CN101369817B - Interpretation method and apparatus for tail-biting convolutional code - Google Patents

Abstract

Embodiment of the present invention discloses a decoding method and apparatus for tail-biting convolution code. The method includes the steps of implementing Viterbi decode to a sequence obtained by repeating a transmission block end-to-end for multiple times, wherein after decoding each transmission block of the sequence, judging whether meeting output condition based on a maximum path obtained by the decode; when meeting output condition, outputting decode data of the sequence using the maximum path as backtracking path. In the embodiment of the invention, judging the Viterbi decode of a long sequence obtained by linking a plurality of transmission blocks based on the head end status of the maximum path, when meeting presetting output condition, a decode data can be obtained directly without calculating all transmission blocks, thus it is able to obtain right decode output using less transmission blocks, and computational complexity and decode time delay are all saved.

Description

The interpretation method of tail-biting convolutional code and device

Technical field

The present invention relates to communication technical field, relate in particular to a kind of interpretation method and device of tail-biting convolutional code.

Background technology

Having proposed the code modulation mode of tail-biting convolutional code in the prior art, is that example describes with the tail-biting convolutional code of using in LTE (Long TermEvolution, the Long Term Evolution) system, and (3,1,6) encoder as shown in Figure 1.

The constraint length of encoder is 7, and code check is 1/3.Generator polynomial G among Fig. 1 _iThe binary sequence of (i=0,1,2) represents to import the connection status of data and 6 shift registers and the output of encoder i road.Binary Zero is represented not connect, and binary one is represented to connect.Adder is carried out in GF (2) territory among Fig. 1.The shift register initial condition is last 6 bits of input bit sequence, makes η ₀, η ₁, η ₂..., η ₅Represent this 6 shift registers successively.The input bit sequence of chnnel coding is designated as c ₀, c ₁, c ₂, c ₃..., c _K-1, bit sequence length is K.I road output bit sequence behind the coding is designated as

Wherein D is a sequence length, D=K for tail-biting convolutional code.η is arranged when initial condition _i=c _(K-1-i)(i=0,1 ... initial condition when 5), the state of shift register is with the coding beginning when the input bit EOS like this is identical.

The decoding of tail-biting convolutional code is based on Viterbi decoding algorithm (Viterbi Algorithm).Introduce the Viterbi decoding algorithm of convolution code below earlier.

Suppose that encoder for convolution codes once imports a Bit data.If the state set of encoder is S={s ₁, s ₂..., s _N, N is total status number, and N=2 is arranged ^M, wherein M is the number of shift register in the encoder, shift register is designated as η ₀, η ₁, η ₂..., η _M-1If C={c ₀, c ₁, c ₂, c ₃..., c _K-1Be the coding list entries, wherein K is a sequence length.Bit c _k(value 0 or 1) moment t=k send into encoder (k=0,1 ..., K-1), time delay is 1 in the encoder, so constantly at t=k+1, and bit c _kCoding finish and bit c _K+1Enter encoder.c _kCoding be output as

Wherein R is the inverse of convolution code code check.The output sequence of encoder is designated as:

$D=\{d_0^{\left(1\right)},d_0^{\left(2\right)},\·\·\·,d_0^{\left(R\right)},d_1^{\left(1\right)},\·\·\·,d_{K-1}^{\left(1\right)},d_{K-1}^{\left(2\right)},\·\·\·,d_{K-1}^{\left(R\right)}\}.$

Through the transmitting sequence after the mapping 0 →-1,1 → 1 is (emitted energy is 1):

$E=\{e_0^{\left(1\right)},e_0^{\left(2\right)},\·\·\·,e_0^{\left(R\right)},e_1^{\left(1\right)},\·\·\·,e_{K-1}^{\left(1\right)},e_{K-1}^{\left(2\right)},\·\·\·,e_{K-1}^{\left(R\right)}\}.$

The data sequence that receives behind its process AWGN (Additive White Gaussian Noise, additive white Gaussian noise) channel is

$Y=\{y_0^{\left(1\right)},y_0^{\left(2\right)},\·\·\·,y_0^{\left(R\right)},y_1^{\left(1\right)},\·\·\·,y_{K-1}^{\left(1\right)},y_{K-1}^{\left(2\right)},\·\·\·,y_{K-1}^{\left(R\right)}\}.$

And satisfy: $y_k^{\left(i\right)}=e_k^{\left(i\right)}+n_k^{\left(i\right)},$ Wherein

Be independent noise, meeting the expectation is that 0 variance is σ ²Real Gaussian Profile.

Output is according to the decoding of ML (Maximum Likelihood, maximum likelihood) criterion, i.e. Maximum likelihood sequence $\hat{C}=\arg \underset{C\∈\mathrm{\Ω}}{\max }\ln \mathrm{Pr\Σ}\mathrm{\μ}\left(Y\right|C)$ Be decoding output.The set that Ω forms for all code words.Suppose that channel is memoryless, then:

$\ln \mathrm{Pr}\left(Y\right|C)=\underset{i,k}{\mathrm{\Σ}}\ln \mathrm{Pr}\left(y_k^{\left(i\right)}\right|e_k^{\left(i\right)}).---\left(1\right)$

Definition lnPr (Y|C) is the path metric of C for list entries, ${\mathrm{\μ}}_k\left(C\right)=\underset{i=1}{\overset{R}{\mathrm{\Σ}}}\ln \mathrm{Pr}\left(y_k^{\left(i\right)}\right|e_k^{\left(i\right)})$ Be path metric.Probability density function according to noise

$p\left(y_k^{\left(i\right)}\right|e_k^{\left(i\right)})=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}\exp [-\frac{1}{2{\mathrm{\σ}}^2}{|y_k^{\left(i\right)}-e_k^{\left(i\right)}|}^2],$

Omit the public keys in path, path metric can be reduced to:

${\mathrm{\μ}}_k\left(C\right)=\underset{i=1}{\overset{R}{\mathrm{\Σ}}}{y}_k^{\left(i\right)}{e}_k^{\left(i\right)}.---\left(2\right)$

Then ML decoding is output as $\hat{C}=\arg \underset{C\∈\mathrm{\Ω}}{\max }\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}{\mathrm{\μ}}_k\left(C\right).$

The general maximum-likelihood decoding that adopts viterbi algorithm to realize convolution code.Compose initial cumulative path metrics value at moment t=0 for each state, if initial condition is uncertain, then the accumulative total path metric value of each state of initial time equates.Have only two branch roads to point to the equal state s of t=k+1 constantly at moment t=k _n, the cumulative metric that the cumulative metric of this two paths equals the previous moment state adds current branch metric.At t=k+1 constantly to pointing to s _nThese two paths compare, choose path metric the greater as survivor path, its metric is as new state s constantly _nCumulative path metrics.Adding of Viterbi decoding algorithm than selecting process as shown in Figure 2.Until the last moment, choose the maximum as recall path to the survivor path of each state this moment as time passes.And then obtain decoding output.

For tail-biting convolutional code,, can utilize this characteristic to improve performance when therefore deciphering because known first and last moment coder state is identical.If a corresponding reception data block that TB is Block (transmission block) because encoder first and last state is identical, therefore can receives data block with one and repeat L time, decipher long sequence the back of promptly connecting.

Be example with L=3 in the existing interpretation method, three data blocks all are used to calculate survivor path during decoding, only will recall when recalling at last the path corresponding to the data of second data block as decoding output.First TB Block can regard as second TB Block provides correct initial condition, and the 3rd TB Block can regard as second TB Block the correct state of recalling is provided.

The inventor is in realizing process of the present invention, find that there is following problem in implementation of the prior art: the Viterbi decoding algorithm decoding delay and the amount of calculation of existing tail-biting convolutional code are fixed, even it is fine to work as channel quality, just can produce decoding output after also must calculating L TB piece when receiving sequence makes a mistake seldom, and in fact may only just can obtain correct decoding output with less TB piece, therefore existing method has increased amount of calculation and decoding delay.

Summary of the invention

Embodiments of the invention provide a kind of interpretation method and device of tail-biting convolutional code, are used for reducing the time delay and the amount of calculation of the Viterbi decoding algorithm decoding of prior art tail-biting convolutional code.

Embodiments of the invention provide a kind of interpretation method of tail-biting convolutional code, comprising:

The long sequence that obtains that joins end to end after repeating repeatedly to same transmission block is carried out Viterbi decoding, and after each transmission block decoding finished in the described long sequence, the head and the tail state that obtains maximum path according to described decoding was identical, then judges and satisfies output condition;

Judge when satisfying output condition that the maximum path that described head and the tail state is identical is as recalling the path, recall the path and obtain the decoding data of described long sequence and export according to described;

The maximum path that described decoding obtains is:

After the decoding end to each transmission block, obtain the survivor path that obtains in the process that described transmission block is deciphered, obtain survivor path conduct and described transmission block is deciphered the maximum path that obtains with maximum path tolerance.

Embodiments of the invention also provide a kind of code translator of tail-biting convolutional code, comprising:

Decoding unit, the long sequence that obtains that joins end to end after being used for repeating repeatedly to same transmission block is carried out Viterbi decoding;

Judging unit is used for if the head and the tail state that obtains maximum path according to described transmission block decoding is identical, then judges and satisfying output condition after described decoding unit is to each the transmission block decoding end of long sequence;

The decoding output unit is used for when described judgment unit judges satisfies output condition, and the maximum path that described head and the tail state is identical is as recalling the path, recalls the path and obtains the decoding data of described long sequence and export according to described;

Description of drawings

The maximum path that described decoding obtains is:

After the decoding end to each transmission block, obtain the survivor path that obtains in the process that described transmission block is deciphered, obtain survivor path conduct and described transmission block is deciphered the maximum path that obtains with maximum path tolerance.

Compared with prior art, embodiments of the invention have the following advantages:

The first and last state of the maximum path that decoding obtains according to transmission block, the Viterbi decoding situation that the continuous long sequence that obtains of a plurality of transmission blocks is carried out is judged, when satisfying default output condition, needn't all calculate to finish to all transmission blocks by the time and can directly obtain decoding data, therefore only promptly can obtain correct decoding output, save amount of calculation and decoding delay with less transmission block.

Fig. 1 is the schematic diagram of tail-biting convolutional code encoder in the prior art;

Fig. 2 is the adding than selecting the process schematic diagram of Viterbi decoding algorithm in the prior art;

Fig. 3 is the interpretation method flow chart of tail-biting convolutional code in the embodiments of the invention;

Fig. 4 is the SNR curve of the interpretation method of tail-biting convolutional code in the embodiments of the invention;

Fig. 5 is the BLER curve of the interpretation method of tail-biting convolutional code in the embodiments of the invention;

Fig. 6 is the structural representation of the code translator of tail-biting convolutional code in the embodiments of the invention;

Fig. 7 is another structural representation of the code translator of tail-biting convolutional code in the embodiments of the invention.

Embodiment

For above-mentioned purpose of the present invention, feature and advantage can be become apparent more, the present invention is further detailed explanation below in conjunction with the drawings and specific embodiments.

A kind of interpretation method of tail-biting convolutional code is provided in the embodiments of the invention, as shown in Figure 3, comprises:

Step s301, the sequence that obtains that joins end to end after repeating repeatedly to same transmission block are carried out Viterbi decoding, and after each transmission block decoding finished in the described sequence, the maximum path that obtains according to described decoding judged whether to satisfy output condition.

Step s302, judge when satisfying output condition, described maximum path as recalling the path, is obtained the decoding data of described long sequence.

In the embodiments of the invention, the first and last state of the maximum path that decoding obtains according to transmission block, the Viterbi decoding situation that the continuous long sequence that obtains of a plurality of transmission blocks is carried out is judged, when satisfying default output condition, needn't all calculate to finish to all transmission blocks by the time and can directly obtain decoding data, therefore only promptly can obtain correct decoding output, save amount of calculation and decoding delay with less transmission block.

Concrete, embodiments of the invention provide improving one's methods of three kinds of Viterbi decoding algorithms, below represent with Viterbi-a, Viterbi-b and Viterbi-c respectively, and every kind improved one's methods are described in detail.

For the decoding algorithm Viterbi-a in the embodiment of the invention: joining end to end after repeating repeatedly to same transmission block obtains long sequence, a plurality of transmission blocks in the long sequence are carried out Viterbi decoding successively, when the Viterbi decoding of first transmission block finishes, obtain the maximum path in the survivor path, if the first and last state of described maximum path is identical, then judges and satisfy output condition; And with the maximum path of described first transmission block as recalling the path, obtain the decoding data and the output of this sequence according to recalling the path, concrete: the decoding data of exporting the transmission block corresponding with this maximum path.

Concrete: as to obtain long sequence after L TB piece repeated to link to each other, long sequence is carried out Viterbi decipher.When the calculating for first TB piece finishes, in survivor path, seek maximum path, remember that this maximum path is

, suppose that first TB piece moment corresponding is t=0 to t=k, then if Identical at moment t=0 with the first and last state of moment t=k, then directly return

As recalling the path, this path is an optimal path, and then obtains decoding data.Otherwise carry out according to existing Viterbi algorithm fully, promptly after having calculated L TB piece, produce decoding output.

For the decoding algorithm Viterbi-b in the embodiment of the invention: joining end to end after repeating repeatedly to same transmission block obtains long sequence, a plurality of transmission blocks in the long sequence are carried out Viterbi decoding successively, the maximum path that obtains as if a transmission block decoding is identical corresponding to the first and last state of described transmission block, then judges and satisfies output condition; And the maximum path that described first and last state is identical is as recalling the path, according to recall the path obtain this sequence decoding data and output, concrete: this maximum path is identical corresponding to the first and last state of which transmission block, then exports the decoding data of this maximum path corresponding to this transmission block.

Concrete: obtain long sequence to joining end to end behind the same transmission block repetition L, long sequence is carried out Viterbi decoding.When the calculating for first TB piece finishes, in survivor path, seek maximum path, remember that this maximum path is

, suppose that first TB piece moment corresponding is t=0 to t=k, then if

Moment t=0 and constantly t=k the first and last state identical, then directly return

As recalling the path.Otherwise continue to calculate second TB piece, when second TB block end, seek the maximum path of this moment

Suppose that second TB piece moment corresponding is t=k to t=2k, then if

First and last state at moment t=k and t=2k constantly is identical, i.e. this maximum path

In first and last state corresponding to second TB piece identical, then return As recalling the path, and then obtain decoding data corresponding to second TB piece.Otherwise, continue to calculate the 3rd TB piece, until reaching L TB piece.If maximum path during last block end

First and last state corresponding to L TB piece is identical, then returns maximum path

As recalling the path, and then obtain decoding data corresponding to L TB piece.Otherwise, return optimal path

Corresponding to

The decoding data of individual TB piece.

For the decoding algorithm Viterbi-c in the embodiment of the invention: same transmission block repeated to join end to end behind the L obtains long sequence, a plurality of transmission blocks in the long sequence are carried out Viterbi decoding successively, the maximum path that obtains as if a transmission block decoding is identical corresponding to the first and last state of any transmission block, then judges and satisfies output condition; And the maximum path that described first and last state is identical is as recalling the path, according to recall the path obtain this sequence decoding data and output, concrete: this maximum path is identical corresponding to the first and last state of which transmission block, then exports the decoding data of this maximum path corresponding to this transmission block.

Concrete: obtain long sequence to joining end to end behind the same transmission block repetition L, long sequence is carried out Viterbi decoding.When the calculating for first TB piece finishes, in survivor path, seek maximum path, remember that this maximum path is

, suppose that first TB piece moment corresponding is t=0 to t=k, then if

Moment t=0 and constantly t=k the first and last state identical, then directly return

As recalling the path.Otherwise continue to calculate second TB piece, when second TB block end, seek the maximum path of this moment

Suppose that second TB piece moment corresponding is t=k to t=2k, then if First and last state at moment t=0 and moment t=k is identical or identical with the first and last state of moment t=2k at moment t=k, i.e. this maximum path In first and last state corresponding to first TB piece or second TB piece identical, then return

As recalling the path, and then obtain decoding data corresponding to first TB piece or second TB piece.Otherwise, continue to calculate the 3rd TB piece, until reaching L TB piece.If maximum path during last block end

Corresponding to l (l=1 ..., L) the first and last state of individual TB piece is identical, then returns maximum path

As recalling the path, and then obtain decoding data corresponding to l TB piece.Otherwise, return optimal path

Corresponding to

The decoding data of individual TB piece.

Among the decoding algorithm Viterbi-b in the foregoing description: right $P_{\max }^l(l=\mathrm{1,2},\·\·\·,L)$ When recalling, just relatively whether maximum path is identical corresponding to the first and last state of l TB piece.In decoding algorithm Viterbi-c, right $P_{\max }^l(l=\mathrm{1,2},\·\·\·,L)$ When recalling, relatively whether maximum path has identical situation corresponding to the first and last state of each TB piece of front l TB piece.If have, then return the decoding data of the identical TB piece of corresponding first and last state.If maximum path is all different corresponding to the first and last state of each TB piece during last block end, then return maximum path

Corresponding to The decoding data of individual TB piece.

Below provide awgn channel R=2 respectively, K=88, L=3 and R=3, K=88, three kinds of SNR (Signal Noise Ratio, signal to noise ratio) and BLER (error rate) performance curves that improve algorithm (corresponding successively Viterbi-a/b/c) under the L=3 situation described in the Viterbi algorithm of tail-biting convolutional code and the foregoing description.

As shown in Figure 4, for Viterbi (R=2, K=88, L=3), Viterbi_a (R=2, K=88, L=3), Viterbi_b (R=2, K=88, L=3) and Viterbi_c (R=2, K=88, L=3); And Viterbi (R=3, K=88, L=3), Viterbi_a (R=3, K=88, L=3), Viterbi_b (R=3, K=88, L=3) and Viterbi_c (R=3, K=88, SNR L=3) and BLER performance curve.As can be seen from Figure 4 and Figure 5, the improvement of three kinds in embodiment of the invention algorithm has identical decoding BER and BLER performance curve with original Viterbi algorithm.

As shown in Table 1 and Table 2, in the embodiment of the invention three kinds improve Viterbi algorithms (corresponding successively Viterbi-a/b/c) than original Viterbi algorithm " savings " length calculation amount comparative result of connecting.

The amount of calculation comparison of table 1.Viterbi algorithm and improvement algorithm (R=3, K=88, L=3)

The amount of calculation comparison of table 2.Viterbi algorithm and improvement algorithm (R=2, K=88, L=3)

Annotate: 100000 of simulation runs, original algorithm need 300000 series connection length calculation.Save percentage=saving amount of calculation/300000.

Can find out easily that by above data along with improving the increase that algorithm Viterbi-a/b/c recalls, the amount of calculation of saving also presents the trend that increases progressively.Regardless of encoder bit rate, the limiting value (200000) that various improvement algorithms can both very approaching saving amount of calculation during high SNR.When low code check (R=3), three kinds are improved algorithm and just can reduce decoding calculating about 50% when low SNR (0dB).When high code check (R=2), three kinds improve algorithm in the decoding that also can reduce about 50% during low SNR (2dB) calculate.Only need increase less resource because three kinds of improvement algorithms are compared original algorithm, it is appreciable therefore saving such amount of calculation.

Therefore, in the embodiments of the invention, the first and last state of the maximum path that decoding obtains according to transmission block, the Viterbi decoding situation that the continuous long sequence that obtains of a plurality of transmission blocks is carried out is judged, only promptly can obtain correct decoding output with less transmission block, when satisfying default output condition, needn't all calculate to finish to all transmission blocks by the time and can directly obtain decoding data, therefore save amount of calculation and decoding delay.

A kind of code translator of tail-biting convolutional code also is provided in the embodiments of the invention, as shown in Figure 6, comprises:

Decoding unit 10, the sequence that obtains that joins end to end after being used for repeating repeatedly to same transmission block is carried out Viterbi decoding;

Judging unit 20 is used for after each the transmission block decoding of 10 pairs of sequences of decoding unit finishes, and the maximum path that obtains according to described transmission block decoding judges whether to satisfy output condition;

Decoding output unit 30 is used for when output condition is satisfied in judging unit 20 judgements described maximum path as recalling the path, being exported the decoding data of described long sequence.

Concrete, as shown in Figure 7:

Described judging unit 20 comprises first judgment sub-unit 21, is used for obtaining the maximum path in the survivor path when the Viterbi decoding of first transmission block finishes, if the first and last state of described maximum path is identical, then judges and satisfies output condition;

Described decoding output unit 30 comprises the first decoding output subelement 31, is used for the maximum path of described first transmission block as recalling the path, obtains the decoding data of described sequence and exports according to recalling the path.

Or:

Described judging unit 20 comprises second judgment sub-unit 22, and it is identical corresponding to the first and last state of described transmission block to be used for deciphering the maximum path that obtains as if a transmission block, then judges and satisfies output condition;

Described decoding output unit 30 comprises the second decoding output subelement 32, is used for maximum path as recalling the path, recalls the path and obtains the decoding data of described sequence and export according to described.

Or

Described judging unit 20 comprises the 3rd judgment sub-unit 23, and it is identical corresponding to the first and last state of any transmission block to be used for deciphering the maximum path that obtains as if a transmission block, then judges and satisfies output condition;

Described decoding output unit 30 comprises the 3rd decoding output subelement 33, is used for the maximum path that described first and last state is identical as recalling the path, recalls the path and obtains the decoding data of described sequence and export according to described.

In addition, described decoding output unit 30 also is used for: after the continuous long sequence that obtains of 20 pairs of a plurality of transmission blocks of described judging unit is carried out Viterbi decoding, when not finding to satisfy output condition, return the decoding data of maximum path corresponding to the transmission block in centre in described a plurality of transmission blocks.

In the code translator of the tail-biting convolutional code of the embodiment of the invention, the first and last state of the maximum path that decoding obtains according to transmission block, the Viterbi decoding situation that the continuous long sequence that obtains of a plurality of transmission blocks is carried out is judged, when satisfying default output condition, needn't all calculate to finish to all transmission blocks by the time and can directly obtain decoding data, therefore only promptly can obtain correct decoding output, save amount of calculation and decoding delay with less transmission block.

Through the above description of the embodiments, those skilled in the art can be well understood to the present invention and can realize by the mode that software adds essential general hardware platform, can certainly pass through hardware, but the former is better execution mode under a lot of situation.Based on such understanding, the part that technical scheme of the present invention contributes to prior art in essence in other words can embody with the form of software product, this computer software product is stored in the storage medium, comprises that some instructions are used so that an equipment is carried out the described method of each embodiment of the present invention.

More than disclosed only be several specific embodiment of the present invention, still, the present invention is not limited thereto, any those skilled in the art can think variation all should fall into protection scope of the present invention.

Claims (4)

1. the interpretation method of a tail-biting convolutional code is characterized in that, comprising:

The long sequence that obtains that joins end to end after repeating repeatedly to same transmission block is carried out Viterbi decoding, and after each transmission block decoding finished in the described long sequence, the head and the tail state that obtains maximum path according to described decoding was identical, then satisfies output condition;

Judge when satisfying output condition that the maximum path that described head and the tail state is identical is as recalling the path, recall the path and obtain the decoding data of described long sequence and export according to described;

The maximum path that described decoding obtains is:

After the decoding end to each transmission block, obtain the survivor path that obtains in the process that described transmission block is deciphered, obtain survivor path conduct and described transmission block is deciphered the maximum path that obtains with maximum path tolerance.

2. the interpretation method of tail-biting convolutional code described in claim 1 is characterized in that, a plurality of transmission blocks are linked to each other after the long sequence obtain carries out Viterbi decoding, when output condition is not satisfied in discovery, also comprises:

Return the decoding data of maximum path corresponding to the transmission block in centre in described a plurality of transmission blocks.

3. the code translator of a tail-biting convolutional code is characterized in that, comprising:

Decoding unit, the long sequence that obtains that joins end to end after being used for repeating repeatedly to same transmission block is carried out Viterbi decoding;

Judging unit is used for if the head and the tail state that obtains maximum path according to described transmission block decoding is identical, then judges and satisfying output condition after described decoding unit is to each the transmission block decoding end of long sequence;

The decoding output unit is used for when described judgment unit judges satisfies output condition, and the maximum path that described head and the tail state is identical is as recalling the path, recalls the path and obtains the decoding data of described long sequence and export according to described;

The maximum path that described decoding obtains is:

After the decoding end to each transmission block, obtain the survivor path that obtains in the process that described transmission block is deciphered, obtain survivor path conduct and described transmission block is deciphered the maximum path that obtains with maximum path tolerance.

4. the code translator of tail-biting convolutional code described in claim 3, it is characterized in that: described decoding output unit also is used for: when described judging unit links to each other to a plurality of transmission blocks after the long sequence obtain carries out Viterbi decoding, when not finding to satisfy output condition, return the decoding data of maximum path corresponding to the transmission block in centre in described a plurality of transmission blocks.

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