Method and apparatus for generating parity-check bits from a symbol set

An apparatus for determining values for parity check bits (p1, . . . , pm) based on a current symbol set (s1, . . . , sk), the apparatus comprising:

• a database storing a transformation of a matrix;
• and
• a microprocessor receiving the current symbol set (s1, . . . , sk) and using the transformation of the matrix to determine the parity check bits, wherein the matrix is defined by:
• a deterministic section with N2 columns of weight-2;
• for column i, 1≦i≦└m/2┘, assign a value of 1 to row position i and a value of 1 to row position i+└m/2┘, all other row positions have a value of 0;
• and
• for column i, └m/2┘+1≦i≦N2<m, assign a value of 1 to row position i−└m/2┘ and a value of 1 to row position i+1, all other row positions have a value of 0;
• and;
• a non-deteministic section with most columns of weight greater than or equal to 2;
• and wherein the matrix is equal to:
• [ I ( m / 2 ) × ( m / 2 ) I ( N 2 - m / 2 ) × ( N 2 - m / 2 ) 0 ( m - N 2 ) × ( N 2 - m / 2 ) C ( m / 2 ) × ( n - N 2 ) I ( m / 2 ) × ( m / 2 ) 0 1 × ( N 2 - m / 2 ) I ( N 2 - m / 2 ) × ( N 2 - m / 2 ) 0 ( m - N 2 - 1 ) × ( N 2 - m / 2 ) D ( m / 2 ) × ( n - N 2 ) ] ⁢ ⁢ or ⁢ [ I ⌊ m / 2 ⌋ × ⌊ m / 2 ⌋ I ( N 2 - ⌊ m / 2 ⌋ ) × ( N 2 - ⌊ m / 2 ⌋ ) 0 ( m - 1 - N 2 ) × ( N 2 - ⌊ m / 2 ⌋ ) C ⌊ m / 2 ⌋ × ( n - N 2 ) I ⌊ m / 2 ⌋ × ⌊ m / 2 ⌋ 0 1 × ⌊ m / 2 ⌋ 0 1 × ( N 2 - ⌊ m / 2 ⌋ ) I ( N 2 - ⌊ m / 2 ⌋ ) × ( N 2 - ⌊ m / 2 ⌋ ) 0 ( m - N 2 - 1 ) × ( N 2 - ⌊ m / 2 ⌋ ) D ( m + 1 ) / 2 × ( n - N 2 ) ]
• where C and D comprise a non-deterministic section of the matrix.

A method for determining values for parity check bits (p1, . . . , pm) based on a current symbol set (s1, . . . , sk), the method comprising the steps of:

• receiving the current symbol set (s1, . . . , sk);
• determining values for a first portion of the parity check bits, wherein the first portion of parity check bits is computed using the current symbol set (s1, . . . , sk);
• determining values for a second portion of the parity check bits, wherein the second portion of parity check bits is computed using the current symbol set (s1, . . . , sk) and the first portion of parity check bits;
• determining values for a third portion of the parity check bits, wherein the third portion of parity check bits is computed using the current symbol set (s1, . . . , sk), the first portion of parity check bits, and a parity check bit not within the first portion of parity check bits;
• and
• transmitting the parity check bits along with the current symbol set.