1. A message-passing decoder for low-density parity-check (LDPC) codes, which is for decoding block codes encoded with LDPC codes by a message-passing decoding algorithm, the message-passing decoder comprising:
a log likelihood ratio calculator for receiving a code word having a consecutive value from block codes encoded with the LDPC codes, and calculating a log likelihood ratio;
a bit node function unit for calculating a bit message using the log likelihood ratio calculated by the log likelihood ratio calculator and an input parity-check message;
a check node function unit for calculating the parity-check message using the bit message calculated by the bit node function unit, and outputting the calculated parity-check message to the bit node function unit; and
a parity checker for receiving a code word decoded by the bit node function unit from the final parity-check message calculated by a repeated decoding of the bit node function unit and the check node function unit, and checking a parity,
wherein the parity-check message corresponding to a logic function output for an input from the bit node function unit is calculated according to a linear approximation function determined for each divided interval of the logic function.
2. The message-passing decoder as claimed in claim 1, wherein the check node function unit comprises:
a multiplier for multiplying the input from the bit node function unit by a slope of the linear approximation function for each interval;
a summator for adding a boundary value of the linear approximation function for each interval to an output value of the multiplier; and
a multiplexor for selecting an output of the summator according to an interval range of the input.
3. The message-passing decoder as claimed in claim 1, wherein the check node function unit comprises:
a slope calculator for calculating a slope, to be multiplied, from a bit of the highest order other than \u201c0\u201d in the input from the bit node function unit, and multiplying the slope with a bit shifter and a summator;
a boundary calculator for calculating a boundary value of the linear approximation function for each interval from the bit of the highest order other than \u201c0\u201d in the input; and
a summator for adding the boundary value calculated by the boundary calculator to an output of the slope calculator.
4. The message-passing decoder as claimed in claim 3, wherein the slope calculator comprises:
a bit shifter for shifting each bit of the input to the left or right side so as to construct the slope;
a ground for expressing a value of \u201c0\u201d used in the calculation of the slope;
a word negater for inverting an output of the bit shifter by each word sign to express the slope; and
a switch for combining the outputs of the word negater and the ground to output a final result.
5. The message-passing decoder as claimed in claim 4, wherein the boundary calculator comprises:
a bit shifter for shifting each bit of the input to the left or right side so as to construct the boundary value;
a ground for expressing a value of \u201c0\u201d used in the calculation of the boundary value;
a word negater for inverting an output of the bit shifter by each word sign to express the boundary value; and
a switch for combining the outputs of the word negater and the ground to output a final result.
6. The message-passing decoder as claimed in claims 1, wherein the logic function \u03a6(x) satisfies the following equation:
\u03a6
\u2061
(
x
)
=
–
log
\u2061
(
tanh
\u2061
(
\uf603
x
\uf604
2
)
)
wherein x is the input from the bit node function unit.
7. The message-passing decoder as claimed in claim 6, wherein the interval Ii of the linear approximation is determined by the following equation:
Ii=\u25142K+i2K+1+i\u2518, i\u2208{0, . . . , n1\u22121}, K=\u2212n2
wherein n1 is the length of a word expressing the input, i.e., a word length; and n2 is the bit corresponding to a minimum resolution of decimal places expressing the input,
the boundary value on either side of the interval being the power of 2.
8. The message-passing decoder as claimed in claim 7, wherein the linear approximation function y satisfies the following equation:
y=si\u03b3+xi, i\u2208{0, . . . , |{Ii}|\u22121}, r\u2208Ii
wherein si is the slope; and xi is the boundary value.
9. The message-passing decoder as claimed in claim 8, wherein the slope si satisfies the following equation:
s
i
=
ROUND
\u2061
(
\u03a6
\u2061
(
2
K
+
n
1
–
i
–
1
)
–
\u03a6
\u2061
(
2
K
+
n
1
–
i
)
2
K
+
n
1
–
i
–
1
–
2
K
+
n
1
–
i
,
n
2
)
,
\u2062
i
\u2265
0
wherein the ROUND function is a function for designating the input as the most approximate one of binary numbers given by 2\u2212n2 as the minimum resolution,
the ROUND function satisfying the following equation:
ROUND
\u2061
(
x
,
n
2
)
=
2
–
n
2
\u2062
\u230a
x
2
–
n
2
+
1
2
\u230b
.
10. The message-passing decoder as claimed in claim 9, wherein the boundary value x, satisfies the following equation:
xi=ROUND((2K+n1\u2212i\u22122K+n1\u2212i+1)si+xi\u22121, n2), i\u22671,
x0=ROUND(\u03a6(2K+n1), n2).
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
What is claimed is:
1. An auto body dent repair, comprising:
(A) a tool body, comprising:
(a) a rearward shaft comprising a simple shaft having rear end and a forward end carrying an adjustable fastener;
(b) a forward shaft having an adjustable fastener, carried by a rearward portion of the forward shaft, mated with the adjustable fastener carried by the rearward shaft, and having a tip fastener peg carried by a forward portion of the forward shaft; and
(c) a handle, carried by a rearward portion of the rearward shaft; and
(B) a tip, attached to the tip fastener peg of the forward shaft.
2. An auto body dent repair, comprising:
(A) a tool body, comprising:
(a) a rearward shaft comprising a compound shaft comprising forward and rearward portions separated by a fixed joint, having a rear end and a forward end carrying an adjustable fastener;
(b) a forward shaft having an adjustable fastener, carried by a rearward portion of the forward shaft, mated with the adjustable fastener carried by the rearward shaft, and having a tip fastener peg carried by a forward portion of the forward shaft; and
(c) a handle, carried by a rearward portion of the rearward shaft, defines a hole through which passes the rearward portion of the rearward shaft; and
(B) a tip, attached to the tip fastener peg of the forward shaft.
5. A kit of parts for auto body dent repair, comprising:
(A) a plurality of tool bodies, wherein each tool body comprises:
(a) a rearward shaft comprising a simple shaft having rear end and a forward end carrying an adjustable fastener;
(b) a forward shaft having an adjustable fastener, carried by a rearward portion of the forward shaft, mated with the adjustable fastener carried by the rearward shaft, and having a tip fastener peg carried by a forward portion of the forward shaft; and
(c) a handle, carried by a rearward portion of the rearward shaft, defines a hole through which passes the rearward portion of the rearward shaft;
(B) a plurality of tool bodies, wherein each tool body comprises:
(a) a rearward shaft comprising a compound shaft comprising forward and rearward portions separated by a fixed joint, having a rear end and a forward end carrying an adjustable fastener;
(b) a forward shaft having an adjustable fastener, carried by a rearward portion of the forward shaft, mated with the adjustable fastener carried by the rearward shaft, and having a tip fastener peg carried by a forward portion of the forward shaft; and
(c) a handle, carried by a rearward portion of the rearward shaft, defines a hole through which passes the rearward portion of the rearward shaft;
(C) a plurality of integral dent repair tips, wherein each integral dent repair tip may be installed on the adjustable fastener of the rearward shaft; and
(D) a plurality of tips, wherein any of a plurality of tips may be attached in turn to the tip fastener peg of the forward shaft.