### Table 5. Performance comparison on two-dimensional FFT codes. .0

"... In PAGE 9: ... Then the FORTRAN subroutine in SGEFA performing matrix-vector multiplications was replaced with the corresonding CAL routine, MXV A. A consider- able increase in performance resulted, as shown in Table5 . However, the times reported here for the CRA Y -2 should not be taken as optimal for solving linear equations on the CRA Y -2.... In PAGE 9: ...Table5... ..."

### Table 2 Structure of two-dimensional spectrum over GF(8).

"... In PAGE 13: ... To do this constructively in the frequency domain, only an independent set of frequencies may be specified. Theo- rem 3 is easily extended to a two-dimensional version which requires that apos;?j1 = apos;(Zj mod n)(Zj apos; mod n) apos; from which we can construct Table2 . Each row of the table shows a constrained set of frequencies.... In PAGE 14: ... There are only 16 open frequencies which, because of the constraints, can encode 16 bits. This is a consequence of the fact that row 1 and column 1 have their parity symbols scattered among different rows of Table2 . The code is an unimpressive (49, 16, 9) code.... ..."

### TABLE VIII Two-dimensional code with 4 information bits and 4 code bits.

### TABLE IX Another two-dimensional code with 4 information bits and 4 code bits.

### TABLE X Two-dimensional code with 4 information bits and 5 code bits.

### TABLE XI Another two-dimensional code with 4 information bits and 5 code bits.

### Table 1: A list of type-I two-dimensional EG- LDPC codes

2001

"... In PAGE 24: ...f decoding iterations to 50. Many codes have been simulated. Simulation results of all these codes show that the SPA decoding converges very fast. For example, consider the type-I two- dimensional (4095,3367) EG-LDPC code, the fifth code given in Table1 . Figure 8 shows the con- vergence of the SPA decoding for this code with C1 D1CPDC BP BDBCBC.... In PAGE 26: ... Example 3. For D1 BP BE and D7 BP BI, the type-I two-dimensional EG-LDPC code BV B4BDB5 BXBZ B4BEBN BIB5 is a (4095,3367) code with minimum distance 65, the fifth code given in Table1 . The parity check matrix of this code has row weight AQ BP BIBG and column weight AD BP BIBG, respectively.... In PAGE 26: ... Example 4. For D1 BP BE and D7 BP BJ, the type-I two-dimensional EG-LDPC code is a (16383, 14197) code with minimum distance 129, the sixth code in Table1 . The column and row weights of its parity check matrix are both 128.... In PAGE 29: ... Example 7. Again we consider the (4095,3367) type-I two-dimensional EG-LDPC code BV B4BDB5 BXBZ B4BEBN BIB5 given in Table1 . If we split each column of the parity check matrix H of this code into 16 columns and each row of H into 3 rows, we obtain a new parity check matrix C0 BC with column weight 4 and row weights 21 and 22.... ..."

Cited by 18

### Table 2: A list of type-I two-dimensional PG- LDPC codes

2001

Cited by 18

### Table 1. Bit-codes for the classification of points in the two-dimensional Cohen-Sutherland

### Table 14. Two-dimensional test problems.

1995

"... In PAGE 24: .... ALBERT, B. COCKBURN, D. FRENCH, AND T. PETERSON scheme: vi;j + H vi+1;j vi 1;j 2 x ; vi;j+1 vi;j 1 2 y !x vi+1;j 2vi;j + vi 1;j x2 !y vi;j+1 2vi;j + vi;j 1 y2 = fi;j; where we can take, for example, !x =sup (x;y)2 x 2 H1 @f @x(x; y); @f @y(x; y) ; !y =sup (x;y)2 y 2 H2 @f @x(x; y); @f @y(x; y) ; and Hi(p1;p2)=@H @pi (p1;p2)fori =1; 2. We apply this scheme to the two test problems in Table14 ; note that p =(p1;p2). In our numerical examples, in order to reduce the arti cial viscosity of the scheme, we replace f by the exact solution u in the formulae de ning !x and !y.... In PAGE 27: ...i usion. These subjects will also be considered in forthcoming papers. Acknowledgments. The authors would like to thank one of the referees, whose criticisms led to a complete revision of the paper, and also Timothy Barth for pointing out mistakes in Table14 and in the choice of the parameter ! for the computation of Tables 15 to 17 in an earlier version of the paper. References 1.... ..."

Cited by 12