JP2710696B2 - Soft-decision Viterbi decoding method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a phase shift keying (PS) system.
K) The present invention relates to a soft-decision Viterbi decoding method for convolutional codes in wireless communication such as cellular mobile communication employing a modulation method.

[0002]

2. Description of the Related Art Conventionally, techniques in such a field include:
Some of them were described in the following documents.

Reference 1: IEE Transactions on Communications Technology (IEEE Transactions on C)
communications Technology
y), COM-19 [5] (1971-10) (US)
A. J. VITERBI "Convolutional Codes and There Performance In Communication Synthems (Convolution Co.)
des and Their Performance
in Communication System
s) "P.751-772 Reference 2; B.SKLAR" DIGITAL COMMUNICATIONS
S) "(1988) PRENTICE HALL (US)
sec. 6.3.4, p. 333-337 Generally, in wireless communication such as mobile communication and satellite communication,
Various measures such as diversity reception, equalization, and code error control are taken in order to improve the quality degradation of the received signal due to the influence of multipath fading or the like in a wireless channel. Convolutional coding, which is a kind of code error control, is performed based on a convolutional code generation rule uniquely determined by a coding rate, a constraint length, and a generator polynomial. A graphic representation of this generation rule is a kind of state transition diagram called a trellis graphic. The convolutional code can correct the bit error of the received signal by comparing the received signal with a possible path (path) on the trellis figure at the time of decoding and selecting the most suitable path (optimal path). It is possible. Viterbi decoding is the most common method for decoding a convolutional code. Hard decision is made by comparing a signal value itself with a selectable signal sequence of a trellis figure, and the likelihood that the signal value takes that value (likelihood). And soft decision for comparison.

[0004] In the PSK modulation method, which is one of the digital modulation methods, a bit value is assigned to the phase of a carrier. For example, in the case of 4-phase PSK (QPSK), 2
Bits are allocated and at phase π / 4 (0,0), 3
π / 4 (0,1), 5π / 4 (1,1), 7π
At (/ 4), (1, 0) is obtained. However, it is generally difficult to determine the absolute phase of the received signal. The PSK scheme is more realistic.

[0005] A conventionally proposed soft decision Viterbi decoding method is described in the above-mentioned reference 1, and the method will be described with reference to FIGS. 2 and 3.

FIG. 2 is an explanatory diagram of convolutional coding.

In the case of performing convolutional coding, when n output bits are generated for m input bits, the coding rate is m / n. Past k including the latest input bit
When generating an output from bits, it is called a constraint length k. In this case, n generator polynomials of length k are required. FIG. 2 shows a coding rate of 1/2, a constraint length of 3, a generator polynomial 111, 101
The case of is shown.

In FIG. 2, three bits including the latest input bit are stored in the buffer 10, and a 2-bit output is obtained by convolution. Since the generator polynomials are 111 and 101, one of the outputs is the logical sum of all the bits of the buffer 10 and the other is the logical sum of the first and third bits of the buffer 10.

FIG. 3 is a trellis diagram showing a state transition diagram of the generation rule of the convolutional coding of FIG.

The vertical direction in FIG. 3 shows a state in the buffer 10 not including the latest bit, and a state of 2 ^{k -1} occurs. In the example, it is 4. In each state, when 0 is input, the state shifts to the next state along the solid line, and two bits on the line are output. When 1 is input, the state shifts to the next state along the broken line, and 2 bits on the line are output.

Referring to FIG. 3, the most general Viterbi algorithm will be described as a method of decoding a convolutionally encoded code.

On the decoding side, a signal corresponding to a bit string on a solid line or a broken line on the trellis diagram is received, and the original signal is reproduced by predicting a path on the trellis diagram. However, as described later, a delay corresponding to the path memory length occurs. As shown in the trellis diagram, there are two paths (branches) input to each state, and a 2-bit branch symbol is assigned to each branch based on the same rules as in the coding.

First, when two bits are input, for each input branch to each state, a branch metric (metric) with the input bit is calculated, and the better of the branch metric is selected. The sum of the branch metric accumulation (path metric) in the state before the selected branch is connected and the metric of the selected branch is taken as a new path metric in each state. In this way, every time a branch leading to each state is determined, path (path) information leading to each state is stored in a memory (path memory). Here, the accumulation of the results of branch selection is a path. Alternatively, the minimum unit of the path is a branch.

When the above processing is repeated for each 2-bit input,
In the course of the path narrowing down described in Document 2, the past paths are eventually narrowed down to one, so that a signal before convolutional coding is obtained from the obtained path. Since the path memory length of the actual device is finite, if the path does not converge even if the path memory length is exceeded, the path with the best path metric will be selected at that time.

Next, the difference between the hard decision and the soft decision will be described.

A method of calculating a metric with a possible path on a trellis diagram using the input bit value itself is called hard decision. On the other hand, a method using the likelihood that an input bit value takes that value is called soft decision.
The soft decision has a higher metric calculation accuracy and a higher bit error correction capability than the hard decision.

For example, in the case of hard decision in digital signal transmission as well as wireless communication, a certain reception level is set as a threshold, and when the level of a received signal is larger than the threshold, the input bit is set to 1; To determine the signal value. On the other hand, in the case of the soft decision, first, a seven-valued threshold is set, divided into eight regions according to the level of the received signal, and a value Ns of 0 to 7 is given to each region. That is, 1
Region where it is certain to be, region where it is certain to be 0,
The region is divided into a region where either 0 or 1 can be taken, and a region which is rather close to 1 or the like. Here, the branch symbols 0 and 1 on the trellis diagram of FIG. 3 are set to −1 and 1 and the value Ns of 0 to 7 is converted into (2 × Ns−7), so that the product sum of the input bit and the branch symbol is obtained. A Viterbi algorithm that selects a branch having a large (correlation) becomes possible.

[0018]

However, in the prior art, there has been no soft-decision Viterbi decoding method considering use in a differential PSK modulation method.

For example, in the π / 4 shift differential 4-phase PSK modulation method (π / 4 shift DQPSK modulation method), (2
The (n + 1) th transmitted phase is (0, π / 2, π, 3
π / 2), and the phase transmitted at the 2nth position is any of (π / 4, 3π / 4, 5π / 4, 7π / 4), but the detected phase is in the reception state. 0-2
Take any value of π. Therefore, one of the four phases is selected according to the order and the value of the phases detected by the demodulation unit. Since the selected phase is a relative phase, a difference between successively detected phases is obtained. The phase difference is (π / 4, 3π
/ 4, 5π / 4, 7π / 4). The phase differences are (0, 0), (0, 1), (1, 1),
(1, 0) correspond, and by calculating the phase difference,
The bits sent can be determined.

In the case of hard-decision Viterbi decoding, the obtained bit string may be used as it is, but in the case of soft-decision Viterbi decoding, not the bit value itself but the likelihood of taking the bit value (likelihood) is represented by trellis. Since it is characterized by being used for determining the optimum path on the drawing, a process of calculating the likelihood of taking the bit string is required in the process of obtaining the bit string from the phase detection of the received carrier. In the case of differential type,
Since the bit likelihood is affected by the likelihood of each of the consecutively received phases, how to calculate it is an important issue, and it has been difficult to solve them.

The present invention solves the problem of the prior art that the bit likelihood is difficult to calculate when the soft decision Viterbi decoding method is used in a differential PSK modulation method. It is intended to provide a decision Viterbi decoding method.

[0022]

SUMMARY OF THE INVENTION In order to solve the above-mentioned problems, the present invention assigns a bit sequence to a difference in phase of a carrier continuously received in time based on Gray coding. When the convolutional code is modulated by the DQPSK method, the detected phase of the carrier detected on the receiving side is converted into bit likelihood by soft decision data calculation processing, and this bit likelihood is used for soft decision Viterbi decoding. And

That is, in the soft decision data calculation processing, the detected phase of the carrier detected on the receiving side is compared with the inherent phase transmitted by the differential phase shift keying method, and the absolute value of the phase shift is small. Phase selection processing for selecting two unique phases, and monotonically decreasing with respect to the magnitude of the phase shift;
When the absolute value of the phase shift is 0, the maximum value of the likelihood is obtained. When the absolute value of the phase shift is (2π / the number of unique phases transmitted by the differential phase shift keying method), the likelihood is calculated. And a phase likelihood calculation process for calculating the phase likelihood by a function that takes the minimum value of the two, and a combination of two phases selected successively in time based on the result of the phase likelihood calculation process. And a phase difference calculation process for calculating the different phases.

Further, a phase difference likelihood calculation process for calculating the phase difference likelihood of each phase difference as the smaller of the likelihood of the phase used for calculating the phase difference, A first phase difference, and a phase difference selecting process of selecting a second phase difference having a maximum phase difference likelihood among phase differences different from the first phase difference; A corresponding bit readout / bit likelihood calculation process of reading a plurality of bits of a corresponding bit string and calculating a bit likelihood assuming that the likelihood of each bit is equal to the likelihood of the first phase difference;
Bit likelihood correction processing for correcting a bit likelihood that maximizes the likelihood of a bit equal to the bit of the bit string corresponding to the second phase difference among the bits of the bit string corresponding to the first phase difference And execute. Then, the result of the bit likelihood correction processing is used for calculating a metric in the Viterbi algorithm.

[0025]

According to the present invention, the soft-decision Viterbi decoding method is configured as described above. When converting the phase of a received carrier into bit likelihood, first, the phase selection processing is performed to input the phase signal. According to the order, two close ones are selected from the predetermined phases transmitted by the π / 4 shift DQPSK method. The phase likelihood is calculated by the phase likelihood calculation process in accordance with the absolute value of the phase shift from a predetermined phase. Next, a phase difference is calculated from two phases selected successively in time by a phase difference calculation process. The phase difference likelihood is the smaller one of the likelihood of the phase used for obtaining the phase difference by the phase difference likelihood calculation process. By the phase difference selection processing, two phase differences are selected from the one with the largest phase difference likelihood.

Then, the likelihood of the bit sequence corresponding to the selected phase difference is set as the likelihood of the selected phase difference by the corresponding bit readout / bit likelihood calculation process, and then selected by the bit likelihood correction process. The calculation is performed in accordance with the values of the first and second candidates for the phase difference. This corrected bit likelihood is
If used for calculating the metric in the Viterbi algorithm, an accurate reproduced signal can be obtained. Therefore, the above problem can be solved.

[0027]

FIG. 1 is a flow chart of processing steps of a soft-decision Viterbi decoding method according to an embodiment of the present invention, and FIG. 4 is a block diagram of a soft-decision Viterbi decoding device for executing the soft-decision Viterbi decoding method. is there.

First, the soft decision Viterbi decoder shown in FIG. 4 will be described.

FIG. 4 shows a receiving section of the radio signal transmitting / receiving apparatus. This receiving unit receives a radio frequency band signal (RF
Band signal) a and demodulates the bit error of the baseband signal to obtain a reproduced signal C.
, And a soft-decision Viterbi decoding device 30.

Although a diagram of a transmission unit provided in the radio signal transmission / reception apparatus is omitted, the transmission unit performs convolutional coding of an original signal and interleaving (interleave).
e, crossover) conversion, and modulates with a π / 4 shift DQPSK method. As an example, a coding rate of convolutional coding 1
/ 2, constraint length 3, and generator polynomials 111 and 101. Interleave conversion means that the signal bits input to the memory are
Conversion that rearranges and outputs has the effect of replacing successive bit errors with random errors. Soft-decision Viterbi decoding device 30 provided on the output side of demodulation section 20
Has a soft decision data calculator 31 with a built-in memory for calculating soft decision data from the phase b detected by the demodulator 20, and a deinterleave memory 32 is connected to the output side. The deinterleaving memory 32 has a function of storing the soft decision data calculated by the soft decision data calculation unit 31.

A Viterbi algorithm execution unit 34 is connected to the deinterleave memory 32 and the path memory 33 for storing paths that are candidates in the process of finding the optimum path. The data stored in the deinterleaving memory 32 is read out to the Viterbi algorithm execution unit 34 while restoring the bit order rearranged at the time of transmission, so that the read soft decision It has a function of obtaining an optimal path on the trellis diagram using data and outputting a reproduction signal C. The soft-decision Viterbi decoding device 30 includes a large-scale integrated circuit (LS
It is composed of an individual circuit using I) or the like, or a program control using a processor.

Next, the soft-decision Viterbi decoding method of this embodiment will be described with reference to FIG.

When the RF band received signal a is input, the demodulation section 20 shown in FIG. 4 detects the phase b of the RF band received signal a in step S40, and converts the detected phase b into a soft-decision Viterbi decoder. 30 to the soft decision data calculation unit 31.

In the soft decision data calculating section 31, step S
According to 51 to S59, a soft decision data calculation process S50 is performed.

That is, when the phase b is input, step S
At 51, phase selection is performed. Since the phase b detected by the demodulation unit 20 has an arbitrary value of 0 to 2π, when the phase signal is inputted in an odd number, (0, π / 2,
One of the four phases (π, 3π / 2) is selected, and when an even number is input, (π / 4, 3π / 4, 5π / 4,
7π / 4) is selected. As shown in Expression 1, the selected value irad (1, t) of the t-th input phase is the detected phase zirad and the candidate phase k
The phase at which the absolute value θ (k) of the difference of π / 4 is minimized.

[0036]

(Equation 1)

Irad (1, t) = kπ / 4 | θ (k)
Where k (θ) = | zirad−kπ / 4 | k = 0,2,4,6 t = 2n + 1 k = 1,3,5,7 t = 2n k that satisfies the expression 1 On the other hand, θ (k) is 0 ≦ θ
(K) ≦ (π / the number of unique phases transmitted by the differential PSK method). The number of unique phases transmitted in the π / 4 shift DQPSK scheme is four.

As shown in Equation 2, as the second candidate of the selected value, the phase having the second smallest absolute value of the difference between the detected phase zirad and the candidate phase kπ / 4 is irad.
(2, t).

[0039]

(Equation 2)

Irad (2, t) = k _a π / 4 | θ (k
_a) small _{K a} where are the _{second, θ (k a) = |} zirad-k a π / 4 | k a = 0,2,4,6 t = 2n + 1 k a = 1,3,5,7 t = 2n to ka which satisfies the number 2, θ _{(k a)} is (number of unique phase of sending by [pi / differential PSK method) ≦ theta
(K _a ) ≦ (2π / the number of unique phases transmitted by the differential PSK method).

FIG. 5 shows the relationship among the detected phase zirad, the selected phases irad (1, t), irad (2, t), and the absolute values θ (k) and θ (k _a ) of the phase shift.
FIG. 5 shows a case where t = 2n + 1. From the value of the detected phase zirad, irad (1, t) = 0 and irad (2, t) =
π / 2. When the detected phases are the same and t = 2n, irad (1, t) = π / 4, irad (2,
t) = 7π / 4. Next, in step S52 of FIG. 1, the probability (likelihood) of taking the phase selected in step S51 is calculated. The likelihood is a function of the phase shift θ (k) between the selected phase kπ / 4 and the detected phase zirad, and is expressed as in the following Expressions 3 and 4. The first candidate irad (1,
t) is taken as prad (1, t), and the second candidate i
Let rad (2, t) be the likelihood of taking rad (2, t). The likelihood was considered from 0 to 1.

[0042]

(Equation 3)

Prad (1, t) = (cos 2θ (k) +1) / 2

[0044]

(Equation 4)

Prad (2, t) = 1−prad (1, t) In step S53, the phase difference between the phase selected in S51 and the phase selected immediately before is calculated. The previously selected phase and its likelihood are stored in the memory of the soft decision data calculation unit 31 up to the second candidate. Since each of the selected phases is up to the second candidate, there are four ways of obtaining the phase difference. Therefore, four phase differences are calculated by the following equation (5).

[0046]

(Equation 5)

Idif (a) = irad (1, t) −irad (1, t−1) idif (b) = irad (1, t) −irad (2, t−1) idif (c) = irad ( (2, t) -irad (1, t-1) idif (d) = irad (2, t) -irad (2, t-1) However, when Equation 5 is calculated, two of the four phases are obtained. Always match, there are only three actual phase differences. This is because the absolute value of the phase difference between the first candidate and the second candidate selected at a certain point in time is always π / 2.

The likelihood of the phase difference obtained in step S53 is calculated in step S54. The phase difference likelihood is the lower likelihood of the phase likelihood at successive points in time, as shown in the following Expression 6.

[0049]

(Equation 6)

Pdif (a) = min ( prad (1, t) , pr
d (1, t-1)) pdif (b) = min ( prad (1, t) , pr
d (2, t-1)) pdif (c) = min ( prad (2, t) , pr
d (1, t-1)) pdif (d) = min ( prad (2, t) , pr
d (2, t-1)) Since two of idif (a) to idif (d) match, if the phase difference idif () matches, the larger of the phase difference likelihood pdiff () This is the likelihood of the phase difference. In step S55, the phase difference id reduced to three
Of the if (), two are selected from the larger of the phase difference likelihood pdif (), and the two are selected as idif (1),
(2), and the phase difference likelihood at this time is pdif (1), p
dif (2).

In step S56, a bit string corresponding to the phase difference thus obtained is read from the memory in the soft decision data calculation unit 31. When the phase difference is π / 4 (0, 0),
3π / 4 (0, 1), 5π / 4 (1, 1), 7
The time (1, 0) of π / 4 corresponds. Bits corresponding to idif (1) are referred to as ib1 (1) and ib2 (1), respectively.
Bits corresponding to idif (2) are sequentially set as ib1
(2) and ib2 (2). ib1 (1), ib1
(2), ib2 (1) and ib2 (2) are 0 or 1
Take.

Idif (1)-> (ib1 (1), ib2 (1)) idif (2)-> (ib1 (2), ib2 (2)) In step S57, the bit likelihood is calculated. The bit likelihood pb1 (1) is calculated by the following equations (7) and (8). ib1
When (1) = 0, it is calculated by Expression 7, and when ib1 (1) = 1, it is calculated by Expression 8. The same applies to pb2 (1).
The bit likelihood was considered to be -1 to 1.

[0053]

(Equation 7)

Pb1 (1) = 1-2pdif (1)
ib1 (1) = 0

[0055]

(Equation 8)

Pb1 (1) = 2pdif (1) -1
ib1 (1) = 1 Here, the bit string (ib1 (1) corresponding to idif (1)
(1), ib2 (1)) and a bit string (ib1 (2), ib2 (2)) corresponding to idif (2) are idif.
The absolute value of the phase difference between (1) and idif (2) is always π / 2
Therefore, the following equation 9 holds.

[0057]

(Equation 9)

Ib1 (1) = ib1 (2), ib2 (1) ≠ ib2 (2) or ib1 (1) ≠ ib1 (2), ib2 (1) = ib2 (2) Since the assignment is determined by Gray encoding, a bit string assigned to a certain phase difference and a bit string shifted in phase by π / 2 means that one of the bits always matches.

Using the property of equation 9, step S5 in FIG.
In step 8, the bit likelihood calculated in step S57 is corrected according to the following equation (10).

[0060]

(Equation 10)

[0061] Pb1 (1), pb2 obtained by the above processing
Let (1) be the bit likelihood, indicating that the bit value may be 0 or 1. pb1 (1) takes an arbitrary value between -1 and 1, and is likely to be 1 when pb1 (1) is close to 1, and is 0 when pb1 (1) is close to -1. Probability is high. The same applies to pb2 (1). When the soft decision data calculation process is completed, the soft decision data is output to the Vidabi algorithm execution unit 34 in FIG. 4 in step S59.

In step S60, the Viterbi algorithm execution unit 34 refers to the contents of the path memory 33,
An optimal path on the trellis diagram is obtained using the input soft decision data, and a reproduced signal c is output.

FIG. 6 shows a simulation result of the bit error characteristic by the soft decision Viterbi decoding method of this embodiment.
The horizontal axis represents the ratio Eb / No between the average signal energy Eb per bit and the noise power density No, and the vertical axis represents the bit error rate. The curve in the figure indicates the case where △ did not perform the convolutional coding, the case where □ performed the hard decision Viterbi decoding of the conventional convolutional code, and the case of ○ the case where the soft decision Viterbi decoding of the present embodiment was performed.

The simulation conditions of FIG. 6 will be described. Class 1 for 17-bit original signal per slot
(89 bits) and class 2 (82 bits), and only the signal of class 1 is subjected to convolutional coding. Coding rate of convolutional coding 1/2, constraint length 6, generator polynomial 11
0101 and 101111. After convolutional encoding,
Class 1 signal (178 bits) and class 2 signal (8 bits)
(2 bits) are interleaved in a 13 × 10 array, and modulated by the π / 4 shift DQPSK method, and then an error is randomly given to phase information. On the receiving side, the phase information is converted into bit information (bit likelihood in the case of soft decision), then deinterleaved, and Viterbi decoding is performed only for class 1. The above process is executed for 200 slots, and the bit error rate is calculated for each of class 1 and class 2.

As is apparent from FIG. 6, in the present embodiment, when transmitting at the same Eb / No, the bit error rate is smaller than that of the conventional hard decision Viterbi decoding. Conversely, when the same bit error rate is desired, the transmission power can be reduced.

The present invention is not limited to the illustrated embodiment, and various modifications are possible. For example, there are the following modifications.

(1) In step 52 in FIG. 1, the equation for calculating the phase likelihood is not limited to the equations (3) and (4), but monotonically decreases with respect to the magnitude of θ (k), and θ (k) is If the value is 0, the maximum value of the likelihood is obtained, and if θ (k) is (2π / the number of unique phases transmitted by the differential PSK method), a function that takes the minimum value of the likelihood may be used. In the above embodiment, the likelihood is considered to be 0 to 1, but depending on the case, it is 0 to 100 or −1 to 1
It is good.

(2) In step S59 of FIG. 1, the bit likelihood obtained in step S58 may be used directly as soft decision data. However, since the bit likelihood in step S58 is a real number, appropriate quantization is performed. The value may be used as soft decision data. In addition, this bit likelihood can be used as it is when performing a product-sum operation as a metric operation method of the Viterbi algorithm, and when calculating the metric by another method such as a difference operation, the bit likelihood should be diverted with a slight change. Is possible.

(3) Soft decision data calculation processing S50 in FIG.
Can also be used for a soft decision decoding method of a block code. Also in the case of soft-decision decoding of a block code, the calculation based on bit likelihood improves the bit error correction capability for the same reason as in the case of soft-decision Viterbi decoding. It is also possible to use both block code decoding and Viterbi decoding.

(4) The Viterbi decoding of FIG. 1 can be used in combination with various diversity receptions. A combination with the decision feedback type equalization is also possible. In addition to block codes and interleaving, ARQ (AUTOMATIC REPEAT)
REQUEST) type code error control (a method of retransmitting information when an error is detected) is also possible.

[0071]

As described above in detail, according to the present invention, when a convolutional code is transmitted in a differential PSK modulation method, a bit sequence is obtained in a process of obtaining a bit sequence from phase detection of a received carrier. Is calculated and soft-decision Viterbi decoding is performed, so that the bit error rate of the original signal can be reduced and high-precision decoding can be performed as compared with conventional hard-decision Viterbi decoding.

[Brief description of the drawings]

FIG. 1 is a flowchart of a soft-decision Viterbi decoding method according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram of convolutional coding.

FIG. 3 is a diagram showing a trellis figure.

FIG. 4 is a block diagram illustrating a configuration of a soft-decision Viterbi decoding apparatus according to an embodiment of the present invention.

FIG. 5 is a relationship diagram between a detected phase and a selected phase.

FIG. 6 is a bit error characteristic diagram of FIG. 1;

[Explanation of symbols]

 Reference Signs List 30 soft decision Viterbi decoding device 31 soft decision data calculation unit 32 memory for deinterleaving 33 path memory 34 Viterbi algorithm execution unit S50 soft decision data calculation process S51 phase selection S52 phase likelihood calculation S53 phase difference calculation S54 phase difference likelihood calculation S55 Phase difference selection S56 Read corresponding bit S57 Bit likelihood calculation S58 Bit likelihood correction S59 Judgment data output S60 Viterbi algorithm implementation

Continuation of the front page (56) References JP-A-52-106212 (JP, A) JP-A-3-502029 (JP, A) Masami Abe, Genhiro Shiino, Yasuo Shoji, “Softness in differential PSK modulation method” Judgment Decoding Method ", IEICE Transactions C, 1991, Vol. 111, NO. 11, p. 563-568

Claims (1)

(57) [Claims] When a convolutional code is modulated by a differential phase shift keying method for allocating a bit string based on Gray coding to a phase difference of a carrier wave transmitted continuously in time, a receiving side is used. Comparing the detected phase of the carrier detected in the phase with the unique phase transmitted by the differential phase shift keying method, and selecting two of the unique phases having a small absolute value of the phase shift; and When the magnitude of the phase shift monotonically decreases and the absolute value of the phase shift is 0, the maximum value of the likelihood is obtained, and the absolute value of the phase shift is (2π / the differential type phase shift keying system). (The number of unique phases), the phase likelihood calculation processing for calculating the phase likelihood by using the function that takes the minimum value of the likelihood, and the temporally continuous selection based on the result of the phase likelihood calculation processing. Done it A phase difference calculation process of calculating four types of phases by combining the two phases, and calculating a phase difference likelihood of each of the phase differences as a smaller one of the likelihood of the phase used to calculate the phase difference. Phase difference likelihood calculation processing, the first phase difference having the largest phase difference likelihood, and the second phase difference having the largest phase difference likelihood among the phase differences different from the first phase difference. Phase difference selection processing for selecting
A corresponding bit readout / bit likelihood calculation process of reading out a plurality of bits of a bit string corresponding to the phase difference, calculating the likelihood of each bit as the likelihood of the first phase difference, and calculating the bit likelihood. A bit likelihood correction for correcting a bit likelihood that maximizes a likelihood of a bit equal to a bit of a bit string corresponding to the second phase difference among bits of a bit string corresponding to the first phase difference; And using the result of the bit likelihood correction process for calculating a metric in a Viterbi algorithm.