Parallel precoder circuit

A parallel precoder circuit that executes an exclusive-OR operation on an n-row parallel input, and outputs an n-row parallel output, where n is an integer equal to or larger than two, the parallel precoder circuit comprising:

• an nth-row delay circuit that delays an output of an exclusive-OR circuit having a largest column number from among exclusive-OR circuits disposed in nth row;
• a zeroth-column exclusive-OR circuit that executes the exclusive-OR operation of an output of the nth-row delay circuit and a first-row parallel input;
• an (r×k)th-row first-column exclusive-OR circuit that executes the exclusive-OR operation of an output of the zeroth-column exclusive-OR circuit and parallel inputs from second row to rth row when k is 1, and executes the exclusive-OR operation of parallel input from (r×k−r+1)th row to (r×k)th row when k is larger than 1, where r is a maximum number of inputs to a plurality of multiple-input exclusive-OR circuits, r is an integer equal to or larger than two, and k is an integer equal to or larger than one and equal to or smaller than n/r;
• an (r×k)th-row mth-column multiple-input exclusive-OR circuit that executes the exclusive-OR operation with an output of an (r×k−p×r^(m−1))th-row (m−1)th-column multiple-input exclusive-OR circuit from (r×k−(r−1)×r^(m−1))th row to (r×k)th row as an input when r×k−p×r^(m−1) is equal to or larger than one, and executes the exclusive-OR operation with an output of a multiple-input exclusive-OR circuit having a largest column number from among multiple-input exclusive-OR circuits disposed in (r×k−p×r^(m−1))th row as the input when no multiple-input exclusive-OR circuit is disposed in (r×k−p×r^(m−1))th row (m−1)th column, where m is an integer equal to or larger than 2 and equal to or smaller than h−1, h is a smallest integer equal to or larger than logr n+1, and p is an integer equal to or larger than zero and equal to or smaller than r−1;
• and
• an (r×k−q)th-row hth-column multiple-input exclusive-OR circuit that executes the exclusive-OR operation of a parallel input from (r×k−1)th row to (r×k−q)th row and an output of a multiple-input exclusive-OR circuit having a largest column number from among multiple-input exclusive-OR circuits disposed in (r×k−r)th row, where q is an integer equal to or larger than one and equal to or smaller than r−1, wherein
• outputs of exclusive-OR circuits each of which having a largest column number from among exclusive-OR circuits disposed in first to (n−1)th rows become first-row to (n−1)th-row parallel outputs, respectively, and
• the output of the nth-row delay circuit becomes an nth-row parallel output.

A parallel precoder circuit that executes an exclusive-OR operation on an n-row parallel input, and outputs an n-row parallel output, where n is an integer equal to or larger than two, the parallel precoder circuit comprising:

• an nth-row delay circuit that delays an output of an exclusive-OR circuit having a largest column number from among exclusive-OR circuits disposed in nth row;
• a zeroth-column exclusive-OR circuit that executes the exclusive-OR operation of an output of the nth-row delay circuit and a first-row parallel input;
• a kth-row first-column exclusive-OR circuit that executes the exclusive-OR operation of a kth-row parallel input and an output of the zeroth-column exclusive-OR circuit when k is two or a (k−1)th-row parallel input when k is larger than two, where k is an integer equal to or larger than two and equal to or smaller than n;
• and
• a kth-row mth-column exclusive-OR circuit that executes the exclusive-OR operation of an output of a kth-row (m−1)th-column exclusive-OR circuit and an output of a (k−2^(m−1))th-row (m−1)th-column, when k−2^(m−1) is equal to or larger than one, and executes the exclusive-OR operation of the output of the kth-row (m−1)th-column exclusive-OR circuit and an output of an exclusive-OR circuit having a largest column number from among exclusive-OR circuits disposed in (k−2^(m−1))th row when no exclusive-OR circuit is disposes in (k−2^(m−1))th-row (m−1)th-column, where m is an integer equal to or larger than two and equal to or smaller than h, and h is a smallest integer equal to or larger than log2 n, wherein
• outputs of exclusive-OR circuits each of which having a largest column number from among exclusive-OR circuits disposed in first to (n−1)th rows become first-row to (n−1)th-row parallel outputs, respectively, and
• the output of the nth-row delay circuit becomes an nth-row parallel output.

A parallel precoder circuit that executes an exclusive-OR operation on an n-row parallel input, and outputs an n-row parallel output, where n is an integer equal to or larger than two, the parallel precoder circuit comprising:

• an nth-row delay circuit that delays an output of an exclusive-OR circuit having a largest column number from among exclusive-OR circuits disposed in nth row;
• a zeroth-column exclusive-OR circuit that executes the exclusive-OR operation of an output of the nth-row delay circuit and a first-row parallel input;
• a kth-row first-column exclusive-OR circuit that executes the exclusive-OR operation of an output of the zeroth-column exclusive-OR circuit and a (k−q)th-row parallel input from second row to kth row when k−q is one, or a (k−q)th-row parallel input from (k−r+1)th row to the kth row when k−q is larger than one, where r is a maximum number of inputs to a plurality of multiple-input exclusive-OR circuits, r is an integer equal to or larger than two, k is an integer equal to or larger than two and equal to or smaller than n, and q is an integer equal to or larger than zero and equal to or smaller than r−1;
• and
• a kth-row mth-column multiple-input exclusive-OR circuit that executes the exclusive-OR operation with an output of a (k−p×r^(m−1))th-row (m−1)th-column multiple-input exclusive-OR circuit from (k−(r−1)×r^(m−1))th row to the kth row as an input when k−p×r^(m−1) is equal to or larger than one, and executes the exclusive-OR operation with an output of a multiple-input exclusive-OR circuit having a largest column number from among multiple-input exclusive-OR circuits disposed in (k−p×r^(m−1))th row when no multiple-input exclusive-OR circuit is disposed in (k−p×r^(m−1))th-row (m−1)th-column, where m is an integer equal to or larger than two and equal to or smaller than h, h is a smallest integer equal to or larger than log2 n, and p is an integer equal to or larger than zero and equal to or smaller than r−1, wherein
• outputs of exclusive-OR circuits each of which having a largest column number from among exclusive-OR circuits disposed in first to (n−1)th rows become first-row to (n−1)th-row parallel outputs, respectively, and
• the output of the nth-row delay circuit becomes an nth-row parallel output.

A parallel precoder circuit that executes an exclusive-OR operation on an n-row parallel input, and outputs an n-row parallel output, where n is an integer equal to or larger than two, the parallel precoder circuit comprising:

• an nth-row delay circuit that delays an output of an exclusive-OR circuit having a largest column number from among exclusive-OR circuits disposed in nth row;
• a zeroth-column exclusive-OR circuit that executes the exclusive-OR operation of an output of the nth-row delay circuit and a first-row parallel input;
• a (2k)th-row first-column exclusive-OR circuit that executes the exclusive-OR operation of a (2k)th-row parallel input and an output of the zeroth-column exclusive-OR circuit when k is one or a (2k−1)th-row parallel input when k is larger than one, where k is an integer equal to or larger than one and equal to or smaller than n/2;
• a ((2^m)×k)th-row mth-column exclusive-OR circuit that executes the exclusive-OR operation of an output of a ((2^m)×k)th-row (m−1)th-column exclusive-OR circuit and an output of a ((2^m)×k−2^(m−1))th-row (m−1)th-column exclusive-OR circuit when (2^m)×k−2^(m−1) is equal to or larger than one and when (2^m)×k is equal to or smaller than n, where m is an integer equal to or larger than two and equal to or smaller than hh, and hh is a smallest integer equal to or larger than log2 n satisfying h=2×hh−1, where h indicates a last column where an exclusive-OR circuit is disposed;
• and
• a ((2^hh−(2kk−1)×2^(2hh−m−1))th-row mth-column exclusive-OR circuit that executes the exclusive-OR operation of an output of an exclusive-OR circuit having a largest column number from among exclusive-OR circuits disposed in ((2^hh−(2kk−1)×2^(2hh−m−1))th row and an output of an exclusive-OR circuit having a largest column number from among exclusive-OR circuits disposed in ((2^hh−2kk×2^(2hh−m−1))th row when m is equal to or larger than hh and equal to or smaller than 2×hh−1, where kk is an integer equal to or larger than one, wherein
• outputs of exclusive-OR circuits each of which having a largest column number from among exclusive-OR circuits disposed in first to (n−1)th rows become first-row to (n−1)th-row parallel outputs, respectively, and
• the output of the nth-row delay circuit becomes an nth-row parallel output.