JPH08251144A - Method and device for generating reliability information - Google Patents

Abstract

PURPOSE: To optimize a method for calculating the reliability information in a communication system improved in the performance of RS decoding by obtaining reliability information of each symbol through the use of a convolution code as an internal code and an RS(read Solomon) as an external code. CONSTITUTION: A symbol defined at the point of a time (k) by a maximum likelihood path 1SV is set to be Uk ,sv . An opposing path merging to the maximum likelihood path 1SV at the points of times k+1 to k+3 is set to be 1k+1 to 1k+3 and a logarithmic maximum likelihood rates at a merging place is set to be Δk+1 to Δk+3 . Then, the set Φk of lower subscripts (j) satisfying the condition of (Uk ,j ≠Uk ,sv ) are obtained and a minimum is selected from among the logarithmic maximum likelihood rates Δj (but (j) belongs to the set Φk ) as reliability information.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a reliability information generating method and a reliability information generating apparatus suitable for use in signal transmission in symbol units.

[0002]

2. Description of the Related Art A transmission method using a concatenated code composed of a convolutional code as an inner code and a Reed-Solomon code (or another symbol correction code) as an outer code is known. One example is shown in FIG. In the figure, 1 is an RS (Reed-Solomon) encoder, which converts an input digital signal into a Reed-Solomon code in symbol units. Reference numeral 2 denotes a convolutional encoder, which performs a convolutional operation on this Reed-Solomon code and outputs it via the transmission path 3.

Reference numeral 4 is a convolutional decoder using the Viterbi algorithm ^* (" ^* " refer to the remarks column), which decodes the code data supplied through the transmission line 3 into a Reed-Solomon code and also reads the code data. Generate reliability information ^* for each symbol of the Solomon code. An RS decoder 5 restores the original digital signal based on the decoded Reed-Solomon code and the reliability information. As described above, it is known that when the reliability information for each symbol is obtained in the convolutional decoder 4 and is supplied to the RS decoder 5, the error correction capability in the RS decoder 5 can be improved. Such a technique is disclosed in the following documents, for example.

(1) Genneauer and Heher "Viterbi algorithm for outputting soft decision information and its application"
(J. Hagenauer and P. Hoeher, "A Viterbi Algorithm wi
th Soft-Decision Outputs and its Applications "), I
EEE GCOM, No.47.1.1, 1989. (2) Masayoshi Ohashi, Yutaka Yasuda "Decoding Algorithms for Convolutional Codes that Minimize Bit Error Rate and Its Evaluation", IEICE Technical Report IT89-88 PP.35-40 , 1989. (3) Hajime Tanaka, "Reliability of most-likelihood-decoded codewords and its application to decoding concatenated codes" IEICE Transactions A V
ol. J75-A No.9 pp.1503-1508. (4) Honda, Kubota, Kato “FEC Supplement to Dual Soft Decision for Mobile Satellite Communication Systems” (S.Honda, S.Kubot
a and S.Kato, "DSD (Double Soft Decision) Concatena
ted FEC Scheme in Mobile Satellite Communication S
ystem "), IEEE, J. Select. Areas Commun., Vol.10, N
o.8, Oct. 1992.

In the process of executing the Viterbi algorithm in the convolutional decoder 4, the maximum likelihood path is merged with another path (hereinafter referred to as a counter path) at each time point in each bit period. Then, the reliability information for each bit is obtained from the difference between the path metrics of the merged paths. conventionally,
The “reliability information for each symbol” has been obtained by summing the reliability information for each bit that constitutes each symbol.
In this specification, likelihood (metric) and reliability information are represented by logarithms.

[0006]

However, according to the studies made by the present inventors, it is doubtful that the reliability information of a symbol is obtained from the sum of reliability information for each bit for the following reason. That is, the reliability information of the symbol should be considered for the symbol as a whole. Although the total sum of reliability information for each bit is recognized to have a certain degree of correlation with the reliability of the symbol, if such total is used as the reliability information of the symbol, an appropriate result may not be obtained in some cases.

For example, it is assumed that "1 symbol" is composed of "2 bits" and the decoding result of the symbol of the maximum likelihood path is "00". In this case, in the conventional case, symbols (“11”, “01”) different from the maximum likelihood path are used.
And “10”), only the branch metrics corresponding to the bits different from the symbol of the maximum likelihood path (all bits of “11”, lower bits of “01” and upper bits of “10”) are the reliability information of the symbol. Will be involved in.

However, if information is transmitted on a symbol-by-symbol basis, a symbol in which some of the bits are different from those of the maximum likelihood path should be considered as "information completely different from the symbols of the maximum likelihood path". If this is the case, accurate reliability information will not be obtained unless the branch metrics related to the high-order bits of "01" and the low-order bits of "10" are involved in the reliability information.

The present invention has been made in view of the above circumstances, and an object thereof is to provide a reliability information generating method and a reliability information generating device capable of generating appropriate reliability information.

[0010]

In order to solve the above-mentioned problems, the method according to claim 1 is based on an input signal,
The maximum likelihood path is selected from the paths that the decoding result of this input signal may follow, and the decoding result within a predetermined period consisting of a plurality of branches among the paths other than the above maximum likelihood path is decoded by the maximum likelihood path. The reliability of the decoding result in the predetermined period is obtained based on the result different from the result and the maximum likelihood path.

Further, according to the method of claim 2, the maximum likelihood path is selected from the paths in which the decoding result of the input signal may follow, based on the input signal, and the path other than the maximum likelihood path is selected. Of the decoding results in the predetermined period based on the maximum likelihood path and the one that is not merged with the maximum likelihood path within a predetermined period composed of a plurality of branches among the paths and is merged with the maximum likelihood path after the predetermined period has elapsed. It is characterized by obtaining reliability.

Further, according to the method of claim 3, a maximum likelihood path is selected based on the input signal from the paths which may be followed by the decoding result of the input signal, and the maximum likelihood path other than the maximum likelihood path is selected. If the decoding result is different from the decoding result in the maximum likelihood path and is not merged with the maximum likelihood path within a predetermined period consisting of a plurality of branches of the path and is merged with the maximum likelihood path after the predetermined period has elapsed, The reliability of the decoding result in the predetermined period is obtained based on the likelihood path.

According to a fourth aspect of the present invention, in the reliability information generating method according to the third aspect, the decoding result in the predetermined period constitutes a symbol having a fixed number of bits.

Further, according to the method of claim 5, in the reliability information generating method of claim 3, the reliability is the maximum likelihood path within the predetermined period among paths other than the maximum likelihood path. Is merged with the maximum likelihood path after the lapse of the predetermined period without being merged with the maximum likelihood path, and the decoding result is different from the decoding result in the maximum likelihood path, and a log-likelihood ratio of the maximum likelihood path.

Further, according to the method of claim 6, in the reliability information generating method of claim 5, there are a plurality of logarithmic likelihood ratios, and the smallest one is selected as the reliability. Characterize.

Further, according to the configuration of claim 7, a maximum likelihood path selecting means for selecting the maximum likelihood path from the paths that the decoding result of the input signal may follow based on the input signal, A decoding result in a predetermined period including a plurality of branches of paths other than the maximum likelihood path is different from the decoding result in the maximum likelihood path, and the reliability of the decoding result in the predetermined period based on the maximum likelihood path. And a calculation means for obtaining

Further, according to the structure of claim 8, a maximum likelihood path selecting means for selecting a maximum likelihood path based on the input signal from paths which may be followed by the decoding result of the input signal, Based on the maximum likelihood path and the one that is not merged with the maximum likelihood path within a predetermined period of a plurality of branches other than the maximum likelihood path and is merged with the maximum likelihood path after the predetermined period has elapsed, And a calculation means for obtaining the reliability of the decoding result in a predetermined period.

[0018]

According to the structure of claims 1 and 7, among the paths other than the maximum likelihood path, the decoding result in a predetermined period consisting of a plurality of branches is different from the decoding result in the maximum likelihood path, and the maximum likelihood path. The reliability of the decoding result in the predetermined period is calculated based on

Further, in the configurations according to claims 2 and 8, the maximum likelihood path is not merged with the maximum likelihood path within a predetermined period of a plurality of branches other than the maximum likelihood path, and the maximum likelihood path is passed after the predetermined period. The reliability of the decoding result in the predetermined period is obtained based on what is merged with the path and the maximum likelihood path.

Further, in the methods according to claims 3 to 6, the maximum likelihood path is not merged with the maximum likelihood path within a predetermined period of a plurality of branches other than the maximum likelihood path and the maximum likelihood path is not merged. The reliability of the decoding result in the predetermined period is calculated based on the maximum likelihood path and the decoding result different from the decoding result in the maximum likelihood path while merging with the path.

[0021]

【Example】

A. Configuration and Operation of Embodiment One embodiment of the present invention will be described below. The physical configuration of this embodiment is similar to that of the conventional one (FIG. 1), but this embodiment is different from the conventional one in the process of generating reliability information in symbol units. The details will be described with reference to FIG.

FIG. 2 is a "four-state" trellis diagram used when executing the Viterbi algorithm in the convolutional decoder 4, in which the maximum likelihood path l _SV is indicated by a solid line. Also, the counter paths l _{k + 1} , l _{k + 2,} and l _{k + 3} to be merged with the maximum likelihood path l _SV at time points k + 1, k + 2, and k + 3 are indicated by broken lines. At the time of merging, the result (log likelihood ratio) obtained by subtracting the path metric of the counter path from the path metric of the maximum likelihood path l _SV is Δ _{k + 1} , Δ _{k + 2} , Δ.
_{Set to k + 3} .

The decoded bits in each branch forming each path are displayed in the form of "u _{i, j} ". Here, i is a time point (..., k-2, k-1, k, k + 1, k + 2, ...
..) and j is the path (l _SV , l
_{k + 1} , lk _{+ 2} or lk _{+ 3} ) is the subscript. Further, as shown in the figure, the decoded bits of each pass constitute "1 symbol" for every "2 bits", and the time i of the pass l _j
The value of the symbol in −2 to _i is “U _{i, j} ”.

Hereinafter, the symbol U in the maximum likelihood path
_An algorithm for obtaining _{k, sv} (decoding result) and its reliability information will be described. First, the symbol U _{k, sv} is the decoded bit u
_Since it is only a set consisting of _{k-1, sv} and u _{k, sv} , if the maximum likelihood path l _SV within the time points k-2 to k is determined, it can be immediately obtained. When the decoding result of the symbol U _{k, sv} is obtained, the convolutional decoder 4 supplies the content to the RS decoder 5. At this time, the counter paths l _{k + 1 to} l _{k + 3} have not been determined, but there is no particular problem.

After that, when the code data is sequentially supplied through the transmission path 3, the maximum likelihood path l _SV is determined in the time axis direction. Then, when the maximum likelihood path l _SV is determined for each symbol, the content thereof is supplied to the RS decoder 5 as described above. Here, when the maximum likelihood path l _SV is determined up to the time point k + 3, the counter path l _{k + 1} ~ corresponding to the symbol U _{k, sv}
l _{k + 3} is determined, and the log-likelihood ratios Δ _{k + 1} , Δ _{k + 2} , and Δ _{k + 3} are also determined. That is, all the information displayed in FIG. 2 can be obtained.

Next, in the convolutional decoder 4, "U
_{k, j} ≠ U _{k, sv} ”, the set of subscripts j (hereinafter,
The set Ф _k ) is required. As an example, the symbols U _{k, k + 1} and U _{k, k + 3} (indicated by thick broken lines in FIG. 2) are different from the symbols U _{k, sv,} and the symbols U _{k, k + 2} and U Assuming that _{k and sv} are equal, the elements of the set Φ _k are “k + 1” and “k + 3”.

Next, the logarithmic likelihood ratio Δ _j (where j is the set Φ _k
Belonging to the RS decoder 5 is supplied as the reliability information of the symbol U _{k, sv} . That is, in the above example, the log likelihood ratio Δ
_The smaller of _{k + 1} and Δk _{+ 3} is the reliability information.

B. Effects of the Embodiment As described above, in this embodiment, reliability information is selected from the log-likelihood ratio Δ _{j in which j} belongs to the set Φ _k . That is, only symbols having a value different from the symbol of the maximum likelihood path l _SV are candidates for reliability information. Also, the reliability information of the symbol U _{k, sv} is obtained based on the log-likelihood ratio after the time point k. In other words, the reliability information is obtained for each symbol, not based on the reliability information of each decoded bit.

C. Modifications The present invention is not limited to the above-described embodiments, and various modifications are possible as follows, for example. In the above embodiment, an example in which the "4 state" trellis diagram and the "2 bit" symbol are used has been described, but generally, the "n state" trellis diagram and "m bit" are used.
Even when the symbol is used, appropriate reliability information can be obtained in the same manner as the above operation.

Further, in the above embodiment, the reliability information is obtained by the difference (log likelihood ratio) of the path metrics of the two merged paths. However, the reliability information may be obtained based on both path metrics. For example, the reliability information may be obtained by another method.

In the above embodiment, "the decoding result in the predetermined period consisting of a plurality of branches other than the maximum likelihood path is different from the decoding result in the maximum likelihood path,
"Determining the reliability of the decoding result in the predetermined period based on the maximum likelihood path", and "without merging with the maximum likelihood path within a predetermined period including a plurality of branches of paths other than the maximum likelihood path" After the lapse of a predetermined period, it will be merged with the maximum likelihood path,
“Determining the reliability of the decoding result in the predetermined period based on the maximum likelihood path”. However, it is not necessary to execute both of these, and if either one is executed,
Within the range, the above-mentioned effects can be exhibited.

D. Experimental Results First, FIG. 3 shows the results of performance comparison between the present example and the conventional example according to the literature (1). The figure shows the distribution of error probabilities when Reed-Solomon codes in units of "8 bits" are transmitted by "40 symbols". The horizontal axis of the figure shows the reliability rankings of symbols (“1” to “40”), and the higher the ranking, the lower the reliability. The vertical axis represents the error probability. The transmission parameter is “fading pitch f _D T =
2.0 × 10 ₋₃ ”,“ signal-to-interference power ratio Eb / I ₀ =
2.75 dB (after inner code decoding) ". According to the present embodiment, the errors tend to be biased toward the symbol with the highest rank (lowest reliability), and the error probabilities in other ranks tend to decrease. From this fact, this embodiment is obviously advantageous over the conventional example.

Next, FIG. 4 shows the result of comparing the error rates after RS decoding between the conventional example in which hard decision is made and this example. Here, RS (40, 3) is used as the outer code.
0) was used and the number of disappearances was set to “4”. In this case, R
The error correctable number of S (40, 30) is “3”. In the figure, for reference, the inner code (convolutional code) is used.
Only the characteristics and the limit characteristics of erasure error correction are shown.

This marginal characteristic is calculated when the reliability is ideally calculated and "the reliability of all erroneous symbols does not exceed the minimum value of the reliability of non-erroneous symbols". It is a decoding characteristic. According to this embodiment, it is clear that the average error rate is reduced, and the required Eb / I ₀ satisfying “average bit error rate 10 ⁻⁶ ” can be set to about “4.0 dB”.

E. Remark E-1. Viterbi Algorithm It is assumed that the convolutional encoder 2 of FIG. 1 is configured as shown in FIG. In the figure, 101 and 102 are D flip-flops, and 103 to 105 are OR circuits. When the contents “D ₁ D ₂ ” of the D flip-flops 101 and 102 are the internal states of the circuit and the input / output signals are expressed as “S _i / S _o1 S _o2 ”, the state transition diagram of the convolutional encoder 2 is It becomes like FIG.

Next, consider the time point τ (τ = 0, 1, 2, ...) At each bit period of the input signal S _i , and at τ = 0, D
It is assumed that the flip-flops 101 and 102 are reset. As shown in FIG. 7, the subsequent state transition can be represented by a diagram with the vertical axis representing the state and the horizontal axis representing the time.
This diagram is called a trellis diagram. In the figure, the solid line is S _i
= 0 and the broken line shows the state transition when S _i = 1. The line segment that connects the states at each time point is called a "branch", and the one that connects the branches in the time axis direction is called a "path". In the figure, the values of the output signals S _o1 and S _o2 are added to each branch.

These output signals S _o1 and S _o2 are modulated by some method and then output through the transmission line 3.
Here, if BPSK modulation is used as the modulation method, logical values "0" and "1" are code data "-1" and "+".
However, the code data received by the convolutional decoder 4 is, for example, “−0”. It becomes a value such as .8, -0.7 ".

In the convolutional decoder 4, the same trellis diagram as shown in FIG. 7 is prepared, and the likelihood (branch metric) indicating the “probability” of each branch is based on the received code data. ) Is calculated. Various methods of calculating the likelihood are known according to the transmission method and the transmission characteristics. The simplest method is to find the "square of the distance on the number line" between the received code data and the code data on the trellis diagram, and then sum the results and express the natural logarithm as a negative value. be able to.

In FIG. 7, there are two branches from τ = 0 to τ = 1. Here, when the code data “−0.8, −0.7” described above is supplied, the likelihoods of both branches are obtained. First, the likelihood of the branch of the solid line is “-In (0.2 ² +0.3 ² )”, and the likelihood of the branch of the broken line is “-In (1.8 ² +1.7 ² )”. The likelihood is high. That is, the original output signal S _o1 ,
S _o2 is “0, 0” (the output code data is “−1, −
It is most probable to think of it as 1 ").

Thereafter, the likelihood of each branch is obtained in the same manner. And the likelihood of each path (path metric)
Is represented by the sum of the branch metrics of the branches forming each path. D flip-flops 101, 1
If the period after 02 is reset until it is reset again is “n times” the bit period, there are “2 ⁿ ” paths in the trellis diagram. Of these paths, the path with the highest likelihood is called the “maximum likelihood path”. That is, the decoded sequence along the maximum likelihood path is most likely.

Next, a method of sequentially (partially) finding the maximum likelihood path in the decoding process will be described. In FIG. 8, paths A and B on the trellis diagram are assumed. Paths A and B have τ = 0
It matches at j, branches at τ = j, and matches again after τ = k (this is called “merging”). Note that j may be “0”. Since all paths start from “time 0, state 00”, the two merged paths always have the time j at which they were branched. If the likelihood of the path A is high when comparing the likelihoods of the paths A and B only during the period of τ = j to k, the path B
Can never be the maximum likelihood path. Therefore, the path B can be excluded from the maximum likelihood path candidates.

When the paths that cannot be the maximum likelihood paths are excluded in this way, the trellis diagram shown in FIG. 7 is transformed as shown in FIG. 9, for example. The maximum likelihood path candidates are “4” when viewed at τ = 3, which matches the number of states (4) in the trellis diagram. At τ = 4, the path is branched into “8” again, but each candidate is merged with any other candidate.
Therefore, in each state of τ = 4, “1” is added, and “4” in total is excluded from the candidates. Eventually, the “4” maximum likelihood path candidates will extend to the right in the figure.

Eventually, the "4" candidates will match at an early point (left part of the trellis diagram). Since the part where all candidates match is a part of the maximum likelihood path, the decoded sequence of that part may be output as the decoding result.
The above is the outline of the Viterbi algorithm.

E-2. Likelihood and reliability Likelihood (metric) and reliability (reliability) are quantities that represent "likelihood". However, the likelihood is a quantity determined by the relationship between the decoded sequence of one path (or branch) and the input code data, while the reliability is merged with one path and another path. In this case, it is the amount determined by the mutual relationship between the two.

[0045]

As described above, claims 1, 3 to 7 are as follows.
According to the described configuration, a decoding result in a predetermined period including a plurality of branches of paths other than the maximum likelihood path is different from the decoding result in the maximum likelihood path, and in the predetermined period based on the maximum likelihood path. The reliability of the decoding result is obtained. Further, according to the configurations of claims 2 to 6, the reliability is not merged with the maximum likelihood path within a predetermined period of a plurality of branches other than the maximum likelihood path. The reliability of the decoding result in the predetermined period is obtained based on what is merged with the maximum likelihood path after the lapse of the predetermined period and the maximum likelihood path. As a result, it is possible to obtain appropriate reliability information regardless of the configuration.

[Brief description of drawings]

FIG. 1 is a block diagram showing configurations of a conventional example and an example.

FIG. 2 is a diagram illustrating the operation of the embodiment.

FIG. 3 is a characteristic comparison diagram of a conventional example and an example.

FIG. 4 is a characteristic comparison diagram of another conventional example and one example.

FIG. 5 is an explanatory diagram of a Viterbi algorithm.

FIG. 6 is an explanatory diagram of a Viterbi algorithm.

FIG. 7 is an explanatory diagram of a Viterbi algorithm.

FIG. 8 is an explanatory diagram of a Viterbi algorithm.

FIG. 9 is an explanatory diagram of a Viterbi algorithm.

[Explanation of symbols]

 4 Convolutional decoder (maximum likelihood path selection means, calculation means)

Claims (8)

[Claims] 1. A maximum likelihood path is selected from paths that may be followed by a decoding result of the input signal based on the input signal, and a predetermined period including a plurality of branches among paths other than the maximum likelihood path. The reliability information generation method is characterized in that the reliability of the decoding result in the predetermined period is obtained based on the decoding result in the maximum likelihood path different from the decoding result in the maximum likelihood path. 2. A maximum likelihood path is selected from paths that may be followed by a decoding result of the input signal based on the input signal, and a predetermined period including a plurality of branches among paths other than the maximum likelihood path. The reliability characterized in that the reliability of the decoding result in the predetermined period is obtained based on the maximum likelihood path and the maximum likelihood path that is not merged with the maximum likelihood path after the predetermined period has elapsed. Degree information generation method. 3. A maximum likelihood path is selected from paths that may be followed by a decoding result of the input signal based on the input signal, and a predetermined period including a plurality of branches among paths other than the maximum likelihood path. That the decoding result is different from the decoding result in the maximum likelihood path while being merged with the maximum likelihood path after the predetermined period without merging with the maximum likelihood path, and in the predetermined period based on the maximum likelihood path. A reliability information generation method characterized by obtaining reliability of a decoding result. 4. The reliability information generating method according to claim 3, wherein the decoding result in the predetermined period constitutes a symbol having a fixed number of bits. 5. The reliability does not merge with the maximum likelihood path within the predetermined period out of the paths other than the maximum likelihood path, merges with the maximum likelihood path after the predetermined period, and the decoding result is the maximum. 4. The reliability information generation method according to claim 3, wherein the logarithmic likelihood ratio between the maximum likelihood path and the one different from the decoding result in the likelihood path is used. 6. The reliability information generating method according to claim 5, wherein there are a plurality of log likelihood ratios, and the smallest one is selected as the reliability. 7. A maximum likelihood path selecting means for selecting a maximum likelihood path from paths that a decoding result of the input signal may follow based on the input signal, and a plurality of paths other than the maximum likelihood path. A branching result of a decoding result in a predetermined period different from the decoding result in the maximum likelihood path, and an arithmetic means for obtaining the reliability of the decoding result in the predetermined period based on the maximum likelihood path. A characteristic reliability information generation device. 8. A maximum likelihood path selecting means for selecting a maximum likelihood path from paths that may be followed by a decoding result of the input signal based on the input signal, and a plurality of paths other than the maximum likelihood path. Of the decoding result in the predetermined period based on the maximum likelihood path and the one that is not merged with the maximum likelihood path within a predetermined period consisting of A reliability information generating apparatus, comprising: a computing means.