type, and to the n variable nodes of the second type by a total of two edges of the second type,
in the protograph, each of the n variable nodes of the first type is connected to the n check nodes of the first type by a total of one edge of the first type, and
in the protograph, each of the n variable nodes of the second type is connected to the n check nodes of the first type by a total of two edges of the second type.
6. The apparatus according to claim 1 , wherein the encoding unit comprises:
a division unit configured to divide the data bit sequence into first to (L−1) th sections in time series;
a first local encoding unit configured to encode the first section to obtain a first sub-codeword, and to encode each of the second to (L−1) th sections by using encoding result of previous section to obtain each of second to (L−1) th sub-codewords; and
a second local encoding unit configured to encode encoding result of the (L−1) th section to generate an L th sub-codeword;
the codeword is composed of the first to L th sub-codewords.
7. A communication apparatus comprising:
an encoding unit configured to encode a data bit sequence to generate a codeword corresponding to a parity check matrix;
a modulation unit configured to modulate the codeword to obtain a modulation signal;
a digital-to-analog conversion unit configured to carry out a digital-to-analog conversion on the modulation signal to obtain a baseband transmission signal; and
a frequency conversion unit configured to up-convert the baseband transmission signal to obtain an RF transmission signal,
wherein:
the parity check matrix matches a matrix obtained by performing a copy and permutation operation on a spatially-coupled matrix,
the spatially-coupled matrix comprises L first matrices arranged in a diagonal direction, where L denotes an integer of at least 2,
elements in the spatially-coupled matrix other than the first matrices are all zero,
each of the first matrices comprises (d+1) expanded matrices coupled together in a row direction, where d denotes an integer of at least 1,
each of the expanded matrices is an m p rows×n p columns matrix, where m p denotes an integer of at least 2, and n p denotes an integer of at least 2,
a first total number of non-zero elements included in any row among 1 st to m p th rows of the spatially-coupled matrix is smaller than a second total number of non-zero elements included in any row among m p d+1 th to m p L th rows of the spatially-coupled matrix,
a third total number of non-zero elements included in any row among m p (L+d−1)+1 th to m p (L+d) th rows of the spatially-coupled matrix is smaller than the second total number,
a summation of the expanded matrices is equal to a fundamental matrix,
the fundamental matrix corresponds to a protograph comprising a check node of a first type, a check node of a second type, a variable node of a first type, a variable node of a second type, a variable node of a third type, at least one edge of a first type, at least two edges of a second type, r edges of a third type, and g edges of a fourth type, where r denotes an integer of at least 3, and g denotes an integer of at least 2,
in the protograph, the check node of the first type is connected to the variable node of the first type by the at least one edge of the first type, and to the variable node of the second type by the at least two edges of the second type, and
in the protograph, the check node of the second type is connected to the variable node of the second type by the r edges of the third type, and to the variable node of the third type by the g edges of the fourth type.
8. The apparatus according to claim 7 , wherein:
the protograph further comprises a check node of an i+1 th type, a variable node of an i+2 th type, r edges of a 2i+1 th type, and g edges of a 2i+2 th type, where i means all integers of at least 2 and at most k and k means any integer of at least 2,
in the protograph, the check node of the i+1 th type is connected to the variable node of the second type by the r edges of the 2i+1 th type, and to the variable node of the i+2 th type by the g edges of the 2i+2 th type,
in the protograph, the variable node of the i+2 th type is connected to the check node of the i+1 th type by the g edges of the 2i+2 th type, and
in the protograph, the variable node of the second type is further connected to the check node of the i+1 th type by the r edges of the 2i+1 th type.
9. The apparatus according to claim 7 , wherein:
the protograph further comprises a variable node of an i+3 th type, and r edges of an i+4 th type, where i means all integers of at least 1 and at most e, and e means any integer of at least 1,
in the protograph, the variable node of the i+3 th type is connected to the check node of the second type by the r edges of the i+4 th type, and
in the protograph, the check node of the second type is further connected to the variable node of the i+3 th type by the r edges of the i+4 th type.
10. The apparatus according to claim 7 , wherein r=3 and g=2.
11. The apparatus according to claim 7 , wherein:
in the protograph, the check node of the first type is connected to the variable node of the first type by one edge of the first type, and to the variable node of the second type by two edges of the second type,
in the protograph, the variable node of the first type is connected to the check node of the first type by one edge of the first type, and
in the protograph, the variable node of the second type is connected to the check node of the first type by two edges of the second type.
12. The apparatus according to claim 7 , wherein:
the expanded matrices comprise a first expanded matrix and a second expanded matrix,
the protograph corresponding to the fundamental matrix is equal to a summation of a first partial protograph corresponding to the first expanded matrix and a second partial protograph corresponding to the second expanded matrix,
in the first partial protograph, the check node of the second type is connected to the variable node of the second type by one edge of the third type, and to the variable node of the third type by one edge of the fourth type,
in the second partial protograph, the check node of the first type is connected to the variable node of the first type by the at least one edge of the first type, and to the variable node of the second type by the at least two edges of the second type, and
in the second partial protograph, the check node of the second type is connected to the variable node of the second type by r−1 edges of the third type, and to the variable node of the third type by g−1 edges of the fourth type.
13. A storage apparatus comprising:
an encoding unit configured to encode a data bit sequence to generate a codeword corresponding to a parity check matrix; and
a non-volatile computer-readable memory configured to store computer-readable data corresponding to the generated codeword,
wherein:
the non-volatile computer-readable memory comprises an array structure in which a plurality of memory cells are connected together, wherein each of the memory cells is assigned with at least two threshold voltages and can store data of at least 1 bit, and the non-volatile computer-readable memory stores the generated codeword in the memory cells as page data output by the encoding unit,
the parity check matrix matches a matrix obtained by performing a copy and permutation operation on a spatially-coupled matrix,
the spatially-coupled matrix comprises L first matrices arranged in a diagonal direction, where L denotes an integer of at least 2,
elements in the spatially-coupled matrix other than the first matrices are all zero,
each of the first matrices comprises (d+1) expanded matrices coupled together in a row direction, where d denotes an integer of at least 1,
each of the expanded matrices is an m p rows×n p columns matrix, where m p denotes an integer of at least 2, and n p denotes an integer of at least 2,
a first total number of non-zero elements included in any row among 1 st to m p th rows of the spatially-coupled matrix is smaller than a second total number of non-zero elements included in any row among m p d+1 th to m p L th rows of the spatially-coupled matrix,
a third total number of non-zero elements included in any row among m p (L+d−1)+1 th to m p (L+d) th rows of the spatially-coupled matrix is smaller than the second total number,
a summation of the expanded matrices is equal to a fundamental matrix,
the fundamental matrix corresponds to a protograph comprising n check nodes of a first type, n check nodes of a second type, n variable nodes of a first type, n variable nodes of a second type, n variable nodes of a third type, at least n edges of a first type, at least 2n edges of a second type, rn edges of a third type, and gn edges of a fourth type, where n denotes an integer of at least 1, r denotes an integer of at least 3, and g denotes an integer of at least 2,
in the protograph, each of the n check nodes of the first type is connected to the n variable nodes of the first type by a total of at least one edge of the first type, and to the n variable nodes of the second type by a total of at least two edges of the second type,
in the protograph, each of the n check nodes of the second type is connected to the n variable nodes of the second type by a total of r edges of the third type, and to the n variable nodes of the third type by a total of g edges of the fourth type,
in the protograph, each of the n variable nodes of the first type is connected to the n check nodes of the first type by a total of at least one edge of the first type,
in the protograph, each of the n variable nodes of the second type is connected to the n check nodes of the first type by a total of at least two edges of the second type, and to the n check nodes of the second type by a total of r edges of the third type, and
in the protograph, each of the n variable nodes of the third type is connected to the n check nodes of the second type by a total of g edges of the fourth type.
14. The apparatus according to claim 13 , wherein the protograph further comprises n check nodes of an i+1 th type, n variable nodes of an i+2 th type, rn edges of a 2i+1 th type, and gn edges of a 2i+2 th type, where i means all integers of at least 2 and at most k and k means any integer of at least 2,
in the protograph, each of the n check nodes of the i+1 th type is connected to the n variable nodes of the second type by a total of r edges of the 2i+1 th type, and to the n variable nodes of the i+2 th type by a total of g edges of the 2+2 th type,
in the protograph, each of the n variable nodes of the i+2 th type is connected to the n check nodes of the i+1 th type by a total of g edges of the 2i+2 th type, and
in the protograph, each of the n variable nodes of the second type is further connected to the n check nodes of the i+1 th type by a total of r edges of the 2i+1 th type.
15. The apparatus according to claim 13 , wherein the protograph further comprises n variable nodes of an i+3th type, and rn edges of an i+4th type, where i means all integers of at least 1 and at most e, and e means any integer of at least 1,
in the protograph, each of the n variable nodes of the i+3 th type is connected to the n check nodes of the second type by a total of r edges of the i+4 th type, and
in the protograph, each of the n check nodes of the second type is further connected to the n variable nodes of the i+3th type by a total of r edges of the i+4th type.
16. The apparatus according to claim 13 , wherein r=3 and g=2.
17. The apparatus according to claim 13 , wherein in the protograph, each of the n check nodes of the first type is connected to the n variable nodes of the first type by a total of one edge of the first type, and to the n variable nodes of the second type by a total of two edges of the second type,
in the protograph, each of the n variable nodes of the first type is connected to the n check nodes of the first type by a total of one edge of the first type, and
in the protograph, each of the n variable nodes of the second type is connected to the n check nodes of the first type by a total of two edges of the second type.
18. A communication method for a communication apparatus comprising an encoding unit, a modulation unit, a digital-to-analog conversion unit, and a frequency conversion unit, the communication method comprising:
encoding, by the encoding unit, a data bit sequence to generate a codeword corresponding to a parity check matrix;
modulating, by the modulation unit, the codeword to obtain a modulation signal;
carrying out, by a digital-to-analog conversion unit, a digital-to-analog conversion on the modulation signal to obtain a baseband transmission signal; and
up-converting, by a frequency conversion unit, the baseband transmission signal to obtain an RF transmission signal,
wherein:
the parity check matrix matches a matrix obtained by performing a copy and permutation operation on a spatially-coupled matrix,
the spatially-coupled matrix comprises L first matrices arranged in a diagonal direction, where L denotes an integer of at least 2,
elements in the spatially-coupled matrix other than the first matrices are all zero,
each of the first matrices comprises (d+1) expanded matrices coupled together in a row direction, where d denotes an integer of at least 1,
each of the expanded matrices is an m p rows×n p columns matrix, where m p denotes an integer of at least 2, and n p denotes an integer of at least 2,
a first total number of non-zero elements included in any row among 1 st to m p th rows of the spatially-coupled matrix is smaller than a second total number of non-zero elements included in any row among m p d+1 th to m p L th rows of the spatially-coupled matrix,
a third total number of non-zero elements included in any row among m p (L+d−1)+1 th to m p (L+d) th rows of the spatially-coupled matrix is smaller than the second total number,
a summation of the expanded matrices is equal to a fundamental matrix,
the fundamental matrix corresponds to a protograph comprising n check nodes of a first type, n check nodes of a second type, n variable nodes of a first type, n variable nodes of a second type, n variable nodes of a third type, at least n edges of a first type, at least 2n edges of a second type, rn edges of a third type, and gn edges of a fourth type, where n denotes an integer of at least 1, r denotes an integer of at least 3, and g denotes an integer of at least 2,
in the protograph, each of the n check nodes of the first type is connected to the n variable nodes of the first type by a total of at least one edge of the first type, and to the n variable nodes of the second type by a total of at least two edges of the second type,
in the protograph, each of the n check nodes of the second type is connected to the n variable nodes of the second type by a total of r edges of the third type, and to the n variable nodes of the third type by a total of g edges of the fourth type,
in the protograph, each of the n variable nodes of the first type is connected to the n check nodes of the first type by a total of at least one edge of the first type,
in the protograph, each of the n variable nodes of the second type is connected to the n check nodes of the first type by a total of at least two edges of the second type, and to the n check nodes of the second type by a total of r edges of the third type, and
in the protograph, each of the n variable nodes of the third type is connected to the n check nodes of the second type by a total of g edges of the fourth type.