IS-GPS-800A - US Coast Guard Navigation Center

IS-GPS-800A - US Coast Guard Navigation Center IS-GPS-800A - US Coast Guard Navigation Center

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Figure 3.2-5. Parity Check Matrix H for LDPC CodeTables 6.2-2, 6.2-3, 6.2-4, 6.2-5, 6.2-6, and 6.2-7 shall define the coordinates of elements with value “1” in each of thesubmatrices A, B, C, D, E, and T, respectively, for Subframe 2. Tables 6.2-8, 6.2-9, 6.2-10, 6.2-11, 6.2-12, and 6.2-13shall define the coordinates of elements with value “1” in each of the submatrices A, B, C, D, E, and T, respectively,for Subframe 3. The inverse of T is not included in this document, however T is a lower triangular matrix andtherefore, the inverse of T can be easily identified.The rate ½ LDPC encoder shall use the given matrices A, B, T, C, D, and E of Section 6.2.4 to generate the encodedsymbols using the following algorithm:where,andtp 1 = 1 (E T 1 A + C) s ttp 2 = 1 (A s t + B p t 1 ) = E T 1 B + D,s = subframe 2 or subframe 3 data,[ ] t indicates transpose,elements of matrices p 1 and p 2 are modulo 2 numbers.The encoded symbols for broadcast are comprised of (s;p 1 ;p 2 ) where s is the systematic portion of the codeword, and{p 1, p 2} comprise the combined parity bits.22 IS-GPS-800A8 June 2010

3.2.3.5 InterleavingThe 1748 encoded symbols of subframes 2 and 3 are combined and interleaved using a block interleaver. The blockinterleaver is conceptually described using a two-dimensional array of 38 rows and 46 columns, as depicted inFigure 3.2-6. The LDPC encoded subframe 2 symbols are written first (MSB first) into the interleaver from left toright starting at Row 1. After Row 1 is filled, Row 2 is filled from left to right and this process continues until the1748 th symbol (LSB of LDPC encoded subframe 3) is written into the rightmost cell of the last (38 th ) row. Once all1748 symbols are written into the array, the symbols are sequentially read out of the array, for broadcast to user,from top to bottom starting at Column 1. After reading out the last symbol of the 38 th row in Column 1, Column 2symbols are read out from top to bottom and this process continues until the last symbol in the 38 th row of the lastcolumn (46 th ) is read out.23 IS-GPS-800A8 June 2010

3.2.3.5 InterleavingThe 1748 encoded symbols of subframes 2 and 3 are combined and interleaved using a block interleaver. The blockinterleaver is conceptually described using a two-dimensional array of 38 rows and 46 columns, as depicted inFigure 3.2-6. The LDPC encoded subframe 2 symbols are written first (MSB first) into the interleaver from left toright starting at Row 1. After Row 1 is filled, Row 2 is filled from left to right and this process continues until the1748 th symbol (LSB of LDPC encoded subframe 3) is written into the rightmost cell of the last (38 th ) row. Once all1748 symbols are written into the array, the symbols are sequentially read out of the array, for broadcast to user,from top to bottom starting at Column 1. After reading out the last symbol of the 38 th row in Column 1, Column 2symbols are read out from top to bottom and this process continues until the last symbol in the 38 th row of the lastcolumn (46 th ) is read out.23 <strong>IS</strong>-<strong>GPS</strong>-<strong>800A</strong>8 June 2010

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