JP2001352257A - Decoder and decoding method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce the scale of circuit while increasing the processing speed without deteriorating the performance of decoding. SOLUTION: The decoder comprises an operating circuit performing operations represented by general formulas (1) and (2) where at least the difference of probability logarithmic likelihood at each state is a part of variables. Using the operation results from the operating circuit, the decoder calculates a logarithmic soft output representing a soft output at each time by logarithmic likelihood using natural logarithm.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a decoding device and a decoding method for performing soft output decoding.

[0002]

2. Description of the Related Art In recent years, studies have been made to reduce the symbol error rate by making the decoded output of an inner code in a concatenated code or the output of each iterative decoding operation in an iterative decoding method softer. Research on the law has been actively conducted. For example, as a method of minimizing the symbol error rate when decoding a predetermined code such as a convolutional code, “Bahl, Cocke, Jelinek and Raviv,“ Optimal
decoding of linear codes for minimizing symbol err
or rate ”, IEEE Trans. Inf. Theory, vol. IT-20, p
p. 284-287, Mar. 1974 ", the BCJR algorithm is known. As an implementation method for reducing the amount of computation of the BCJR algorithm," Robertson, Ville
brun and Hoeher, “A comparison of optimal and sub
-optimal MAPdecoding algorithms operating in the d
omain ”, IEEE Int. Conf. on Communications, pp. 10
09-1013, June 1995 ".
An algorithm (hereinafter, referred to as a Log-BCJR algorithm) is known. In the BCJR algorithm and the Log-BCJR algorithm, the likelihood of each symbol is output instead of outputting each symbol as a decoding result. Such output is a soft output (so
ft-output). Hereinafter, the contents of the BCJR algorithm and the Log-BCJR algorithm will be described. In the following description, as shown in FIG. 9, the digital information is convolutionally encoded by an encoding device 201 provided in a transmitting device (not shown), and the output is transmitted via a no-memory communication channel 202 with noise to a receiving device (not shown). , And decoding by the decoding device 203 included in the receiving device and observation.

[0003] First, the BCJR algorithm will be described.

A shift register included in the encoding device 201
M states (transition states) representing the contents of m (0,
,..., M−1), and the state at time t is S_t
Expressed by Also, k-bit information is inserted in one time slot.
If the input at time t is i_t=
(I_t1, I_t2, ..., i_tk), And the input system is I₁ ^T
= (I₁, I_Two, ..., i_T). At this time,
If there is a transition from state m 'to state m,
The information bit corresponding to the transition is represented by i (m ', m) = (i
₁(M ', m), i_Two(M ', m), ..., i
_k(M ', m)). In addition, one time slot
Assuming that an n-bit code is output, at time t
X_t= (X_t1, X_t2, ..., x_tn)
Output system₁ ^T= (X₁, X_Two, ..., x_T)
You. At this time, the transition from state m 'to state m
In some cases, the sign bit corresponding to the transition is x
(M ', m) = (x₁(M ', m), x_Two(M ', m),
..., x_n(M ', m)).

Convolutional coding by coding apparatus 201
Is the state S₀= 0, X₁ ^TAnd output S_T=
It shall end with 0. Here, the transition between each state
Probability P _t(M | m ') is defined by the following equation (9).

[0006]

(Equation 9)

Incidentally, Pr shown on the right side in the above equation (9)
{A | B} is the conditional probability that A will occur under the condition that B occurs. The transition probability P _t (m | m ') is as shown in the following equation (10), state m at input i' when transitioning from the state m, the input i _t at time t is i
It is equal to the probability Pr {i _t = i} is.

[0008]

(Equation 10)

The no-memory storage channel 202 with noise receives X ₁ ^T as input and outputs Y ₁ ^T. Here, assuming that an n-bit received value is output in one time slot, time t
_Are represented by y _t = (y _t1 , y _t2 ,..., Y _tn ) and Y ₁ ^T = (y ₁ , y ₂ ,..., Y _T ). The transition probabilities of the noisy memoryless channel 202 are all t (1
≦ t ≦ T) can be defined using the transition probability Pr {y _j | x _j } of each symbol as shown in the following equation (11).

[0010]

[Equation 11]

Here, λ _tj is defined as in the following equation (12). Λ _tj shown in the following equation (12) represents the likelihood of input information at time t when Y ₁ ^T is received, and is a soft output that should be originally obtained.

[0012]

(Equation 12)

In the BCJR algorithm, probabilities α _t , β _t and γ _t are defined as shown in the following equations (13) to (15). Note that Pr {A; B} represents the probability that both A and B occur.

[0014]

(Equation 13)

[0015]

[Equation 14]

[0016]

(Equation 15)

Here, these probabilities α_t, Β_tAnd γ_tof
About the contents, in the state transition diagram in the encoding device 201,
A trellis will be described with reference to FIG. Smell
And α _t-1Is the encoding start state S₀= 0 from the received value
Each of the stays at time t-1 calculated in chronological order
Corresponding to the passing probability of the Also, β_tIs the encoding end
Tate S_TCalculated in reverse chronological order based on received values from = 0
It corresponds to the passing probability of each state at the time t.
Furthermore, γ_tIs a relation between the received value at time t and the input probability.
Output of each branch transitioning between states at the time t calculated based on
Corresponds to the force reception probability.

Using these probabilities α _t , β _t and γ _t , the soft output λ _tj can be expressed by the following equation (16).

[0019]

(Equation 16)

By the way, for t = 1, 2,..., T, the following equation (17) holds.

[0021]

[Equation 17]

Similarly, the following equation (18) holds for t = 1, 2,..., T.

[0023]

(Equation 18)

Further, the following equation (19) holds for γ _t .

[0025]

[Equation 19]

Therefore, the decoding device 203 outputs the BCJR
When applying the algorithm performs soft output decoding, based on these relationships, determine soft output lambda _t Through the series of steps shown in FIG. 11.

First, the decoding device 203 is configured as shown in FIG.
In step S201, y _tEvery time you receive
Using the above equations (17) and (19), the probability α
_t(M) and γ_t(M ', m) is calculated.

Subsequently, the decryption device 203 determines in step S2
02, after receiving all of the series Y ₁ ^T , each state m at all times t is calculated using the above equation (18).
, The probability β _t (m) is calculated.

Then, the decoding device 203 determines in step S2
03, step S201 and step S202
The probabilities α _t , β _t and γ _t calculated in the above are calculated by the above equation (16)
To calculate the soft output λ _t at each time t.

The decoding device 203 can perform soft output decoding to which the BCJR algorithm is applied by going through such a series of processing.

Incidentally, in such a BCJR algorithm, it is necessary to perform the operation while holding the probability as a direct value, and there is a problem that the amount of operation is large because it involves a product operation. Therefore, as a method of reducing the amount of computation,
"Robertson, Villebrun and Hoeher," A com
parison of optimal and sub-optimal MAP decodingalg
orithms operating in the domain ”, IEEE Int. Conf.
on Communications, pp. 1009-1013, June 1995 ”, by expressing the probabilities α _t , β _{t and} γ _t , and the soft output λ _t in log likelihood using natural logarithm, As shown in Expression (20), there is a method in which a product operation of probabilities is replaced with a logarithm sum operation, and a probability sum operation is performed as a so-called log-sum operation as shown in the following Expression (21). In the following, "SS Pietrobo
n, “Implemntation and performance of a turbo / MAP
decoder ”, Int. J. Satellite Commun., vol. 16, pp.
23-46, Jan.-Feb. 1998], the operator of the log-sum operation is expressed as “#” (for convenience) as shown in the following equation (21). In the dissertation,
“E”. ). Further, the operator of the cumulative addition operation of the log-sum operation is represented as “# Σ” (however, in the same paper, “E”) as shown in the following equation (22).

[0032]

(Equation 20)

[0033]

(Equation 21)

[0034]

(Equation 22)

Here, for the sake of simplicity, the natural logarithm is abbreviated as I, and the natural logarithms of α _t , β _t , γ _t , and λ _t are respectively _{expressed by} the following equation (23). Iα _t , Iβ _t , I
γ _t, it is intended to refer to the Iλ _t.

[0036]

(Equation 23)

Therefore, the accuracy of these log likelihood notations is
Log likelihood Iα _t, Iβ_t, Iγ_t,
And log soft output Iλ_tAre given by the following equations (24) to (2)
7). Note that the following equation (24)
Of the log-sum operation in the state m 'on the right side
The accumulative addition operation is performed in the state where the transition to the state m exists.
M ′, and the right side of the following equation (25)
Cumulative addition of log-sum operation in state m 'of edge
Arithmetic operation is a state where a transition from state m exists.
m '. Also, the following equation (27)
Addition operation of log-sum operation of the first term on the right side
Indicates that there is a transition to state m when the input is "1"
In the state m ', and the log-sum performance of the second term
When the input is “0”, the state of the state m
In the state m 'where the transition to
You.

[0038]

(Equation 24)

[0039]

(Equation 25)

[0040]

(Equation 26)

[0041]

[Equation 27]

As described above, one of the methods for implementing the BCJR algorithm that handles the probability in the form of log likelihood by expressing the log likelihood is the above-described Log-BCJR algorithm. Hereinafter, the Log-BCJR algorithm will be described. In the following, the probability log likelihoods Iα _t , Iβ _t , and Iγ _t expressed in log likelihood are respectively the probability log likelihood ratio (log likelihood rat) which is the log likelihood notation of the ratio of the probability.
io).

The Log-BCJR algorithm calculates the probability α
_t , β _t , γ _t , and soft output λ _t are represented by natural logarithms, and as shown in the above equation (20), the product operation of probabilities is replaced with the sum operation of logarithms, and as shown in the following equation (28) The log-sum operation replacing the probability sum operation is an operation in which a correction term is added to the logarithmic maximum value operation, and an accurate log value of the sum operation is obtained. Here, such correction is referred to as log-sum correction. Note that max (x, y) shown in the following equation (28) is a function for selecting one having a larger value among x and y.

[0044]

[Equation 28]

In the Log-BCJR algorithm, the probability log likelihood Iγ _{t is obtained} by the above equation (26), and the probability log likelihoods Iα _t and Iβ _t are calculated by the following equations (29) and (30), respectively. Ask by Here, log− in the state m ′ on the right side in the following equation (29)
The cumulative addition operation of the sum operation is determined in the state m ′ where the transition to the state m exists.
0) log-su in state m ′ on the right side
The cumulative addition operation of the m operation is obtained in a state m ′ where a transition from the state m exists.

[0046]

(Equation 29)

[0047]

[Equation 30]

[0048] In addition, in the Log-BCJR algorithm, the same applies to the log soft-output Iλ _t, the following equation (3
Determined by 1). Here, the cumulative addition operation of the log-sum operation in the state m ′ of the first term on the right side in the following equation (31) is performed in the state m ′ where the transition to the state m exists when the input is “1”. And the log of the second term
The cumulative addition operation of the −sum operation is obtained in a state m ′ in which a transition to the state m exists when the input is “0”.

[0049]

(Equation 31)

Therefore, the decoding device 203 outputs the log-
When applying the BCJR algorithm performs soft output decoding, based on these relationships, it determines the log soft-output Airamuda _t Through the series of steps shown in FIG. 12.

First, the decoding device 203 is configured as shown in FIG.
In step S211, y _tEvery time you receive
Using the above equations (29) and (26), the probability log likelihood
Iα_t(M) and Iγ_t(M ', m) is calculated.

Subsequently, the decryption device 203 determines in step S2
12, after receiving all of the series Y ₁ ^T , each state m at all times t is calculated using the above equation (30).
, The probability log likelihood Iβ _t (m) is calculated.

Then, the decoding device 203 determines in step S2
In step 13, step S211 and step S212
Log likelihood Iα _t , Iβ _t and Iγ _t calculated in
Is substituted into the above equation (31), and the log soft output Iλt at each time _t is calculated.

The decoding device 203 can perform soft output decoding to which the Log-BCJR algorithm is applied by going through such a series of processing. In the above equation (28), the correction term shown in the second term on the right side is a variable |
Since this value is represented by a one-dimensional function for xy |, the decoding device 203 stores this value in a ROM (Read Onl
(Y Memory) or the like in advance, or by approximation using a so-called linear approximation, threshold approximation, or the like, an accurate probability calculation can be performed.

As described above, since the Log-BCJR algorithm does not include a product operation, the amount of operation can be greatly reduced as compared with the BCJR algorithm.
Its output is nothing but the logarithm of the soft output of the BCJR algorithm except for the quantization error.

[0056]

By the way, as described above, the probabilities are expressed in log likelihood and handled in the form of log likelihood.
When implementing the CJR algorithm, the decoding device 20
3 is logarithmic likelihood notation, so many log-
It is necessary to perform a sum operation.

For example, consider a case where a code convolutionally coded by the coding apparatus 201 shown in FIG. 13 is decoded. Here, the probability log likelihood Iα _t (S ₀ ) at time t in state S ₀ is replaced with “U _t ”, and the probability log likelihood Iα _t (S ₁ ) at time t in state S ₁ .
Replaced with "V _t", and the state S replaced with a probability log likelihood Iβ _t (S ₀₎ at time _t "W t" in _0, the probability log likelihood Iβ _t (S at time t in state S _{1 1} )
Is replaced with “Z _t ”.

Here, the trellis in the encoding device 201 is described as shown in FIG. In the figure, the label assigned to each path is the input data i _t
/ Shows the output data x _t. Here, the state is represented by the contents of the shift register, and the states “0” and “1” are referred to as state S ₀ and state S ₁ , respectively. As described above, the number of states in the encoding device 201 is 2, and the trellis has a structure in which two paths reach from each state to the state at the next time.

At this time, the probability log likelihood Iγ _t (m ′,
m) is represented by the matrix shown in FIG. A _t shown in the figure, y _t are respectively the following formulas (32) and equation (3
Represented by 3), A _t is the priori probability information probabilities and the input data i _t input data i _t is "1" is a natural logarithm of the ratio of the probability of "0" (a priori probability infor
mation), and y _t is a posteriori probability information for the code bit C _t of one symbol of the code word determined only from the received value.

[0060]

(Equation 32)

[0061]

[Equation 33]

In this case, the decoding device 203 calculates the following equation (3)
4) through calculation of the following equation (37),
Update the probability log likelihoods U _t , V _t , W _t , and Z _t .

[0063]

(Equation 34)

[0064]

(Equation 35)

[0065]

[Equation 36]

[0066]

(37)

Therefore, the decoding apparatus 203 calculates the following equation (3)
8), the logarithmic soft output Iλ _t
Is calculated.

[0068]

(38)

As described above, when updating the probability log likelihoods Iα _t and Iβ _t , the decoding device 203 executes two l
performs og-sum operation, when calculating the log soft-output Airamuda _t, it is necessary to carry out two more log-sum operation.

In order to describe this in more detail, a decoding device 203 that implements the BCJR algorithm in which the probabilities are represented in log-likelihood and handled in the form of log-likelihood is shown in FIGS.
FIG. Here, FIG. 16 shows a portion for calculating the probability log likelihoods Iα _t and Iγ _t among the components of the decoding device 203, and FIG. 17 shows a portion for calculating the probability log likelihoods Iβ _t and Iγ _t. the shown, in FIG. 18 shows a portion for calculating a log soft-output Iλ _t.

The decoding device 203 shown in FIG. 16 is a part for calculating the probability log likelihood Iα _t and Iγ _t . Decoding device 20
3, as i? Calculation circuit for calculating a probability log likelihood i? _T, comprises four adders 211, 212, 213 and 214. In addition, the decoding device 203 includes two log-sum operation circuits 215 and 216 that perform log-sum operations as Iα calculation circuits that calculate the probability log likelihood Iα _t, and the log-sum operation circuits 215 and 216 A normalization circuit 217 for normalizing the output data to avoid overflow, and two differentiators 218,
219 and two registers 220 and 2 for holding data.
21.

[0072] Adder 211 priori probability information A _t and, before 1 time supplied from the register 220 probability log-likelihood U
_The data (U _t-1 + A _t ) is supplied to the adder 212.

The adder 212 receives the received value (posterior probability information)
y _t and the data supplied from the adder 211 (U _t−1 + A
_t ) and supplies the obtained data (U _t-1 + A _t + y _t ) to the log-sum operation circuit 215.

The adder 213 adds the received value y _t and the probability log likelihood V _t−1 one time ago supplied from the register 221 to obtain data (V _t−1 + y _t ). log-s
um operation circuit 215.

[0075] The adder 214, a priori probability information A _t and, before 1 time, which is supplied from the register 221 probability log-likelihood V
_t-1 and add the obtained data (V _t-1 + A _t ) to lo
It is supplied to the g-sum operation circuit 216.

The log-sum operation circuit 215 performs a log-sum operation using the data supplied from the adder 212 and the data supplied from the adder 213, and converts the obtained data into a normalization circuit 217 and The difference is supplied to a differentiator 218.

The log-sum operation circuit 216 uses the data supplied from the adder 214 and the probability log likelihood U _t−1 one time ago supplied from the register 220 to log-sum.
A g-sum operation is performed, and the obtained data is normalized by a normalization circuit 2
17 and the difference unit 219.

The normalization circuit 217 receives the data output from the log-sum operation circuits 215 and 216 and generates data for normalizing these data. The normalization circuit 217 converts the generated data into differentiators 218, 2
Supply to 19.

The difference unit 218 obtains difference data between the data supplied from the log-sum operation circuit 215 and the data supplied from the normalization circuit 217, and supplies this difference data to the register 220.

The difference unit 219 obtains difference data between the data supplied from the log-sum operation circuit 216 and the data supplied from the normalization circuit 217, and supplies this difference data to the register 221.

The register 220 holds the difference data supplied from the differentiator 218, that is, the probability log likelihood U _t . The probability log likelihood U held in this register 220
_t is supplied to the memory circuit (not shown) for storing a probability log likelihood I.alpha _t.

[0082] register 221, the difference data supplied from the differentiator 219, that is, to hold the probability log-likelihood V _t. The probability log likelihood V held in this register 221
_t is supplied to the memory circuit (not shown) for storing a probability log likelihood I.alpha _t.

Such a decoding device 203 uses the above equation (3)
4) and the calculation shown in the above equation (35) are performed to calculate the probability log likelihoods U _t and V _t .

[0084] Further, the decoding apparatus 203, as shown in FIG. 17, forming a part for calculating a probability log likelihood I beta _t and i? _T. Decoding apparatus 203, as i? Calculation circuit for calculating a probability log likelihood i? _T, 4 adders 222,22
3,224,225. Also, the decoding device 203
Are two log-sum operation circuits 226 and 227 as Iβ calculation circuits for calculating the probability log likelihood Iβ _t ;
A normalization circuit 228, two differentiators 229 and 230,
It has two registers 231 and 232.

[0085] The adder 222 has a priori probability information A _t read from a not-shown memory circuit, it adds the data supplied from the adder _{223 (W t-1 + y} t), obtained data ( _{W t-1 + a t +} y t) the log-sum operation circuit 2
26.

The adder 223 adds the received value y _t read from the storage circuit (not shown) to the probability log likelihood W _t−1 one time ago supplied from the register 231 and obtains the obtained data. (W _t−1 + y _t ) is supplied to the adder 222.

[0087] The adder 224 adds the priori probability information A _t read from a not-shown memory circuit, before 1 time supplied from the register 232 and a probability logarithmic likelihood Z _t-1,
The data obtained _{(Z t-1 + A t} ) and supplies the log-sum operation circuit 227.

The adder 225 adds the received value y _t read from the storage circuit (not shown) to the probability log likelihood W _t−1 one time ago supplied from the register 231 and obtains the obtained data. (W _t−1 + y _t ) is calculated by the log-sum operation circuit 22.
7

The log-sum operation circuit 226 uses the data supplied from the adder 222 and the logarithmic likelihood Z _t−1 one time ago supplied from the register 232 to perform log-sum operation.
A g-sum operation is performed, and the obtained data is normalized by a normalization circuit 2
28 and the difference unit 229.

The log-sum operation circuit 227 performs a log-sum operation using the data supplied from the adder 224 and the data supplied from the adder 225, and converts the obtained data into a normalization circuit 228 and The difference is supplied to a differentiator 230.

The normalization circuit 228 receives the data output from the log-sum operation circuits 226 and 227 and generates data for normalizing these data. The normalizing circuit 228 converts the generated data into differentiators 229 and 2
30.

The difference unit 229 obtains difference data between the data supplied from the log-sum operation circuit 226 and the data supplied from the normalization circuit 228, and supplies this difference data to the register 231.

The difference unit 230 obtains difference data between the data supplied from the log-sum operation circuit 227 and the data supplied from the normalization circuit 228, and supplies this difference data to the register 232.

[0094] register 231, the difference data supplied from the differentiator 229, that is, to hold the probability log-likelihood W _t. Probability log likelihood W held in this register 229
_t is supplied to the memory circuit (not shown) for storing a probability log likelihood I beta _t.

[0095] register 232, the difference data supplied from the differentiator 230, that is, to hold the probability log-likelihood Z _t. Probability log likelihood Z held in this register 232
_t is supplied to the memory circuit (not shown) for storing a probability log likelihood I beta _t.

Such a decoding device 203 uses the above equation (3)
6) and the calculation shown in the above equation (37) are performed to calculate the probability log likelihood W _t , Z _t .

[0097] Further, the decoding apparatus 203, as shown in FIG. 18, as a portion for calculating a log soft-output Iλ _t, 7 adders 233,234,235,236,237,2
38, 242 and two log-sum operation circuits 23
9, 240, and a differentiator 241.

The adder 233 adds the received value y _t read from the storage circuit (not shown) and the probability log likelihood U _t read from the storage circuit (not shown), and obtains data (U _t + Y _t ) to the adder 234.

The adder 234 adds the probability log likelihood W _t read from the storage circuit (not shown) and the data (U _t + y _t ) supplied from the adder 233, and obtains the data (U _t + W _t + y _t) the log-sum operation circuit 239
To supply.

An adder 235 adds the probability log likelihoods V _t and Z _t read from a storage circuit (not shown), and supplies the obtained data (V _t + Z _t ) to a log-sum operation circuit 239. .

The adder 236 adds the probability log likelihoods U _t and Z _t read from a storage circuit (not shown) and supplies the obtained data (U _t + Z _t ) to the log-sum operation circuit 240. .

The adder 237 adds the received value y _t read from the storage circuit (not shown) and the probability log likelihood V _t read from the storage circuit (not shown), and obtains data (V _t + Y _t ) to the adder 238.

The adder 238 adds the probability log likelihood W _t read from the storage circuit (not shown) and the data (V _t + y _t ) supplied from the adder 237, and obtains the data (V _t + W _t + y _t) the log-sum operation circuit 240
To supply.

The log-sum operation circuit 239 performs a log-sum operation using the data supplied from the adder 234 and the data supplied from the adder 235, and supplies the obtained data to the differentiator 241. I do.

The log-sum operation circuit 240 performs a log-sum operation using the data supplied from the adder 236 and the data supplied from the adder 238, and supplies the obtained data to the differentiator 241. I do.

The differentiator 241 calculates difference data between the data supplied from the log-sum operation circuit 239 and the data supplied from the log-sum operation circuit 240.
The difference data is supplied to the adder 242.

[0107] The adder 242 adds the priori probability information A _t read from a not-shown memory circuit, and the difference data supplied from the differentiator 241, and outputs the obtained data as a log soft-output Airamuda _t I do.

[0108] Such a decoding device 203 includes a priori probability information A _t read from a storage circuit (not shown) and a received value y _t.
Using the logarithmic likelihoods U _t , V _t , W _t , and Z _t , the calculation shown in the above equation (38) is performed to calculate the log soft output Iλ _t .

As described above, the decoding device 203 calculates the two log-sum operation circuits 215 and 21 to calculate the probability log likelihood Iα _t , that is, the probability log likelihoods U _t and V _t.
6 and two log-su values for calculating the probability log likelihood Iβ _t , ie, the probability log likelihood W _t , Z _t.
comprising a m arithmetic circuits 226 and 227, further, it is necessary to provide a two log-sum operation circuit 239, 240 in order to calculate the logarithmic soft-output Iλ _t. This log-su
It is very difficult to implement the m operation in a straightforward manner using the Log-BCJR algorithm.
Requires an enormous circuit scale and processing time.

Further, the decoding device 203 calculates the probability log likelihood U
_t, V _t, W _t, in order to avoid overflow of the Z _t,
For the number of states, here two normalization circuits 217 and 22
8, and furthermore, the probability log likelihood U _t ,
In order to perform an iterative operation for calculating V _t , W _t , and Z _t , the number of states × 2, here, four registers 220, 221,
231 and 232, and the probability log likelihoods U _t , V _t , W _t ,
Holding the Z _t, it is necessary to update those values.

As described above, the decoding device 203 that implements such a BCJR algorithm has a large circuit scale,
There was a problem that processing was delayed.

The present invention has been made in view of such circumstances, and provides a decoding apparatus and a decoding method capable of realizing a reduction in the circuit size and an increase in processing speed without deteriorating performance. The purpose is to:

[0113]

A decoding apparatus according to the present invention, which achieves the above-mentioned object, provides a log likelihood notation using a natural logarithm for a probability of passing through an arbitrary state based on a received value which is a soft input. A decoding device that obtains the calculated probability log likelihood and performs decoding using the probability log likelihood, wherein at least the difference value of the probability log likelihood in each state is a part of a variable represented by the following general formula (1): An arithmetic unit for performing an operation represented by the following general formula (2) is provided. Using a result calculated by the arithmetic unit, a soft output at each time is expressed in log likelihood using natural logarithm. It is characterized in that it is calculated.

[0114]

[Equation 39]

[0115]

(Equation 40)

(However, A, B, A ₀ , A ₁ ,..., A
_n is a variable, log is a natural logarithm based on the number e of Nepia, and ＄ is an operator. The decoding device according to the present invention is represented by the above-described general formula (1) and the general formula (2) in which at least the difference value of the probability log likelihood in each state is a part of a variable. Calculate the logarithmic soft output at each time.

The decoding method according to the present invention, which achieves the above-described object, provides a probability that the probability of passing through an arbitrary state based on a received value that is a soft input is represented by log likelihood using natural logarithm. And a decoding method for decoding using the probability log likelihood, wherein at least a difference value of the probability log likelihood in each state is a part of a variable, the following general formula (5) and the following general formula ( And 6) calculating a logarithmic soft output in which the soft output at each time is represented by log likelihood using natural logarithm, using a result calculated in the calculation step. It is characterized by.

[0118]

[Equation 41]

[0119]

(Equation 42)

(However, A, B, A ₀ , A ₁ ,..., A
_n is a variable, log is a natural logarithm based on the number e of Nepia, and ＄ is an operator. The decoding method according to the present invention includes:
The calculation represented by the general formula (5) and the general formula (6) using at least a difference value of the probability log likelihood in each state as a variable is performed to calculate a log soft output at each time.

[0121]

Embodiments of the present invention will be described below in detail with reference to the drawings.

In this embodiment, as shown in FIG. 1, digital information is convolutionally encoded by an encoding device 1 provided in a transmitting device (not shown), and the output is not shown via a memoryless communication path 2 with noise. This is a data transmission / reception system applied to a communication model that is input to a receiving device and decoded by a decoding device 3 included in the receiving device.

In this data transmission / reception system, the decoding device 3 decodes a code that has been convolutionally coded by the coding device 1 and includes “Bahl, Cocke, Jel
inekand Raviv, “Optimal decoding of linear codes
for minimizing symbol error rate ”, IEEE Trans. In
f. Theory, vol. IT-20, pp. 284-287, Mar. 1974 ”based on an improved BCJR algorithm (Maximum A Posteriori p.
robability; hereinafter, referred to as MAP. ) Is configured to perform decoding, and the so-called probabilities α _t , β _t , γ _t , and soft-output λ _t are expressed in log likelihood using natural logarithm. _{t, Iβ t,} I
and requests the γ _t, and log soft force Iλ _t. In particular,
As will be described later in detail, the decoding device 3 performs decoding using at least the difference value between the values of the probability log likelihoods Iα _t and Iβ _t in each state.

In the following, the probability log likelihood Iα _t , Iβ _t , and Iγ _t expressed in log likelihood are respectively the probability log likelihood ratio (log likelihood r) which is the log likelihood notation of the ratio of the probability.
atio). In the following, M states (transition states) representing the contents of the shift register provided in the encoding device 1 are represented by m (0, 1,..., M−1).
Expressed in, representing the state of time t in S _t. Further, 1 when k-bit information is assumed to be inputted to the time slot, enter a i _t at time _{t = (i t1, i t2} , ··
, I _tk ), and the input system is I ₁ ^T = (i ₁ , i ₂ ,...)
, I _T ). At this time, if there is a transition from state m ′ to state m, the information bit corresponding to the transition is set to i (m ′, m) = (i ₁ (m ′, m), i).
₂ (m ', m), ..., i _k (m', m)). Further, assuming that an n-bit code is output in one time slot, the output at time t is x _t = (x _t1 , x _t
t2, · · ·, expressed as x _tn), the output system X ₁ ^T = (x _1,
x ₂ ,..., x _T ). At this time, if there is a transition from the state m ′ to the state m, the sign bit corresponding to the transition is x (m ′, m) = (x ₁ (m ′,
m), x ₂ (m ′, m),..., x _n (m ′, m)). Furthermore, memoryless channel 2 inputs the X ₁ ^T, and outputs an Y ₁ ^T. Here, assuming that an n-bit received value is output in one time slot, the output at time t is represented by y _t = (y _t1 , y _t2 ,...,
expressed by ^{_{y t n), Y 1 T}} = (y 1, y 2, ···, represented by y _T).

The encoding apparatus 1 has one exclusive OR circuit 11 and one shift register 12 as shown in FIG. 2, for example, and is configured to perform a convolution operation.

[0126] exclusive OR circuit 11 has an input data i _t of 1 bit, an exclusive-OR operation by using the data supplied from the shift register 12, the output data X _t of 1 bit operation result Output to the outside as
The data is supplied to the shift register 12.

The shift register 12 continues to supply the held 1-bit data to the exclusive OR circuit 11.
Then, the shift register 12 newly holds 1-bit data supplied from the exclusive OR circuit 11 in synchronization with the clock, and stores this data in the exclusive OR circuit 1.
1 is newly supplied.

[0128] Such encoding device 1 inputs the input data i _t of 1 bit, performs recursive convolutional operation on the input data i _t, outside an operation result as a 1-bit output data x _t Output to That is, the encoding apparatus 1, which is configured to input data i _t as an accumulator (accumulator) which outputs the cumulative addition,
Coding rate performs recursive systematic convolutional operation of "1", and outputs the output data x _t to the outside. That is, the encoding device 1 performs a recursive systematic convolution operation with an encoding rate of “1” and outputs the output data _xt to the outside.

FIG. 3 shows a trellis which is a state transition diagram in the encoding apparatus 1. In the figure, the path indicated by a broken line, the input data i _t is "0"
Indicates the case of the path indicated by a solid line, the input data i _t indicates a case of "1". Further, labels are assigned to each path represents the output data x _t. Here, the state is represented by the contents of the shift register 12,
The states “0” and “1” are called state S ₀ and state S ₁ , respectively. Thus, the number of states in the encoding device 201 is 2, and the trellis is
It has a structure in which two paths reach from each state to the state at the next time.

[0130] encoded output data x _t by such encoding apparatus 1 and output to the receiving apparatus via a memoryless channel 2.

Next, the decoding device 3 will be described.
First, an algorithm applied to the decoding device 3 will be described in detail.

In the BCJR algorithm in which probabilities are expressed in log likelihood and handled in the form of log likelihood, the probability α as the first probability is expressed by the first probability log likelihood expressed in log likelihood using natural logarithm. A certain probability log likelihood Iα _t (m) and a second probability log likelihood Iβ _t (m) which is a second probability log likelihood expressed by using a natural logarithm to represent the probability β which is the second probability. Is essentially required when calculating the probability log likelihood Iα _t (m), Iβ _t (m), but not the probability log likelihood Iα _t (m), Iβ _t (m) Is normalized by the sum of the values in each state, that is, the difference value between the values in each state.

Therefore, the decoding device 3 sets the probability log likelihood Iα for the two states S ₀ and S ₁ in the coding device 1.
_t (m), instead of performing iterative computation of Iβ _t (m), performs operation by paying attention to the difference of the values in the state S _0, S _1. Here, the probability log likelihood Iα _t (S ₀ ) at time t in state S ₀ is replaced with “U _t ”, and the probability log likelihood Iα _t (S ₁ ) at time t in state S ₁ is replaced by “V _t ”
And replace the probability log likelihood Iβ _t (S ₀ ) at time t in state S ₀ with “W _t ”, and replace the probability log likelihood Iβ _t (S ₁ ) at time t in state S ₁ with “Z _t ”
Replace with

[0134] At this time, the input data i _t is "1" is probability and the input data i _t is the natural logarithm of the ratio of the probability of being a "0" prior probability information (a priori probability inf
amation) is A _t, and a posteriori probability information for one code bit C _t of one symbol of the code word determined from only the received value is y _t.
Then, the probability log likelihood Iα in each state
_t (m), that is, the probability log likelihood U _t and V _t are represented by the following equations (39) and (40), respectively. In addition,
The operator “#” in the following expressions (39) and (40)
Indicates a so-called log-sum operation. Hereinafter, the log-sum operation is represented by an operator “#”.

[0135]

[Equation 43]

[0136]

[Equation 44]

[0137] Thus, the difference of the values of probability log likelihood I.alpha _t (m) in each state, that is, the difference value U _t -V _t probability log-likelihood U _t, V _t is the following equation (41) Expanded as shown.

[0138]

[Equation 45]

Note that the operator “＄” in the above equation (41)
"Robert G. Gallager," Low-density parity-che
ck codes ", MIT Press, 1963". For variables A, B∈R → R, the following equation (42)
And is defined as in the following equation (43). Note that log in the following equations (42) and (43) is
The natural logarithm having the number e of Nepia as a base is shown.

[0140]

[Equation 46]

[0141]

[Equation 47]

On the other hand, the probability log likelihood I in each state
beta _t (m), i.e., the probability log likelihood W _t, Z _t are each, using a priori probability information A _t and a posteriori probability information y _t, is expressed by the following equation (44) and the following equation (45) You.

[0143]

[Equation 48]

[0144]

[Equation 49]

[0145] Thus, the difference of the values of probability log likelihood I beta _t (m) in each state, i.e., the probability log likelihood W _t, the difference value W _t -Z _t of Z _t is the following equation (46) Expanded as shown.

[0146]

[Equation 50]

As described above, the above equations (41) and (4)
6) That is, the probability log likelihood Iα in each state
difference value between the value of _{t (m), Iβ t (} m) are both can be expressed by using the addition and operation given by operator "$".

[0148] Thus, the logarithmic soft-output Airamuda _t, using a probability logarithmic likelihood _{U t, V t, W t} , Z t, a priori probability information A _t and a posteriori probability information y _t, tables in the following equation (47) Is done.

[0149]

(Equation 51)

In the above equation (47), the operator “＄”
The second and third terms on the right side of the expression indicate so-called extrinsic information. As described above, the above equation (47), that is, the log soft output Iλ _t is also calculated by the probability log likelihood Iα _t (m), Iβ in each state.
Similar to the difference value of the value of _t (m), it can be expressed using the operation given by the operator “＄” and addition.

Therefore, in the ordinary BCJR algorithm in which probabilities are expressed in the form of log likelihood in the form of log likelihood, when performing an iterative operation for obtaining each of the probability log likelihoods Iα and Iβ, the value corresponding to the number of states is used. However, in this algorithm, the difference value U _t −V _t ,
W _t −Z _t may be obtained, and the “state number−
What is necessary is just to hold the value of 1 ".

Further, in this algorithm, since the difference value is used, the overflow of the held value does not occur and the normalization does not need to be performed unlike the ordinary BCJR algorithm.

Further, in this algorithm, l
Note also that there is no need to perform og-sum operations
It is. In this algorithm, the difference value U_t−
V_t, W _t-Z_tAnd log soft output Iλ_tWhen calculating
You only have to perform the operation represented by the child "@" once each
No.

By the way, for the above-mentioned operator “＄”, the theorem shown in the following equation (48) holds. However, the function f in the following equation (48) is represented by the following equation (49) using a positive number x as a variable.

[0155]

(Equation 52)

[0156]

(Equation 53)

Note that “sgn” in the above equation (48)
Is the sign of the variable A _i , and “| A _i |” indicates the absolute value of the variable A _i .

As described above, the operation represented by the operator “＄” can be realized by conversion and addition by the function f. Here, the function f is a decreasing function given in the first quadrant and asymptotically approaching 0 with an increase in the variable x as shown in FIG.
It can be implemented by various methods such as storing in advance as a table in an OM (Read Only Memory) or the like, or approximating the relationship with the variable x by so-called linear approximation or threshold approximation. The function f is a variable A
_i is a combination of a sign and an absolute value (signed magnitude format), for example, a RAM (Random Access Me
(mory) etc., it is possible to implement a simpler implementation with less calculation amount.

From the above discussion, it can be expected that the decoding device 3 that can reduce the circuit scale and increase the processing speed can be implemented.

The decoding device 3 that implements such an algorithm is provided with each unit as shown in FIGS. Here, FIG. 5, of the respective portions of the decoding device 3, shows a portion of calculating a probability log likelihood I.alpha _t, FIG. 6 shows a part for calculating a probability log likelihood I beta _t, 7 shows a portion of calculating the logarithmic soft-output Iλ _t. The decoding apparatus 3, by calculating the log soft-output Airamuda _t from the received value y _t, which are soft takes an analog value input (soft-input) by the influence of noise generated on the memoryless channel 2, encoding and it estimates the input data i _t in the device 1.

[0161] Incidentally, the probability log likelihood i? _T are those determined by the received value y _t and a priori probability information A _t. That is, the probability log likelihood i? _T, using the received value y _t and a priori probability information A _t, for each received value y _t, the natural logarithm of the probability determined by the received value and sign of the output pattern γ is there. Note that the received value y _t here is the posterior probability information y _t described above.
Is an alternative to In other words, the decoding device 3
It will calculate the probability log likelihood i? _T represented by the matrix shown in.

The decoding device 3 shown in FIG.
As Iα computation circuit for calculating the alpha _t, the arithmetic circuit is an arithmetic means for performing an operation represented by operator "$" described above 3
1; an adder 32; and a register 33 for holding data.

The arithmetic circuit 31 calculates the prior probability information A_tAnd
Difference in probability log likelihood one time ago supplied from the register 33
Minute value U_t-1-V_t-1Is represented by the operator “＄” using
Perform the operation. The arithmetic circuit 31 calculates the data obtained by the operation.
Is supplied to the adder 32. The arithmetic circuit 31
FIG. 9 is a diagram showing a relationship between the function f and the variable x described above,
To refer to a table stored in ROM not shown
To perform the operation shown in the above equation (48).
Or the relationship between the function f and the variable x is linear
A configuration that approximates by approximation or threshold approximation may be used.
No. The arithmetic circuit 31 is a storage unit (not shown)
Variable A in function f stored in RAM _iThe sign and the absolute
Using the combination with the logarithmic value, the performance shown in equation (48) above
The calculation may be performed.

The adder 32 calculates the received value y _t and the arithmetic circuit 3
The data supplied from 1 is added, and the obtained data is supplied to the register 33.

[0165] Registers 33, the data supplied from the adder 32, i.e., to hold the difference value U _t -V _t probability log-likelihood. Difference value U _t -V _t probability log-likelihood held in the register 33 is supplied to a not-shown memory circuit.

As shown in FIG. 6, the decoding device 3
As I beta calculation circuit for calculating a probability log likelihood I beta _t, it includes an adder 34, an arithmetic circuit 35 is an arithmetic unit for performing an operation represented by operator "$", and a register 36.

The adder 34 calculates the difference between the received value y _t read from the storage circuit (not shown) and the difference value W _t-1 -Z _t-1 of the probability log likelihood one time ago supplied from the register 36. And supplies the obtained data to the arithmetic circuit 35.

[0168] calculating circuit 35 performs a priori probability information A _t read from a not-shown memory circuit, by using the data supplied from the adder 34, the same operation as the arithmetic circuit 31. The operation circuit 35 supplies the data obtained by the operation to the register 36.

[0169] Registers 36, the data supplied from the arithmetic circuit 35, i.e., the difference value W of the probability log-likelihood _t -Z _t
Hold. Difference value W _t -Z _t probability log-likelihood held in the register 36 is supplied to a not-shown memory circuit.

[0170] Such a decoding device 3 uses the prior probability information A
_tAnd received value y_tAnd at least in each state
Probability log likelihood Iα_t, Iβ_tAs part of the variable
The calculations shown in (41) and (46) are performed, and each step is performed.
Auto S₀, S₁Log likelihood Iα at_t(S₀), Iα
_t(S₁) Difference value Iα_t(S₀) -Iα_t(S₁) (= U_t
-V_t) And each state S₀, S₁Log likelihood at
Iβ_t(S₀), Iβ_t(S ₁) Difference value Iβ_t(S₀) -I
β_t(S₁) (= W_t-Z_t) Is calculated. That is, decrypt
The device 3 has the prior probability information A_tAnd received value y_tOn the basis of the,
Received value y_tEach time, from the coding start state in chronological order
Probability log likelihood, which is the natural logarithm of the probability α leading to a state
Calculate the difference between the values in each state of Iα
To each state in reverse chronological order from the censored state
Of the probability log likelihood Iβ, which is the natural logarithm of the probability β
Calculate the difference between the values in the tate. And decryption equipment
3 is the difference value U held in the register 33_t-V_tAnd
Difference value W held in the register 36_t-Z_tAre not shown
Supply to storage circuit.

[0171] Further, the decoding device 3
As part of calculating the log soft-output Airamuda _t, it comprises two adders 37 and 39, and an arithmetic circuit 38 is an arithmetic unit for performing an operation represented by operator "$".

The adder 37 adds the received value y _t read from the storage circuit (not shown) and the difference value W _t −Z _t read from the storage circuit (not shown), and calculates the obtained data. Supply to circuit 38.

The arithmetic circuit 38 performs the same arithmetic operation as the arithmetic circuit 31 using the difference value U _t -V _t read from the storage circuit (not shown) and the data supplied from the adder 37. The operation circuit 38 supplies the data obtained by the operation to the adder 39.

The adder 39 reads data from a storage circuit (not shown).
Prior probability information A_tAnd supplied from the arithmetic circuit 38
Data and the resulting data are log-soft output
Iλ _tAnd output to the outside.

[0175] Such decoder 3 uses a priori probability information A _t read from a not-shown memory circuit, receiving value y _t and the difference value U _t -V _t, the W _t -Z _t, at least each state as part the difference value U _t -V _t, the W _t -Z _t variables in performs computation shown in the equation (47), calculates a log soft-output Airamuda _t at each time. Then, the decoding device 3
After you sort the calculated logarithmic soft-output Iλ _t in chronological order,
Output to the outside.

As described above, the decoding device 3 performs the normal BCJ
By improving the R algorithm, it is possible to perform soft-output decoding using an algorithm that performs decoding using the difference between the values of the probability log likelihoods Iα _t and Iβ _t in each state.

The decoding device 3 calculates the difference values U _t −V _t , W _t
−To calculate each of Z _t , “number of states−
1 ", the here comprises a computation circuit 31 and 35 of one, in order to calculate the logarithmic soft-output Airamuda _t, likewise may Sonaere one arithmetic circuit 38. The arithmetic circuit 31,35,38 Since each has a simple configuration as described above, the decoding device 3 can reduce the circuit scale and the processing time.

Further, unlike the conventional decoding device, the decoding device 3 does not need to include a normalizing circuit, and is further required to calculate each of the difference values U _t −V _t and W _t −Z _t. Since the number of registers is only “the number of states−1”, in this case, only one, the circuit scale can be reduced, and the processing speed can be increased.

As described above, the encoding apparatus 1 and the decoding
The data transmission / reception system configured using the device 3 includes:
In the decoding device 3, the probability log likelihood in each state
Iα _t, Iβ_tBy decoding using the difference value of
Therefore, simple and less arithmetic processing is required,
To reduce circuit scale and speed up processing
Can be

That is, the data transmission / reception system constituted by using the encoding device 1 and the decoding device 3 realizes high-speed and high-speed decoding of a convolutional code, and provides a user with high reliability and convenience. It can provide the property.

The present invention is not limited to the above-described embodiment. For example, as an encoding device,
It is not necessary to perform the convolution operation, and the present invention can be applied to any coding rate coding as long as the state transition is a linear trellis code represented by a trellis which is a state transition diagram. For example, when decoding a code having four states, the decoding apparatus uses “state number−
1 ", that is, three difference values may be arbitrarily selected and used. In particular, the present invention is effective for a code having a small number of states, for example," Hui Jin and
Robert J. McEliece, “RA codes achieve AWGN channe
l capacity ”, pp. 10-18, in Proc. 13th International
al Symposium on Applied Algebra, Algebraic Algorit
hms, andError-Correcting Codes. (Springer Lecture
Notes in Computer Science no. 1719) ”has a remarkable effect when the code is decoded by an accumulator which is an element encoder in the RA (Repeat-Accumulate) code.

Further, the present invention is constituted by connecting a plurality of element codes, such as a so-called parallel concatenated convolutional code, a cascade concatenated convolutional code, a code based on a turbo coded modulation scheme or a code based on a cascade concatenated modulation scheme. The present invention can be easily applied to the case of decoding a code.

Further, in the above-described embodiment, the encoding device and the decoding device are applied to the transmitting device and the receiving device in the data transmitting / receiving system, but the present invention is applied to, for example, a floppy (registered trademark) disk, a CD- The present invention can also be applied to a recording and / or reproducing apparatus for performing recording and / or reproduction on a recording medium such as a magnetic or optical or magneto-optical disk such as a ROM or an MO (Magneto Optical).
In this case, the data encoded by the encoding device is recorded on a recording medium equivalent to a memoryless communication channel, and is decoded and reproduced by the decoding device.

As described above, it goes without saying that the present invention can be appropriately changed without departing from the spirit of the present invention.

[0185]

As described above in detail, the decoding apparatus according to the present invention provides a probability that the probability of passing an arbitrary state based on a received value that is a soft input is represented by log likelihood using natural logarithm. A decoding apparatus for calculating log likelihood and performing decoding using the probability log likelihood, wherein at least a difference value of the probability log likelihood in each state is a part of a variable, A calculation means for performing the calculation represented by the formula (2) is provided, and using the result calculated by the calculation means, a logarithmic soft output is calculated by expressing a soft output at each time using natural logarithm as log likelihood. .

[0186]

(Equation 54)

[0187]

[Equation 55]

(However, A, B, A ₀ , A ₁ ,..., A
_n is a variable, log is a natural logarithm based on the number e of Nepia, and ＄ is an operator. )
The decoding device according to the present invention performs the operations represented by the general formulas (1) and (2) using the difference value of the probability log likelihood at least in each state as a part of the variable by the calculating means. By calculating the logarithmic soft output at each time, it is possible to reduce the circuit scale and speed up the processing without deteriorating the performance, requiring only simple and small arithmetic processing.

In addition, the decoding method according to the present invention obtains the probability of passing through an arbitrary state based on the received value that is a soft input by using the natural logarithm to express the probability of logarithmic logarithmic likelihood. This is a decoding method for performing decoding using log likelihood, and is represented by the following general formula (5) and the following general formula (6) in which at least a difference value of the probability log likelihood in each state is a part of a variable. An operation step of performing an operation is provided, and a logarithmic soft output in which a soft output at each time is represented by log likelihood using natural logarithm is calculated using a result calculated in the operation step.

[0190]

[Equation 56]

[0191]

[Equation 57]

(However, A, B, A ₀ , A ₁ ,..., A
_n is a variable, log is a natural logarithm based on the number e of Nepia, and ＄ is an operator. )
In the decoding method according to the present invention, in the calculation step, at least the calculation represented by the general formula (5) and the general formula (6) using the difference value of the probability log likelihood in each state as a part of the variable is performed. By calculating the logarithmic soft output at each time, it is possible to reduce the circuit scale and speed up the processing without deteriorating the performance, with simple and small arithmetic processing.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of a communication model to which a data transmission / reception system shown as an embodiment of the present invention is applied.

FIG. 2 is a block diagram illustrating a configuration of an encoding device in the data transmission / reception system.

FIG. 3 is a diagram illustrating a trellis in the encoding device.

FIG. 4 is a diagram illustrating a function f.

FIG. 5 is a block diagram illustrating a configuration of a decoding device in the data transmission / reception system, and illustrates a probability log likelihood Iα _t
FIG. 6 is a block diagram showing a part for calculating.

FIG. 6 is a block diagram illustrating a configuration of a decoding device in the data transmission / reception system, and illustrates a probability log likelihood Iβ _t
FIG. 6 is a block diagram showing a part for calculating.

[Figure 7] A block diagram illustrating the configuration of a decoding apparatus in the data transmission and reception system, a block diagram illustrating a portion for calculating a log soft-output Iλ _t.

8 is a diagram illustrating a matrix indicates the probability log likelihood i? _T.

FIG. 9 is a block diagram illustrating a configuration of a communication model.

FIG. 10 is a diagram for explaining a trellis in a conventional encoding device, and for explaining the contents of probabilities α _t , β _t and γ _t .

FIG. 11 is a flowchart illustrating a series of steps in performing soft output decoding by applying a BCJR algorithm in a conventional decoding device.

FIG. 12 shows a conventional decoding device, in which Max-Log-
It is a flowchart explaining a series of processes at the time of performing soft output decoding by applying a BCJR algorithm.

FIG. 13 is a block diagram illustrating a configuration of a conventional encoding device.

14 is a diagram illustrating a trellis in the encoding device illustrated in FIG.

FIG. 15 is a diagram illustrating a matrix indicating a probability log likelihood Iγ _t in the case of the encoding device illustrated in FIG. 13;

FIG. 16 is a block diagram illustrating a configuration of a conventional decoding device, and is a block diagram illustrating a part for calculating probability log likelihoods Iα _t and Iγ _t .

FIG. 17 is a block diagram illustrating a configuration of a conventional decoding device, and is a block diagram illustrating a part for calculating probability log likelihoods Iβ _t and Iγ _t .

[Figure 18] A block diagram illustrating the configuration of a conventional decoding apparatus, is a block diagram showing a part for calculating a log soft-output Iλ _t.

[Explanation of symbols]

1 encoding device, 3 decoding device, 31, 35, 38
Arithmetic circuit, 33, 36 registers

 ────────────────────────────────────────────────── ─── Continued on the front page F term (reference) 5B001 AA10 AB02 AC01 AD06 AE02 5J065 AA01 AB01 AC02 AD10 AE06 AF03 AG05 AH02 AH04 AH05 AH06 AH09 AH15 AH21

Claims (20)

[Claims] 1. Probability of passing an arbitrary state based on a soft input value is obtained using natural logarithm to obtain a log likelihood probability, and decoding is performed using the probability log likelihood. A decoding device for performing an operation represented by the following general formula (1) and the following general formula (2) using at least a difference value of the probability log likelihood in each state as a variable: A decoding apparatus which calculates a logarithmic soft output in which a soft output at each time is represented by log likelihood using natural logarithm, using a result calculated by the calculation means. (Equation 1) (Equation 2) (However, A, B, A ₀ , A ₁ ,..., _An are variables, log is a natural logarithm based on the number e of Nepia, and ＄ is an operator.) 2. The arithmetic means performs an arithmetic operation represented by the general formula (1) and the general formula (2) with at least the probability log likelihood as a part of a variable. 2. The decoding apparatus according to claim 1, wherein a difference value of the probability log likelihood in each state is calculated as a function of the difference value of the probability log likelihood at the previous time using the result. 3. The decoding device according to claim 1, wherein said calculation means performs a calculation represented by the following general formula (3). (Equation 3) (Where A ₀ , A ₁ ,..., A _i ,..., _An are variables, sgn is the sign of the variable A _i , and f is This is a function represented by the general formula (4), and | A _i | is the absolute value of the variable A _i .) 4. A storage unit for storing a table indicating a relationship between the function f and the variable x, wherein the operation unit refers to the table stored in the storage unit and calculates the general expression (3). 4. The decoding device according to claim 3, wherein the operation is represented. 5. The arithmetic unit according to claim 1, wherein a relationship between the function f and the x is approximated by a linear approximation or a threshold approximation, and an operation represented by the general formula (3) is performed. 3. The decoding device according to 3. 6. A storage means for storing the variable A _i in a combination of a sign and an absolute value, wherein the arithmetic means comprises the variable A _i stored in the storage means.
_4. The decoding device according to claim 3, wherein the operation represented by the general formula (3) is performed using the sign and the absolute value of _i . 7. The difference value is a log-likelihood representation of a first probability from the coding start state to each state in chronological order for each of the received values, based on the prior probability information and the received values. A second probability that each state is returned from the censored state to the respective states in reverse chronological order, for each of the received values, based on the difference value between the values of the probability log likelihood in each state and the prior probability information and the received value. 2. The decoding apparatus according to claim 1, wherein the second probability is a difference value between values in each state of the second probability log likelihood expressed by log likelihood. 8. The decoding apparatus according to claim 1, wherein a state transition performs decoding of a trellis code represented by a state transition diagram. 9. The decoding device according to claim 8, wherein decoding of the convolutional code is performed. 10. The decoding device according to claim 9, wherein the encoded code is decoded by a cumulative adder that cumulatively adds and outputs the input data. 11. Probability of passing through an arbitrary state based on a received value that is a soft input is calculated using natural logarithm to obtain a probability log likelihood, and decoding is performed using the probability log likelihood. A decoding method for performing the calculation represented by the following general formula (5) and the following general formula (6) in which at least a difference value of the probability log likelihood in each state is a part of a variable: A decoding method characterized by calculating a log soft output in which a soft output at each time is represented by log likelihood using natural logarithm, using a result calculated in the calculation step. (Equation 5) (Equation 6) (However, A, B, A ₀ , A ₁ ,..., _An are variables, log is a natural logarithm based on the number e of Nepia, and ＄ is an operator.) 12. In the operation step, an operation represented by the general formulas (5) and (6) with at least the probability log likelihood as a part of a variable is performed. The difference value of the probability log likelihood in each state is calculated as a function of the difference value of the probability log likelihood at the previous time using the result obtained.
2. The decoding method according to 1. 13. In the calculation step, the following general formula (7)
The decoding method according to claim 11, wherein an operation represented by the following is performed. (Equation 7) (Where A ₀ , A ₁ ,..., A _i ,..., _An are variables, sgn is the sign of the variable A _i , and f is This is a function represented by the general formula (8), and | A _i | is the absolute value of the variable A _i .) 14. The method according to claim 1, wherein the calculating step refers to a table indicating a relationship between the function f and the variable x stored in a storage unit, and performs the calculation represented by the general formula (7). 14. The decoding method according to claim 13, wherein the decoding is performed. 15. The method according to claim 15, wherein in the calculating step, the relationship between the function f and the x is approximated by linear approximation or threshold approximation, and an operation represented by the general formula (7) is performed. 13. The decoding method according to item 13. 16. holds in the storage means the variable A _i in combination with sign and magnitude, in the calculating step, using the sign and the absolute value of the variable A _i held in the storage means 14. The decoding method according to claim 13, wherein an operation represented by the general formula (7) is performed. 17. The method according to claim 17, wherein the difference value is a log likelihood notation representing a first probability from the coding start state to each state in chronological order for each of the received values based on the prior probability information and the received values. 1 based on the difference value between the values of the probability log likelihood in each state, the prior probability information and the received value,
For each of the received values, a second probability obtained from the censored state to each state in the reverse order of the time series is expressed as a logarithmic likelihood, and is a difference value of a value in each state of the second probability log likelihood. The decoding method according to claim 11, wherein 18. The method according to claim 1, wherein the state transition performs decoding of a trellis code represented by a state transition diagram.
2. The decoding method according to 1. 19. The decoding method according to claim 18, wherein the decoding of the convolutional code is performed. 20. The decoding method according to claim 19, wherein the code output by cumulatively adding the input data is decoded.