Computation of Reliability Values
There are disclosed systems and methods for computing a reliability value for a bit of a received symbol value y associated with a constellation. In one embodiment, the method comprises computing the reliability value by obtaining a first minimum distance value, the first minimum distance value being a function of an absolute magnitude of an initial value associated with the bit, and combining the first minimum distance value with a second minimum distance value, the second minimum distance value being a function of a distance between the received symbol value y and a symbol x {circumflex over (b)} in the constellation corresponding to a most likely pattern of bits transmitted given the received symbol value y.
1 . A method of computing a reliability value for a bit of a received symbol value y associated with a constellation; the method comprising:
computing the reliability value by obtaining a first minimum distance value, the first minimum distance value being a function of an absolute magnitude of an initial value associated with the bit, and combining the first minimum distance value with a second minimum distance value, the second minimum distance value being a function of a distance between the received symbol value y and a symbol x {circumflex over (b)} in the constellation corresponding to a most likely pattern of bits transmitted given the received symbol value y.
2 . The method of claim 1 , wherein the second minimum distance value is equal to the distance between the received symbol value y and the symbol x {circumflex over (b)} in the constellation corresponding to the most likely pattern of bits transmitted given the received symbol value y.
3 . The method of claim 1 , wherein said combining the first minimum distance value with the second minimum distance value comprises either subtracting the first minimum distance value from the second minimum distance value or subtracting the second minimum distance value from the first minimum distance value.
4 . The method of claim 1 , further comprising:
receiving a wireless signal from a wireless channel;
obtaining the received symbol value y from the wireless signal;
performing decoding using the reliability value.
5 . The method of claim 1 , wherein the constellation is square QAM or rectangular QAM, wherein the reliability value is computed as part of demapping, and wherein the demapping is performed by decomposing the QAM constellation into two independent PAM constellations representing an in-phase and a quadrature-phase signal respectively, and independently demapping each of the two independent PAM constellations.
6 . The method of claim 1 , further comprising: obtaining a hard decision representing the most likely pattern of bits transmitted given the received symbol value y, and computing the second minimum distance value by directly computing the distance between the received symbol value y and the symbol x {circumflex over (b)} in the constellation corresponding to the hard decision.
7 . The method of claim 1 , wherein the constellation comprises a set of constellation points having a minimum distance of 2d between a pair of the constellation points, and wherein the first minimum distance value is equal to d plus the absolute magnitude of the initial value.
8 . The method of claim 1 , wherein the constellation comprises a set of constellation points having a minimum distance of 2d between a pair of the constellation points, the received symbol value y represents m bits that were transmitted using a modulation scheme of the constellation; the method further comprising:
obtaining m initial values y 0 , y 1 , . . . , y m-1 from the received symbol value y, one for each of the m bits, the initial value being a k th one, y k , of the m initial values;
computing the first minimum distance value as d+|y k |, where |y k | is the absolute magnitude of the initial value;
computing the second minimum distance value as a value equal to the distance between the received symbol value y and the symbol x {circumflex over (b)} in the constellation corresponding to the most likely pattern of bits transmitted given the received symbol value y.
9 . The method of claim 8 , further comprising computing the second minimum distance value as ∥y m-1 |−d|.
10 . The method of claim 8 , wherein Gray coding is used in the constellation, and wherein said obtaining m initial values y 0 , y 1 , . . . , y m-1 from the received symbol value y comprises:
selecting the received symbol value y as a first initial value y 0 ;
for k=1, . . . , m−1, computing a k th initial value, y k , as y k =2 m-k d−|y k-1 |.
11 . The method of claim 8 , wherein natural coding is used in the constellation, and wherein said obtaining m initial values y 0 , y 1 , . . . , y m-1 from the received symbol value y comprises:
selecting the received symbol value y as a first initial value y 0 ;
for k=1, . . . , m−1, computing a k th initial value, y k , as
y
k
=
{
y
k
-
1
-
2
m
-
k
d
,
y
k
-
1
≥
0
y
k
-
1
+
2
m
-
k
d
,
y
k
-
1
<
0
.
12 . The method of claim 8 , further comprising computing m reliability values, one of the m reliability values being said reliability value; wherein the m reliability values are computed by, for i=0, . . . , m−1, computing an i th reliability value including computing d+|y i | to obtain an i th first minimum distance value, and combining the i th first minimum distance value with the second minimum distance value.
13 . The method of claim 12 , wherein the initial values are soft-sliced values, wherein the constellation is either a Pulse Amplitude Modulation (PAM) constellation or a Quadrature Amplitude Modulation (QAM) constellation, and wherein each one of the m reliability values is a Log Likelihood Ratio (LLR) computed as:
L
(
b
i
)
=
min
b
→
,
b
i
=
1
y
-
x
b
→
2
-
min
b
→
,
b
i
=
0
y
-
x
b
→
2
k
,
wherein the i th first minimum distance value is used to compute one of
min
b
→
,
b
i
=
1
y
-
x
b
→
and
min
b
→
,
b
i
=
0
y
-
x
b
→
,
and wherein the second minimum distance value is used to compute the other of
min
b
→
,
b
i
=
1
y
-
x
b
→
and
min
b
→
,
b
i
=
0
y
-
x
b
→
,
and where {right arrow over (b)} is a bit vector of m bits, x {right arrow over (b)} is a symbol in the constellation associated with the bit vector {right arrow over (b)}, {right arrow over (b)},b i =0 is a set of all possible bit vectors whose i th bit is 0, {right arrow over (b)},b i =1 is a set of all possible bit vectors whose i th bit is 1, k is a scaling factor, |y−x {right arrow over (b)} | represents the absolute value of the difference between the received symbol value y and the symbol x {right arrow over (b)} ,
min
b
→
,
b
i
=
1
y
-
x
b
→
is a minimum of the set of values |y−x {right arrow over (b)} | for {right arrow over (b)},b i =1, and
min
b
→
,
b
i
=
0
y
-
x
b
→
is a minimum of the set of values |y−x {right arrow over (b)} | for {right arrow over (b)},b i =0.
14 . An apparatus in a digital communications system, the apparatus comprising a constellation demapper for computing a reliability value for a bit of a received symbol value y associated with a constellation; the constellation demapper for performing operations comprising:
computing the reliability value by obtaining a first minimum distance value, the first minimum distance value being a function of an absolute magnitude of an initial value associated with the bit, and combining the first minimum distance value with a second minimum distance value, the second minimum distance value being a function of a distance between the received symbol value y and a symbol x {circumflex over (b)} in the constellation corresponding to a most likely pattern of bits transmitted given the received symbol value y.
15 . The apparatus of claim 14 , wherein the second minimum distance value is equal to the distance between the received symbol value y and the symbol x {circumflex over (b)} in the constellation corresponding to the most likely pattern of bits transmitted given the received symbol value y.
16 . The apparatus of claim 14 , wherein said combining the first minimum distance value with the second minimum distance value comprises either subtracting the first minimum distance value from the second minimum distance value or subtracting the second minimum distance value from the first minimum distance value.
17 . The apparatus of claim 14 , wherein the apparatus is a mobile device and the apparatus further comprises:
a receiver for receiving a wireless signal from a wireless channel;
processing circuitry for obtaining the received symbol value y from the wireless signal; and
a decoder for decoding using the reliability value.
18 . The apparatus of claim 14 , wherein the constellation comprises a set of constellation points having a minimum distance of 2d between a pair of the constellation points, and wherein the first minimum distance value is equal to d plus the absolute magnitude of the initial value.
19 . The apparatus of claim 14 , wherein the constellation comprises a set of constellation points having a minimum distance of 2d between a pair of the constellation points, the received symbol value y represents m bits that were transmitted using a modulation scheme of the constellation; the constellation demapper for performing further operations comprising:
obtaining m initial values y 0 , y 1 , . . . , y m-1 from the received symbol value y, one for each of the m bits, the initial value being a k th one, y k , of the m initial values;
computing the first minimum distance value as d+|y k |, where |y k | is the absolute magnitude of the initial value;
computing the second minimum distance value as a value equal to the distance between the received symbol value y and the symbol x {circumflex over (b)} in the constellation corresponding to the most likely pattern of bits transmitted given the received symbol value y.
20 . The apparatus of claim 19 , wherein the constellation demapper is further for computing the second minimum distance value as ∥y m-1 |−d|.
21 . The apparatus of claim 19 , wherein Gray coding is used in the constellation, and wherein said obtaining m initial values y 0 , y 1 , . . . , y m-1 from the received symbol value y comprises:
selecting the received symbol value y as a first initial value y 0 ;
for k=1, . . . , m−1, computing a k th initial value, y k , as y k =2 m-k d−|y k-1 |.
22 . The apparatus of claim 19 , wherein natural coding is used in the constellation, and wherein said obtaining m initial values y 0 , y 1 , . . . , y m-1 from the received symbol value y comprises:
selecting the received symbol value y as a first initial value y 0 ;
for k=1, . . . , m−1, computing a k th initial value, y k , as
y
k
=
{
y
k
-
1
-
2
m
-
k
d
,
y
k
-
1
≥
0
y
k
-
1
+
2
m
-
k
d
,
y
k
-
1
<
0
.
23 . The apparatus of claim 19 , wherein the constellation demapper is for computing m reliability values, one of the m reliability values being said reliability value; wherein the m reliability values are computed by, for i=0, . . . , m−1, computing an i th reliability value including computing d+|y i | to obtain an i th first minimum distance value, and combining the i th first minimum distance value with the second minimum distance value.
24 . The apparatus of claim 23 , wherein the initial values are soft sliced values, wherein the constellation is either a Pulse Amplitude Modulation (PAM) constellation or a Quadrature Amplitude Modulation (QAM) constellation, and wherein each one of the m reliability values is a Log Likelihood Ratio (LLR) that is to be computed in the constellation demapper as:
L
(
b
i
)
=
min
b
→
,
b
i
=
1
y
-
x
b
→
2
-
min
b
→
,
b
i
=
0
y
-
x
b
→
2
k
,
wherein the i th first minimum distance value is used to compute one of
min
b
→
,
b
i
=
1
y
-
x
b
→
and
min
b
→
,
b
i
=
0
y
-
x
b
→
,
and wherein the second minimum distance value is used to compute the other of
min
b
→
,
b
i
=
1
y
-
x
b
→
and
min
b
→
,
b
i
=
0
y
-
x
b
→
,
and where {right arrow over (b)} is a bit vector of m bits, x {right arrow over (b)} is a symbol in the constellation associated with the bit vector {right arrow over (b)}, {right arrow over (b)},b i =0 is a set of all possible bit vectors whose i th bit is 0, {right arrow over (b)},b i =1 is a set of all possible bit vectors whose i th bit is 1, k is a scaling factor, | y−x{right arrow over (b)} | represents the absolute value of the difference between the received symbol value y and the symbol x {right arrow over (b)} ,
min
b
→
,
b
i
=
1
y
-
x
b
→
is a minimum of the set of values |y−x {right arrow over (b)} | for {right arrow over (b)},b i =1, and
min
b
→
,
b
i
=
0
y
-
x
b
→
is a minimum of the set of values |y−x {right arrow over (b)} | for {right arrow over (b)},b i =0.
25 . A computer readable medium having stored thereon computer executable instructions that, when executed, cause an apparatus to perform a method of computing a reliability value for a bit of a received symbol value y associated with a constellation; the instructions, when executed, causing the apparatus to perform operations comprising:
computing the reliability value by obtaining a first minimum distance value, the first minimum distance value being a function of an absolute magnitude of an initial value associated with the bit, and combining the first minimum distance value with a second minimum distance value, the second minimum distance value being a function of a distance between the received symbol value y and a symbol x {right arrow over (b)} in the constellation corresponding to a most likely pattern of bits transmitted given the received symbol value y.