JP2003188739A - Turbo-decoder - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To accurately find a mean value μ and a variance V in a turbo- decoder. <P>SOLUTION: A histogram totalizer 37a generates a histogram on the basis of (n) demodulated signals outputted from a demodulation part 7. A Gaussian distribution estimator 37b finds the mean value μ and the variance V of the amplitudes of received signals on the basis of the histogram generated in the histogram totalizer 37a. Thus, the average μ and the variance V of the amplitudes of the received signals can be found so that a probability distribution B1 in which the transmitted signal of a wireless transmitter 2 is '0' and a probability distribution B2 in which the transmitted signal of the wireless transmitter 2 is '1' can respectively become a normal distribution. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a turbo decoder.

[0002]

2. Description of the Related Art Conventionally, the problems to be solved by the invention
As a suitable means for performing communication in an environment where code errors are likely to occur, such as a mobile communication system such as a mobile phone,
Turbo encoders and decoders have been proposed.

As shown in FIG. 8, a turbo encoder 1 is applied to a radio transmitter 10 to convert input block data into a turbo code with a configuration in which a convolutional encoder and interleave are combined. The converted turbo code is modulated by the modulator 2 and transmitted via the transmitting antenna 3. When the transmitted turbo code is received via the receiving antenna 4 of the wireless receiving unit 20, the A / D is received via the receiving unit 5.
It will be input to the converter 6. The received turbo code is sampled by the A / D converter 6 and input to the turbo decoder 8 via the demodulation unit 7. The turbo decoder 8 is based on the output from the demodulation unit 7. Decrypt.

The structure of the turbo decoder 8 will be described below. The turbo decoder 8 includes a serial / parallel converter (S / P) 30 and a soft decision decoder 3 as shown in FIG.
1, 32, interleavers 33 and 34, a deinterleaver 35, and a hard decision unit 36.

First, the serial / parallel converter 30
The demodulated signal output from the demodulator 7 is converted into systematic codes A, B, C.
To serial / parallel conversion. The soft decision decoder 31
Based on the systematic codes A and B and the second likelihood Ra, the first
Of the interleaver 3 and the first likelihood S of the interleaver 3
3 to the soft-decision decoder 32. The interleaver 34 also interleaves the systematic code A. The soft decision decoder 32 obtains the second likelihood R based on the outputs of the interleavers 33 and 34 and the systematic code C. Further, the deinterleaver 35 deinterleaves the second likelihood R to obtain the second likelihood Ra as the soft decision decoder 31.
Give feedback to.

[0006] Such a first by the soft decision decoder 32
Calculation of likelihood S, interleaving of interleaver 33,
The calculation of the second likelihood R by the soft decision decoder and the deinterleaving by the deinterleaver 35 are repeated X times. After that, the hard decision unit 36 makes a hard decision based on the X-th output Ra from the deinterleaver 35, whereby decoded data is obtained.

The decoding of the soft-decision decoders 31 and 32 which are the constituent elements of such a turbo decoder is performed by MAP (Maximum A posteriori: Maximum A Posteriori).
Probability1) decoding is used.

FIG. 10 shows the MA in the soft decision decoder 31.
The arithmetic processing of P decoding is shown. First, the probability PDF of the received signal
(Probability density function of received signal: Probability
Compute a density function) (step 101). The probability (state transition probability) γ of each branch of the trellis is calculated based on this probability PDF and the prior likelihood (LDK) (step 102). Further, the trellis is calculated from the beginning of the data to calculate the probability (state probability by forward iterative calculation) α of each state of each bit (step 103). The trellis is calculated from the end of the data, and the probability of each state of each bit (state probability by backward iteration calculation) β is calculated in the same manner as α (step 104). The probability (likelihood of information symbol) λ of whether each bit of the trellis is 1 or 0 is calculated from γ, α, and β obtained previously (step 105). Then, a priori likelihood (LDK) is calculated in order to feed back the probability obtained by λ as the likelihood P (step 106).

As described above, the probability density function PDF of the received signal is an indispensable constituent element in the arithmetic processing of the MAP decoding.
This probability density function PDF includes a probability density function P (X, 0) in which the transmission signal of the wireless transmitter 2 is “0” and a probability density function P (X in which the transmission signal of the wireless transmitter 2 is “1”. 1)
Composed of and.

Here, the transmission signal of the wireless transmitter 2 is "0".
The probability distribution B1 and the probability distribution B2 in which the transmission signal of the wireless transmitter 2 is “1” are assumed to be normal distributions as shown in FIG. (X, 0) and P (X, 1) are represented by Formula 1.

[0011]

[Equation 1]

From the above, the probability density function P (X, 0),
To obtain P (X, 1), considering that the probability distributions B1 and B2 are normal distributions, the standard deviation σ of the amplitude of the received signal and the variance V (= σ ² ) in a certain period.
Need to ask.

As the received signals received for a certain period, n demodulated signals output from the demodulation unit 7 are adopted, and the n demodulated signals are x (t) (1≤t≤n). It is also conceivable to obtain the standard deviation σ of the amplitude of the received signal by substituting it into Equation 2 as

[0014]

V = {Σ (| x (t) | −μ) 2} / n However, the distribution of the signal values of the n demodulated signals x (t) is as shown in FIG. 11 (b). The probability distribution B1 in which the transmission signal of the wireless transmitter 2 is “0” and the probability distribution B2 in which the transmission signal of the wireless transmitter 2 is “1” are combined, and | x
The distribution of (t) | is such that the probability distributions B1 and B2 deviate from the normal distribution. Therefore, only by substituting the n demodulated signals having such a distribution into Equation 2, the standard deviation σ and the variance V cannot be accurately obtained.

In view of the above points, an object of the present invention is to provide a turbo decoder capable of performing decoding with high accuracy by accurately obtaining a probability density function.

[0016]

According to the present invention, in order to achieve the above object, in the invention described in claim 1, the transmission signal has a first value based on the received signal. A first probability density function and a second value where the transmitted signal is a second value
A turbo decoder that decodes a received signal using the probability density function of
Estimating means (3) for estimating the standard deviation and the average value of the amplitude of the received signal such that the first probability distribution that is the value and the second probability distribution that the transmitted signal is the second value are normal distributions.
7a, 37b), and a computing means (31, 32) for computing the first and second probability density functions based on the estimated standard deviation and average value.

As a result, the standard deviation and the average value of the amplitude of the received signal are estimated so that the first probability distribution and the second probability distribution become normal distributions respectively, so that the standard deviation and the average value with high accuracy can be obtained. Can be asked. Therefore, the probability density function can be obtained with high precision, and decoding can be performed with high precision.

Specifically, as in the second aspect of the invention, the estimating means is based on the received signal, means for obtaining the distribution of the amplitude of the received signal (37a), and based on the obtained distribution. , Means for estimating the standard deviation and the average value such that the first and second probability distributions are normal distributions (37
b) and can be configured to have.

According to the third aspect of the present invention, the first probability density function in which the transmission signal has the first value and the transmission signal in the second value are based on each sampling signal of the reception signal which has received the transmission signal. Is a turbo decoder that decodes a received signal using a second probability density function that is, and calculates an absolute value for each sampling signal, and calculates an average value of the calculated absolute values. Means to ask (38
a, 38b) and means (38c, 38d) for obtaining the standard deviation of the amplitude based on each sampling signal which is equal to or higher than the average value of the respective sampling signals, and based on the obtained standard deviation and the average value, Means (31, 32) for calculating the first and second probability density functions.

As described above, if the standard deviation of the amplitude is obtained based on each sampling signal that is equal to or higher than the average value, the standard deviation with high accuracy can be obtained. Accordingly, the first and second probability density functions are calculated on the basis of the standard deviation and the average value, so that the calculation of the first and second probability density functions, and thus the decoding can be performed accurately. .

According to the fourth aspect of the present invention, the first probability density function in which the transmission signal is the first value and the transmission signal is the second value based on each sampling signal of the reception signal which has received the transmission signal. Is a turbo decoder that decodes a received signal using a second probability density function that is, and obtains an absolute value for each sampling signal, and obtains an average value of the obtained absolute values. At the same time, a means for obtaining a negative value by multiplying the obtained average value by -1 and a means for obtaining a standard deviation of the amplitude based on each sampling signal which is a negative value or less among the sampling signals were obtained. Means for calculating the first and second probability density functions based on the standard deviation and the average value.

As a result, the standard deviation is obtained based on each sampling signal having a negative value or less, so that the standard deviation can be obtained with high accuracy. Along with this, the first and second probability density functions are calculated based on the standard deviation and the average value. Therefore, the calculation of the first and second probability density functions,
As a result, decoding can be performed accurately.

According to the fifth aspect of the invention, the first probability density function in which the transmitted signal has the first value and the transmitted signal have the first value based on each sampling signal of the received signal which has received the transmitted signal. And a second probability density function which is a second value smaller than that of the turbo decoder for decoding the received signal based on each sampling signal. ) And an absolute value for each of the sampling signals, and an average value of the absolute values thus obtained (39b)
And means (39c) for estimating a third probability density function when the sampling signal is equal to or higher than the average value based on the obtained distribution, and the first probability density function is the third probability density. And a fourth probability density function obtained by linearly symmetrically moving the third probability density function, and the second probability density function is a probability density obtained by linearly symmetrically moving the third and fourth probability density functions. It is characterized by being a function.

In this way, the first probability density function is
And a fourth probability density function, the second probability density function is a probability density function obtained by linearly symmetrically moving the third and fourth probability density functions. As a result, the transmitted signal is the first
The first and second probability density functions can be obtained such that the first probability distribution that is the value of and the second probability distribution that the transmission signal is the second value are normal distributions. Therefore, the first and second probability density functions can be obtained with high precision, and decoding can be performed with high precision.

According to the sixth aspect of the present invention, the first probability density function having the first value of the transmitted signal and the first transmitted signal are the first value based on each sampling signal of the received signal which has received the transmitted signal. A turbo decoder that decodes a received signal using a second probability density function that is a second value larger than the value, and means for obtaining the amplitude distribution of the received signal based on each sampling signal ( 39a) and an absolute value for each sampling signal, an average value of the obtained absolute values, and a negative value obtained by multiplying the obtained average value by -1. And a means for estimating a third probability density function when the amplitude is a negative value or less based on the obtained distribution, the first probability density function being the third probability density function and the third probability density function. Move the probability density function of And a fourth probability density function, the second probability density function is characterized that it is the third and fourth probability density function of the probability density function moves the line symmetry.

In this way, the first probability density function is
And a fourth probability density function, the second probability density function is a probability density function obtained by linearly symmetrically moving the third and fourth probability density functions. As a result, the transmitted signal is the first
The first and second probability densities are set so that the first probability distribution that is the received signal when the value of is a normal distribution and the second probability distribution that is the received signal when the transmission signal is the second value are normal distributions. You can ask for a function. Therefore, the first and second probability density functions can be obtained with high precision, and decoding can be performed with high precision.

Incidentally, the reference numerals in the parentheses of the above-mentioned respective means are examples showing the correspondence with the concrete means described in the embodiments described later.

[0028]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS (First Embodiment) FIG. 1 shows a first embodiment of a turbo decoder according to the present invention. FIG. 1 is a block diagram showing the circuit configuration of the turbo decoder 8A.

The turbo decoder 8A comprises a serial / parallel converter 30, soft-decision decoders 31, 32, interleavers 33, 34, a deinterleaver 35, a hard-decision unit 36, and an arithmetic unit 37. . In FIG. 1, the same symbols as those in FIG. 9 indicate the same components.

The calculation section 37 is a histogram aggregator 37.
a and a Gaussian distribution estimator 37b.

First, the histogram aggregator 37a outputs n demodulated signals x (t) (0≤t≤) output from the demodulator 7.
Based on n), a histogram (bar graph) is generated as shown in FIG. In this histogram, the vertical axis represents the number of demodulated signals and the horizontal axis represents the amplitude of the demodulated signals, and the distribution of the amplitudes of the n demodulated signals is shown.

The n demodulated signals x (t) are A / D
The reception signal sampled by the converter 6 for a certain period, that is, each sampling signal is demodulated by the demodulation unit 7.

Next, the Gaussian distribution estimator 37b applies the histogram generated by the histogram aggregator 37a to the following expression 3 to apply LSM (Least-Squa).
re-Method) method, Levenberg-Mar
The average μ of the amplitude of the received signal and the variance V are obtained using the quardt method or the like.

[0034]

[Equation 3]

As a result, the probability distribution B1 in which the transmission signal of the wireless transmitter 2 is "0" and the probability distribution B2 in which the transmission signal of the wireless transmitter 2 is "1" are both normal distributions. The average μ and the variance V are obtained. With this,
The soft-decision decoder 31 substitutes the mean μ and the variance V into Equation 1 to obtain the probability density functions P (X, 0) and P (X, 1), and the probability density functions P (X, 0) and P ( Turbo decoding is performed based on X, 1).

As described above, according to this embodiment,
Since the average μ and the variance V of the amplitude of the received signal are obtained so that the probability distributions B1 and B2 are normal distributions, accurate values can be obtained as the average μ and the variance V. Therefore,
The probability density functions P (X, 0) and P (X, 1) can be obtained with high precision, and turbo decoding can be performed with high precision. (Second Embodiment) In the first embodiment, the probability distribution B
Although an example of obtaining the average μ and the variance V so that 1 and B2 have a normal distribution has been described, in the second embodiment, the variance V is obtained by utilizing the amplitude distribution of the n demodulated signals x (t). An example will be described in which The configuration in this case is shown in FIG.

The turbo decoder 8B of the present embodiment comprises a serial / parallel converter 30, soft decision decoders 31, 32,
The interleaver 33, 34, the deinterleaver 35, the hard decision unit 36, and the calculation unit 38 are included. 3 that are the same as those in FIG. 9 are the same.

The calculation unit 38 includes an absolute unit 38a and an averaging unit 38.
b, and arithmetic units 38c and 38d.
First, the absolute device 38a obtains the absolute value | x (t) | for each of the n demodulated signals x (t). Then, the averaging device 38b calculates the average value μ of the n absolute values | x (t) |
{= (Σ | x (t) |) / n} is calculated.

Next, the calculator 38c outputs n demodulated signals x.
Among (t), a demodulated signal having an average value of μ or more (hereinafter referred to as a demodulated signal xa (t)) is selected, and each selected demodulated signal xa (t) is substituted into Equation 4 to obtain Y.

[0040]

## EQU00004 ## Y = {. SIGMA. (Xa (t)-. Mu.) 2} Next, the calculator 38d substitutes Y into Equation 5 to obtain the standard deviation .sigma. And the variance V.

[0041]

## EQU00005 ## Here, the reason why the standard deviation .sigma. And the variance V are obtained by using each demodulated signal xa (t) having an average value .mu. Or more will be described. n
In the amplitude distribution of the individual demodulated signals x (t), as shown in FIG. 4, although the above-described probability distributions B1 and B2 deviate from the normal distribution, the average value μ or more of the distributions The slope is almost the same as the slope when the probability distribution B2 is a normal distribution. Therefore, by substituting each demodulated signal xa (t) having an average value of μ or more into Expression 4 and Expression 5, the standard deviation σ and the variance V can be obtained with high accuracy. As a result, the probability density functions P (X, 0) and P (X, 1) can be obtained with high accuracy, and turbo decoding can be performed with high accuracy.

In the second embodiment, among the n demodulated signals x (t), each demodulated signal xa having an average value of μ or more is used.
Although the example of obtaining the standard deviation σ and the variance V based on (t) has been described, the present invention is not limited to this, and the n demodulated signals x (t) are not limited thereto.
Among them, the standard deviation σ and the variance V may be obtained based on each demodulated signal xb (t) of −μ or less.

The turbo decoder in this case obtains the absolute value | x (t) | for each of the n demodulated signals x (t), and the average value μ of the absolute values | x (t) | And a means for obtaining −μ (negative value) obtained by multiplying the average value μ by −1, and each demodulated signal xb (t) that is −μ or less of the n demodulated signals x (t) 6, means for obtaining the standard deviation σ and the variance V, and probability density functions P (X, 0), P (X, 1) based on the standard deviation σ and the average value μ.
And means for computing

[0044]

V = {Σ (xa (t) −μ) 2} / n (Third Embodiment) In the first and second embodiments, the standard deviation σ is calculated based on the demodulated signal x (t). , The probability density function P (X, 0) based on the obtained standard deviation σ,
An example of calculating P (X, 1) has been described.
In the embodiment, the probability density functions P (X, 0), P are directly derived from the histograms of the n demodulated signals x (t).
An example in which (X, 1) is calculated will be described. The configuration in this case in this case is shown in FIG.

The turbo decoder 8C of the present embodiment comprises a serial / parallel converter 30, soft decision decoders 31, 32,
The interleaver 33, 34, the deinterleaver 35, the hard decision unit 36, and the calculation unit 39 are included. In FIG. 5, the same symbols as those in FIG. 9 indicate the same components.
The calculation unit 39 includes a histogram aggregator 39a and an averager 39
b and an estimator 39c.

First, the histogram aggregator 39a outputs n demodulated signals x (t) (0≤t≤) output from the demodulator 7.
Generate a histogram (bar graph) based on n).
Then, the averager 39b obtains an absolute value | x (t) | for each of the n demodulated signals x (t), and
Average value of these absolute values | x (t) | μ {= (Σ | x
(T) |) / n} is calculated.

Then, as shown in FIG. 6, the estimator 39b performs interpolation, smoothing, etc. on the section Q1 having the average value μ or more in the generated histogram. Accordingly, the probability density function P1 (x, 1) (P1 (x, 1) when the demodulated signal x (t) is equal to or larger than the average value μ is the third probability density function in the invention according to claim 5. Equivalent to) can be obtained.

This is because the slope of the distribution of n demodulated signals x (t) above the average value μ is almost the same as the slope when the probability distribution B2 is a normal distribution. Note that P1 (x, 1) (x ≧ μ) is defined as a function p1 (x) as shown in Expression 7.

[0049]

## EQU00007 ## P (x, 1) = p1 (x) (x.gtoreq..mu.) Next, the soft-decision decoder 31 calculates the average value .mu. Of the function p1 (x).
Axisymmetrically with respect to the center of the function p1 (2μ-x)
(P1 (2μ-x) corresponds to the fourth probability density function in the invention of claim 5). This function p1
(2μ−x) is the demodulated signal x as shown in Equation 8.
When (t) is less than the average value μ, that is, it is set as the probability density function P (x, 1) in the section Q2 in FIG.

[0050]

P (x, 1) = p1 (2μ−x) (x ≦ μ) Next, in FIG.
A function P (2μ +
x) (x ≧ −μ) and a function P (−x) (x <−μ) obtained by linearly moving this function P (2μ + x) about −μ.
And the probability density function P (x, 0) is generated. That is, the probability density function P (x, 0) is the function p1 (x),
It will be obtained by linearly symmetric movement of p1 (2 μ−x) around zero.

[0051]

P (x, 0) = p1 (2μ + x) (x ≧ −μ) P (x, 0) = p1 (−x) (x <−μ) According to the present embodiment as described above. , The slope of the amplitude distribution of the n demodulated signals x (t) that is equal to or larger than the average value μ is
The slope is almost the same as when the probability distribution B2 is a normal distribution. Therefore, demodulated signal x (t) with an average value of μ or more
Of the probability density functions p1 (x) and P (x, 1), P (x,
0) is calculated. Thereby, the probability distribution function B1 in which the transmission signal of the wireless transmitter 2 is “0” and the probability distribution B2 in which the transmission signal of the wireless transmitter 2 is “1” are normal distributions. P (x, 1) and P (x, 0) can be obtained. Therefore, the probability density function P (x,
1) and P (x, 0) can be accurately obtained.

In the third embodiment, the demodulated signal x
An example of obtaining the probability density functions P (x, 1) and P (x, 0) based on the function p1 (x) when (t) is equal to or larger than the average value μ has been described, but the present invention is not limited to this. Demodulated signal x
The probability density functions P (x, 1) and P (x, 0) may be obtained based on the function p2 (x) when (t) is less than the average value −μ.

The turbo code in this case is a means for obtaining a histogram of the amplitude of the received signal based on the n demodulated signals x (t) and an absolute value | for each of the n demodulated signals x (t). x (t) |, and the absolute value of each | x
(T) | Mean value μ of the mean value μ is multiplied by −1 to obtain −μ (negative value), and the amplitude of the demodulated signal x (t) is −μ based on the histogram. And a means for estimating the probability density function p2 (x) when, the first probability density is the third probability density function p2 (x), and the fourth probability density function is a line-symmetrical movement of the third probability density function p2 (x). And the probability density function p2 (2μ-x), the second probability density is a probability density function obtained by axisymmetrically moving the probability density functions p2 (x) and p2 (2μ-x).

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a turbo decoder according to a first embodiment of the present invention.

FIG. 2 is a diagram for explaining the operation of the turbo decoder according to the first embodiment.

FIG. 3 is a block diagram showing a configuration of a turbo decoder according to a second embodiment of the present invention.

FIG. 4 is a diagram for explaining the operation of the turbo decoder according to the second embodiment.

FIG. 5 is a block diagram showing a configuration of a turbo decoder according to a third embodiment of the present invention.

FIG. 6 is a diagram for explaining the operation of the turbo decoder according to the third embodiment.

FIG. 7 is a diagram for explaining the operation of the turbo decoder according to the third embodiment.

FIG. 8 is a block diagram showing a receiver to which a turbo decoder is applied and a transmitter that transmits a transmission signal to the receiver.

9 is a block diagram showing a configuration of a turbo decoder shown in FIG. 8.

FIG. 10 is a diagram for explaining the operation of the turbo decoder shown in FIG.

FIG. 11 is a diagram for explaining the operation of the turbo decoder shown in FIG. 9.

[Explanation of symbols]

37a ... Histogram aggregator, 37b ... Gaussian distribution estimator.

Claims (6)

[Claims] 1. A first probability density function in which the transmission signal has a first value and a second probability density function in which the transmission signal has a second value based on a reception signal that has received the transmission signal. A turbo decoder that decodes the received signal by using a first probability distribution in which the transmitted signal has a first value and the transmitted signal has a second value based on the received signal. Two
Estimating means (3) for estimating the standard deviation and the average value of the amplitude of the received signal such that the probability distributions of the above and the probability distributions of
7a, 37b) and based on the estimated standard deviation and average value, the first
And a computing means (31, 3) for computing the second probability density function.
2) A turbo decoder comprising: 2. The estimating means obtains an amplitude distribution of the received signal based on the received signal, and the first and second probability distributions based on the obtained distribution. The turbo decoder according to claim 1, further comprising means (37b) for estimating the standard deviation and the average value such that each has a normal distribution. 3. A first probability density function, in which the transmission signal has a first value, and a second, in which the transmission signal has a second value, based on each sampling signal of the reception signal that has received the transmission signal. A turbo decoder that decodes the received signal using a probability density function, and means for obtaining an absolute value for each of the sampling signals and obtaining an average value of the obtained absolute values ( 38a, 38b), a means (38c, 38d) for obtaining the standard deviation of the amplitude based on each sampling signal which is equal to or more than the average value among the sampling signals, and the obtained standard deviation and the average value. Based on the first
And means for calculating a second probability density function (31, 32)
And a turbo decoder. 4. A first probability density function in which the transmission signal has a first value and a second probability in which the transmission signal has a second value based on each sampling signal of the reception signal that has received the transmission signal. A turbo decoder for decoding the received signal using a probability density function, wherein an absolute value is obtained for each of the sampling signals, and an average value of the obtained absolute values is obtained. A unit that obtains a negative value by multiplying the obtained average value by −1; a unit that obtains the standard deviation of the amplitude based on each sampling signal that is equal to or less than the negative value among the sampling signals; Based on the standard deviation and the average value,
And a means for computing a second probability density function, the turbo decoder. 5. A first probability density function, in which the transmission signal has a first value, and the transmission signal are smaller than the first value, based on each sampling signal of the reception signal that has received the transmission signal. A turbo decoder that decodes the received signal using a second probability density function that is a second value, and means (39a) for obtaining an amplitude distribution of the received signal based on the sampling signals. And means (39b) for obtaining an absolute value for each of the sampling signals and obtaining an average value of the obtained absolute values, and the sampling signal is the average value based on the obtained distribution. And a means (39c) for estimating a third probability density function when the value is equal to or more than a value, the first probability density function is a line that includes the third probability density function and the third probability density function. versus And a fourth of the probability density function has moved, the second probability density function,
A turbo decoder, which is a probability density function obtained by line-symmetrically moving the third and fourth probability density functions. 6. A first probability density function, in which the transmission signal is a first value, and the transmission signal are larger than the first value, based on each sampling signal of the reception signal that has received the transmission signal. A turbo decoder that decodes the received signal using a second probability density function that is a second value, and means (39a) for obtaining an amplitude distribution of the received signal based on the sampling signals. And a means for obtaining an absolute value for each of the sampling signals, obtaining an average value of the obtained absolute values, and obtaining a negative value by multiplying the obtained average value by -1. Means for estimating a third probability density function when the amplitude is less than or equal to the negative value based on the obtained distribution, and the first probability density function is the third probability density function. And this third probability Is configured to function and a fourth probability density function moves axisymmetric, the second probability density function,
A turbo decoder, which is a probability density function obtained by line-symmetrically moving the third and fourth probability density functions.