DE102017216264B4 - Decoding method - Google Patents

Abstract

A method of decoding a data bit string û (i = 1, ..., k) in which a) a data signal y (r = 1, ..., n) is received, which is a single-parity check product Code (SPC-PC) signal; b) using an SPC-PC decoder having a plurality of local SPC decoders, wherein the local decoders are arranged in at least one level l, wherein when more than a level the local decoders of a first level (l = 1) are connected to the local decoders of a second level (l = 2) and whereby the local decoders of the last level allow the data bit sequence to be determined c) by the respective possibilities of the data bits û bis û∈ {0,1} P paths, each path p (p = 1, ..., P) having i-1 edges, each edge of a path p each having a data bit û (i '= 1, ..., i-1) d) where, for each of the existing paths p, the soft decisions are respectively determined by the local decoders for m (û = 0) and m (û = 1), Thus, each of the paths branches and thus 2P paths arise e) wherein in the calculation of the soft decisions mfor the i-th bit û all previous decisions, in particular of the respective local decoder are taken into account within the respective path p; f) being continued with the computation of the soft-decisions for the i + 1-th data bit û; g) where upon reaching the k-th data bit û the soft-decisions of the path p with the largest soft-decision value are taken as a decoded data bit sequence.

Description

The present invention relates to a method for decoding a data bit string, a transmission method using such a method for decoding a data bit string, and a transmission device for transmitting a data bit string.

In known methods, a data bit sequence u _i (i = 1,..., K) is first coded by an encoder into a codeword x _r (r = 1,..., N). The codeword coded in this way is transmitted to the receiver via a lossy channel. The receiver receives a data signal y _r , which is then decoded to û _i . If u _i = û _i for all i, the data bit sequence was received correctly.

Due to the lossy transmission channel, however, it is necessary that individual errors in the transmission by the decoder can be corrected. For this purpose, it is known to use a maxium likelihood method in which first soft decisions are calculated. In the case of soft-decision, the definition which is generally familiar to the person skilled in the art is a value which represents the reliability of the respective decision. In the maximum likelihood method, the soft decisions are then selected with the highest soft decision value or with the greatest reliability for the respective code word. The disadvantage of this is that the maximum likelihood method, in particular for longer codewords, that is to say for large values for n, becomes very computationally intensive and thus the decoding performance is reduced.

Especially for large block lengths or long codewords, the use of product codes (PC) is known in which the long codewords are distributed over several decoders by means of iterative decoding. When generating codewords by means of a PC, a generator matrix G = G ₁ (⊕G ₂ ⊕... G _{d is} used and the codewords are generated by means of x = uG, where G _l corresponds to the generator matrix of the I-th component of the product code. This increases the performance of the decoding process, but at the cost of increased complexity, and reduces the block error rate for these methods since individual local decoders are independent of each other.

COSKUN, M.C. [et al.]: Successful Cancellation Decoding of Single Parity-Check Product Codes, IEEE International Symposium on Information Theory, June 2017, p.1763-1767. IEEE Xplore [online]. DOI: 10.1109 / ISIT.2017.8006832. In: IEEE describes a decoding method for Single Parity-Check Product Codes, which is based on the successive stripping of unlikely bits.

The object of the present invention is to provide a decoding method which has a reduced computational complexity, a low block error rate or a high correction capability.

The object is achieved by the method of claim 1, the transmission method according to claim 8, the receiver according to claim 10 and the transmission device according to claim 11.

In the method according to the invention for decoding a data bit sequence û ₁ (i = 1,..., K), first of all a data signal y _r (r = 1,..., N) is received. The signal is a single parity check product code (SPC-PC) signal generated by a corresponding transmitter. In the method according to the invention, an SPC-PC decoder is used, which has a plurality of local PC decoders for decoding the product code codeword y _r . In this case, the local decoders are arranged in at least one level I and in particular a plurality of levels I, the local decoders of a first level (I = 1) being connected to the local decoder of a second level (1 = 2), corresponding to the structure of FIG used product codes. In this case, the data bit sequence û _{i is} determined by the local decoders of the last level. In particular, the SPC-PC decoder has n inputs in the first level and k outputs in the last level. The outputs of the local decoders of the first level are connected to the inputs of the local decoders of the second level, etc.

According to the invention, the respective bit possibilities 0 or 1 of the data bits û _i to û _i-1 ∈ {0,1} P paths are formed, each path having p (p = 1,..., P) i-1 edges and each of these edges of a given path p represents a data bit û _{i '} (i' = 1, ..., i-1), respectively. For example, the data bit û _{1 can have} the options 0 or 1. Thus, if complete, two paths would be present, with the first path (p = 1) representing û ₁ = 0 and the second path (p = 2) representing û ₁ = 1. For each additional data bit û _{i '} , each of these paths branches according to the possibilities {0,1}, so that a maximum of 2 ^(i-1) paths are available.

According to the invention, the soft decisions m _{i are} determined for each of the existing paths p by the local decoders for m _i (û _i = 0) and m _i (û _i = 1). Soft-decisions are the combination of the possible bit value 0 or 1 and a reliability value or soft-decision value, which gives a starting point for the probability of the respective bit value. For example, if m _i (û _i = 0) = -∞, there is a high probability that û _i = 1. Due to the soft-decisions, each of the existing paths p will branch to give 2P paths. In this case, all previous decisions within the respective path p are taken into account in the calculation of the soft-decisions m _i for the i-th bit û _i . In particular, the previous decisions of the respective local decoder are taken into account. Alternatively, the previous decisions regarding the data bits û ₁ to û _i-1 within the respective path p are taken into account. Then continue with the calculation of the soft-decisions for the i + 1-th data bit û _{i + 1} . This results in a corresponding soft decision for each edge of the paths p. When the kth data bit û _k is reached, the soft decision of the path p with the highest soft decision value, ie the greatest reliability, is taken as the decoded data bit sequence û _i . As a result, on the one hand, an improved decoding performance is achieved in comparison to iterative decoding. At the same time, due to the initial determination of soft decisions, the previous decisions in the decoding process are taken into account. This increases the correction capability for erroneously transmitted bits in the data signal y _r and reduces the block error rate.

Preferably, a value L> 1 is set. In the event that the number of existing paths becomes P> L, the paths p are selected which have the largest soft decision value, ie the highest reliability. Then, so many paths are discarded until P ≤ L. Thus, the number of paths to be considered is reduced to L, especially after each decoding of another data bit û _i . If the soft-decisions have been determined for the data bit û _i , it is then checked whether P ≦ L is still satisfied. Otherwise, a corresponding number of paths with a low soft-decision value are discarded.

wobei 1 ≤ I ≤ d und d die Dimension des PC angibt. Dabei ist n_i' die Blocklänge der lokalen Decoder auf dem Level i'.The number η _{1 of} the local decoders preferably results at the level I $${\eta }_l={\displaystyle \underset{i\text{'}=1}{\overset{l-1}{\Pi }}\left(n_{i\text{'}}-1\right){\displaystyle \underset{i\text{'}=l+1}{\overset{d}{\Pi }}{n}_{i\text{'}}.}}$$

where 1≤I≤d and d indicates the dimension of the PC. Where n _{i 'is} the block length of the local decoders at level i'.

Preferably, a Cyclic Redundancy Check (CRC) code is applied to the remaining possibilities after determining the soft-decision of the k-th data bit û _k . If more than one possible data bit sequence û _i then remains, the path with the largest soft decision values is selected from the remaining paths p.

Preferably, the Single Parity Check Product Code (SPC-PC) is a (k, n) -PC block code with k ≥ 4 and n ≥ 9. Preferably, k ≥ 64 and n ≥ 125. Particularly preferably, k ≥ 125 and n ≥ 216. Thus, even long-block length codes n can be efficiently processed and decoded.

$$\begin{array}{c}{m}_{\mathcal{l},j,i}^p\left(1\right)=P_{\mathcal{l},j,i}^p\left(1\right)+{\displaystyle \sum _{i\text{'}=1}^{i-1}{P}_{\mathcal{l},j,i\text{'}}^{\left(\mathcal{l}\right),p}\left({\lambda }_{\mathcal{l},j,i\text{'}}^p\right)}\\ +\underset{c_{i+1},\dots c_{n_{\mathcal{l}}}}{{\displaystyle \text{max}}}*\left[1\left({\lambda }_{\mathcal{l},j\mathrm{,1}}^p\oplus \cdots \oplus {\lambda }_{\mathcal{l},j,i-1}^p\oplus 1\oplus c_{i+1}\oplus \cdots \oplus c_{n_{\mathcal{l}}}=0\right){\displaystyle \sum _{i\text{'}=i+1}^{n_{\mathcal{l}}}{P}_{\mathcal{l},j,i\text{'}}^p\left(c_{i\text{'}}\right)}\right]\end{array}$$

für den jeweiligen Pfad p, wobei I den Level des lokalen Decoders j bezeichnet und P^P _l,_j,_l' die ermittelten Soft-Decision-Werte bzw. Zuverlässigkeitswerte der vorhergehenden Entscheidungen. λ entspricht dabei den vorgehenden Entscheidungen und c_i+1, ..., c_nl ∈ {0,1} werden dabei so gewählt, dass ein Codewort entsteht, insbesondere mit einem Maximalwert für die Soft-Decision. Dabei ist n_l die Blocklänge des j-ten lokalen Decoders im Level l. Somit ist eine komplette Vorschrift für die Soft-Decisions gegeben, wobei die vorhergehenden Entscheidungen λ berücksichtigt werden. Somit wird für jede vorhandene Möglichkeit der Datenbitfolge û_i bzw. für die L-zuverlässigsten Varianten entsprechend dem jeweiligen Pfad die Zuverlässigkeitswerte des i-ten Datenbits û_i ermittelt.Preferably, the soft-decision m _{i is} calculated $$\begin{array}{c}{m}_{\mathcal{l}.j.i}^p\left(0\right)=P_{\mathcal{l}.j.i}^p\left(0\right)+{\displaystyle \underset{i\text{'}=1}{\overset{i-1}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left({\lambda }_{\mathcal{l}.j.i\text{'}}^p\right)}\\ +\underset{c_{i+1}....c_{n_{\mathcal{l}}}}{{\displaystyle \text{Max}}}*\left[1\left({\lambda }_{\mathcal{l}.j\mathrm{,1}}^p\oplus \cdots \oplus {\lambda }_{\mathcal{l}.j.i-1}^p\oplus 0\oplus c_{i+1}\oplus \cdots \oplus c_{n_{\mathcal{l}}}=0\right){\displaystyle \underset{i\text{'}=i+1}{\overset{n_{\mathcal{l}}}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left(c_{i\text{'}}\right)}\right]\end{array}$$

$$\begin{array}{c}{m}_{\mathcal{l}.j.i}^p\left(1\right)=P_{\mathcal{l}.j.i}^p\left(1\right)+{\displaystyle \underset{i\text{'}=1}{\overset{i-1}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^{\left(\mathcal{l}\right).p}\left({\lambda }_{\mathcal{l}.j.i\text{'}}^p\right)}\\ +\underset{c_{i+1}....c_{n_{\mathcal{l}}}}{{\displaystyle \text{Max}}}*\left[1\left({\lambda }_{\mathcal{l}.j\mathrm{,1}}^p\oplus \cdots \oplus {\lambda }_{\mathcal{l}.j.i-1}^p\oplus 1\oplus c_{i+1}\oplus \cdots \oplus c_{n_{\mathcal{l}}}=0\right){\displaystyle \underset{i\text{'}=i+1}{\overset{n_{\mathcal{l}}}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left(c_{i\text{'}}\right)}\right]\end{array}$$

for the respective path p, where I denotes the level of the local decoder j and P ^P _l , _j , _{l '} the determined soft decision values or reliability values of the previous decisions. λ corresponds to the preceding decisions and c _{i + 1} , ..., c _nl ∈ {0,1} are chosen so that a codeword arises, in particular with a maximum value for the soft decision. Where n _{l is} the block length of the j th local decoder in level l. Thus, a complete rule for the soft decisions is given taking into account the previous decisions λ. Thus, for each available possibility of the data bit sequence û _i or for the L-most reliable variants corresponding to the respective path, the reliability values of the i-th data bit û _{i are} determined.

The forwarding of the determined soft decisions from a local decoder j in the level I to the next local decoder j 'in the levels 1 + 1 is preferably carried out by the forwarding of m ^P _{l, j, l} (0) to P ^P l ₊₁ , _{j '} , _l' (0) and for the second possibility for the data bit _i with m ^P _{l, j, l} (1) to P ^P l _{+ 1, j '} , _l' (1).

Furthermore, the invention relates to a transmission method with a transmitter, wherein the transmitter a data bit sequence u = u ₁ , ..., u _k encoded by means of a SPC-PC code in the code word x = x ₁ , ..., x _n . In this case, to code the code word x the generator matrix G = G ₁ ⊕ G ₂ ⊕ ... ⊕ G _d by means of x = uG, where G _{l of} the generator matrix of the I-th component of the product code corresponds and d the dimension of the PC.

In the transmission method according to the invention, the code word x is then transmitted via a transmission channel. This is in particular a disturbed transmission channel or a lossy transmission channel. In particular, it is a binary input discrete memoryless transmission channel (B-DMC). The codeword x is disturbed by the transmission channel, so that a disturbed codeword y = y ₁ ,..., Y _{n is} received by the receiver. If the transmission channel were a lossless ideal channel, the undisturbed codeword y would correspond to the transmitted codeword x.

In the inventive transmission method, the received codeword y is decoded according to the method described above for decoding a data bit string û = û ₁ , ..., û _k , so that û is determined which corresponds to the original data bit sequence u in the case of error-free decoding.

Preferably, before the generation of the code word x, a CRC encoder is initially provided for generating a co-transmitted CRC checksum.

Furthermore, the present invention relates to a receiver for receiving and decoding a data bit sequence u with a receiving device for receiving a data signal y = y ₁ , ..., y _n and a decoder. In this case, the decoder is designed to carry out the method for decoding a data bit sequence û = û ₁ , ..., û _k , as described above.

Furthermore, the present invention relates to a transmission device with a transmitter, wherein the transmitter has a data source and an encoder. In this case, the encoder is designed to encode a data bit sequence u of the data data source by means of a SPC-PC code in a codeword x. Furthermore, the transmission device has a transmission channel. In particular, this is a binary input discrete memoryless transmission channel (B-DMC). Furthermore, the transmission device has a receiver, wherein a disturbed code word y is received by the receiver. In this case, the receiver is designed as described above.

Preferably, a CRC encoder is provided between the data source and the encoder for generating a CRC checksum, which is sent by the transmitter. Furthermore, the receiver has a CRC decoder for checking the decoded data bit sequence.

Preferably, the transmission channel is a radio link or a wired connection or an optical data transmission.

The invention will be explained in more detail below with reference to a preferred embodiment with reference to the accompanying drawings.

• 1 einen Decodiergraph für einen beispielhaft gewählten (9, 4) SPC-PC,
• 2 den Decodiergraph der 1 mit Eingangswerten,
• 3 (a) bis 3 (e): Entscheidungsschritte des Decodierverfahrens gemäß dem Decodiergraph der 1,
• 4 den Decodiergraph der 1, bei der Entscheidung des dritten Bits,
• 5 eine schematische Darstellung der Berücksichtigung der vorhergehenden Entscheidungen für einen ausgewählten lokalen Decoder und
• 6 eine Ausführungsform des erfindungsgemäßen Übertragungsverfahrens.

Show it:

• 1 a decoding graph for an exemplarily chosen (9, 4) SPC-PC,
• 2 the decoding graph of 1 with input values,
• 3 (a) to 3 (e) : Decision steps of the decoding method according to the decoding graph of 1 .
• 4 the decoding graph of 1 in deciding the third bit,
• 5 a schematic representation of the consideration of the previous decisions for a selected local decoder and
• 6 an embodiment of the transfer method according to the invention.

1 shows a Tanner graph for the decoding method according to the invention for decoding a data bit sequence û _i (i = 1, ..., k) using the example of a (n = 9, k = 4) single parity check product code (SPC -PC). The in 1 illustrated SPC-PC decoder has nine inputs, get over the nine bits of the received codeword y _r (r = 1, ..., 9) in the SPC-PC decoder. In the decoder graph of 1 are marked with "=" variable nodes, whereas "+" indicate check nodes. The SPC-PC decoder has a first level 10 as well as a second level 12 on. In the first level 10 are three local SPC-PC decoders 14 whose inputs receive the corresponding bits of the transmitted codeword y _i . The outputs of the local decoder 14 the first level 10 are with inputs from local decoders 16 the second level 12 connected. By the local decoder 16 the second level 12 the transmitted data bits û ₁ to û ₄ can be determined. The structure of in 1 shown SPC-PC decoder depends on the underlying PC structure or the generator matrix used G.

By the individual local decoder 14 . 16 no final decision is made about the respective data bit û _i , but only soft-decisions m _i for the two possible values 0 and 1 of the respective data bit û _i .

$$P_{\mathrm{1,}\text{j}\text{,i}}^1\left(1\right)\triangleq \text{ln}\left[W\left(y\left(j-1\right)n_1+i|1\right)\right]$$

According to 2 the received data signal y _{r is} defined by the SPC-PC decoder as log likelihoods P ^P _{l, j, i} (0) with respect to a possible 0 and P ^P _{l, j, i} (1) with respect to a possible 1, where p indicates the particular path, I denotes the corresponding level, where l = 1 for the first level, and j denotes the respective local level I decoder. This results in the log likelihoods $$P_{}^{}$$$${}_{\mathrm{1,}\text{j}.\text{i}}^1\left(0\right)\triangleq \text{ln}\left[W\left(y\left(j-1\right){\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102017216264B4\_0014.png,DE102017216264B4\_0015.png"\; state="\{\{state\}\}">n</figure-callout>}}_1+i|0\right)\right]$$

$${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="DE102017216264B4\_0014.png,DE102017216264B4\_0015.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{1,}\text{j}\text{i}}^1\left(1\right)\triangleq \text{ln}\left[W\left(y\left(j-1\right){\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102017216264B4\_0014.png,DE102017216264B4\_0015.png"\; state="\{\{state\}\}">n</figure-callout>}}_1+i|1\right)\right]$$

$$\begin{array}{c}{m}_{\mathcal{l},j,i}^p\left(1\right)=P_{\mathcal{l},j,i}^p\left(1\right)+{\displaystyle \sum _{i\text{'}=1}^{i-1}{P}_{\mathcal{l},j,i\text{'}}^{\left(\mathcal{l}\right)p}\left({\lambda }_{\mathcal{l},j,i\text{'}}^p\right)}\\ +\underset{c_{i+1},\dots c_{n_{\mathcal{l}}}}{{\displaystyle \text{max}}}*\left[1\left({\lambda }_{\mathcal{l},j\mathrm{,1}}^p\oplus \cdots \oplus {\lambda }_{\mathcal{l},j,i-1}^p\oplus 1\oplus c_{i+1}\oplus \cdots \oplus c_{n_{\mathcal{l}}}=0\right){\displaystyle \sum _{i\text{'}=i+1}^{n_{\mathcal{l}}}{P}_{\mathcal{l},j,i\text{'}}^p\left(c_{i\text{'}}\right)}\right]\end{array}$$

wobei P den jeweiligen Pfad bezeichnet, I den Level des lokalen Decoders j, λ den bisherigen Entscheidungen entspricht und c_l+1, ..., c_nl ∈ {0,1} mit n_l der Blocklänge des lokalen Decoders j im Level l. Dabei berechnet sich max* gemäß $$\begin{array}{l}\text{max*}\left(x_i\right)=\text{max*}\left(x\mathrm{1,}\dots ,xn\right)=\text{ln}\left(e^{x_1}+\cdots +e^{x_n}\right)\\ X_1,\dots ,x_{\text{n}}\end{array}$$

Then the soft-decisions for the first data bit û _{1 are} calculated according to $$\begin{array}{c}{m}_{\mathcal{l}.j.i}^p\left(0\right)=P_{\mathcal{l}.j.i}^p\left(0\right)+{\displaystyle \underset{i\text{'}=1}{\overset{i-1}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left({\lambda }_{\mathcal{l}.j.i\text{'}}^p\right)}\\ +\underset{c_{i+1}....c_{n_{\mathcal{l}}}}{{\displaystyle \text{Max}}}*\left[1\left({\lambda }_{\mathcal{l}.j\mathrm{,1}}^p\oplus \cdots \oplus {\lambda }_{\mathcal{l}.j.i-1}^p\oplus 0\oplus c_{i+1}\oplus \cdots \oplus c_{n_{\mathcal{l}}}=0\right){\displaystyle \underset{i\text{'}=i+1}{\overset{n_{\mathcal{l}}}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left(c_{i\text{'}}\right)}\right]\end{array}$$

$$\begin{array}{c}{m}_{\mathcal{l}.j.i}^p\left(1\right)=P_{\mathcal{l}.j.i}^p\left(1\right)+{\displaystyle \underset{i\text{'}=1}{\overset{i-1}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^{\left(\mathcal{l}\right)p}\left({\lambda }_{\mathcal{l}.j.i\text{'}}^p\right)}\\ +\underset{c_{i+1}....c_{n_{\mathcal{l}}}}{{\displaystyle \text{Max}}}*\left[1\left({\lambda }_{\mathcal{l}.j\mathrm{,1}}^p\oplus \cdots \oplus {\lambda }_{\mathcal{l}.j.i-1}^p\oplus 1\oplus c_{i+1}\oplus \cdots \oplus c_{n_{\mathcal{l}}}=0\right){\displaystyle \underset{i\text{'}=i+1}{\overset{n_{\mathcal{l}}}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left(c_{i\text{'}}\right)}\right]\end{array}$$

where P denotes the respective path, I the level of the local decoder j, λ corresponds to the previous decisions and c _{l + 1} , ..., c _nl ∈ {0,1} with n _{l of} the block length of the local decoder j in the level l , Hereby max * is calculated according to $$\begin{array}{l}\text{Max*}\left(x_i\right)=\text{Max*}\left(x\mathrm{1,}....xn\right)=\text{ln}\left(e^{x_1}+\cdots +e^{x_n}\right)\\ {\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="DE102017216264B4\_0014.png,DE102017216264B4\_0015.png"\; state="\{\{state\}\}">X</figure-callout>}}_1.....x_{\text{n}}\end{array}$$

Thus, according to 3 (a) two possibilities 0 and 1 with the calculated soft-decisions m _i (0) and m _i (1), where there is a path for each possibility and thus P = 2.

Then according to 3 (b) continued with the decoding of the second data bit û ₂ . For each of the existing paths p, both options for the data bit û _{2 are} taken into account and the corresponding soft-decisions are determined, resulting in four paths. When determining the soft-decisions for û ₂ , the previous decisions λ, which led to the first data bit û ₁ , are taken into account.

4 shows an example of the situation when deciding the third data bit û ₃ . The decisions concerning the first data bits û ₁ and û ₂ are made from left to right in the decoding graph of the 4 is returned and taken into account by the local decoders as λ ^P _{l, j, z} , z = 1, ..., i-1 for the respective path p. The soft decisions for the third data bit û ₃ are thus determined from the previous decisions, with the soft decisions of the first level m ^P _{1, j, i being} input to the local decoders of the second level, wherein $$P_{\mathcal{l}+\mathrm{1,}j\text{'}.i\text{'}}^p\left(0\right)\leftarrow m_{\mathcal{l}.j.i}^p\left(0\right)\text{and}{P}_{\mathcal{l}+\mathrm{1,}j\text{'}.i\text{'}}^p\left(1\right)\leftarrow m_{\mathcal{l}.j.i}^p\left(1\right),$$

According to the 3 (c) Thus, for each additional possibility, another path is created, so that after the determination of the soft-decisions for û _{3 there are} eight paths, each path having exactly three edges. Assuming that a parameter L = 4 is chosen, now the number of paths P exceeds the selected parameters, so that P> L. Then, according to the embodiment of the method described, the paths having the highest reliability are selected and so on many paths with low reliability or lower soft-decision value are deleted until P ≤ L. This is in 3 (d) shown, where only due to the choice of L = 4 exactly four paths are left. This ensures that, in particular for large block lengths, unnecessary, because unlikely, combinations of the data bits û _{i are} still taken into account.

In a further step according to the 3 (e) the last data bit û _{4 is} determined by determining the respective soft-decisions for the possible values of û ₄ with 0 or 1. Thus, each path branches again, so that in turn eight paths arise. Again, the previous decisions are taken into account.

This is exemplary for the general case for a selected local decoder in the 5 represented, in which the previous decisions λ ^P _l , _j , ₁ , ... λ ^P _{l, j, i-1 are} taken into account as well as the corresponding log likelihood values, which flow from the right side. Then, for the j-th local decoder, at the I-th level for the pth path, the soft decisions m ^P _{l, j, l} (0) and m ^P _{l, j, i} (1) for the possible values 0 and 1 determined.
In a first alternative, after determining all soft decisions, for each of the data bits û ₁ to û _4, the path with the highest soft decision value or the highest reliability is selected. Alternatively, as in 6 is shown between the information source 18 and the SPC-PC encoder 10 . 20 a CRC (cyclic redundancy check) encoder 22 is provided, which generates a CRC check number, which in the codeword by the SPC-PC encoder 20 embedded and over the transmission channel 24 is transferred. Through the SPC-PC decoder 26 Then, as described above, the data bits û _{i are} decoded which contain the CRC checksum. The resulting possible paths are then in a CRC decoder 28 based on the transmit CRC checksum to verify their integrity, so that out through the decoder 26 determined possible paths of the one who passes the CRC test. Tunes the checksum for several of the possible paths through the decoder 26 were determined, then the one with the highest soft-decision value or the highest reliability is selected and considered as a transmitted signal or to be transmitted data bit sequence u. Thus, in this variant, on the one hand, the fault-tolerant decoding method is implemented by means of soft-decision, wherein even large block lengths due to the use of the product code can be taken into account. Furthermore, further errors can be avoided by the downstream use of a CRC decoder. Thus, a decoding method is provided with a high performance and a low block error rate or a high correction capability.

Claims (13)

Method for decoding a data bit sequence û _i (i = 1, ..., k), in which a) a data signal y _r (r = 1,..., N) is received, which is a single-parity Check Product Code (SPC-PC) signal trades; b) using an SPC-PC decoder having a plurality of local SPC decoders, wherein the local decoders are arranged in at least one level l i, wherein providing more than one level the local decoders of a first level (l = 1) are connected to the local decoders of a second level (l = 2) and wherein the data bit sequence û _i can be determined by the local decoders of the last level; c) are formed by the respective possibilities of the data bits û ₁ to û _i-1 ∈ {0,1} P paths, each path p (p = 1,..., P) having i-1 edges, each edge a path p represents a data bit û _{i '} (i' = 1, ..., i-1); d) where, for each of the existing paths p, the soft decisions m _i are respectively determined by the local decoders for m _i (û _l = 0) and m _i (û _i = 1), thus each of the paths branches and thus 2P Paths arise; e) wherein in the calculation of the soft-decisions m _i for the i-th bit û _i all previous decisions, in particular of the respective local decoder, are taken into account within the respective path p; f) proceeding with the calculation of the soft-decisions for the i + 1-th data bit û _{i + 1} ; g) when the k-th data bit û _{k is reached,} the soft-decisions of the path p with the largest soft-decision value are taken as the decoded data bit sequence û _i . Method according to Claim 1 in which a value L> 1 is set and, in the case that the number of existing paths P> L, the paths p are selected with the largest soft-decision value, with so many paths discarded until P ≤ L , Method according to Claim 1 or 2 in which the number η _{1 of} the local decoders at level I results $${\eta }_l={\displaystyle \underset{i\text{'}=1}{\overset{l-1}{\Pi }}\left(n_{i\text{'}}-1\right)}{\displaystyle \underset{i=l+1}{\overset{d}{\Pi }}{n}_{i\text{'}}}$$

where 1 ≤ I ≤ d, where d indicates the dimension of the PC and n _{i '} indicates the block length of the local decoder at the level i'. Method according to one of Claims 1 to 3 in which a Cyclic Redundancy Check (CRC) code is applied to the remaining possibilities after determining the soft-decions of the k-th data bit û _k and subsequently selecting the path with the largest soft-decision value from the remaining paths , Method according to one of Claims 1 to 4 , which is a (k, n) -PC block code, where k≥4 and n≥9. Method according to one of Claims 1 to 5 in which the soft-decisions m _i calculate to $$\begin{array}{c}1m_{\mathcal{l}.j.i}^p\left(0\right)=P_{\mathcal{l}.j.i}^p\left(0\right)+{\displaystyle \underset{i\text{'}=1}{\overset{i-1}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left({\lambda }_{\mathcal{l}.j.i\text{'}}^p\right)}\\ +\underset{c_{i+1}....c_{n_{\mathcal{l}}}}{{\displaystyle \text{Max}}}*\left[1\left({\lambda }_{\mathcal{l}.j\mathrm{,1}}^p\oplus \cdots \oplus {\lambda }_{\mathcal{l}.j.i-1}^p\oplus 0\oplus c_{i+1}\oplus \cdots \oplus c_{n_{\mathcal{l}}}=0\right){\displaystyle \underset{i\text{'}=i+1}{\overset{n_{\mathcal{l}}}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left(c_{i\text{'}}\right)}\right]\end{array}$$

$$\begin{array}{c}{m}_{\mathcal{l}.j.i}^p\left(1\right)=P_{\mathcal{l}.j.i}^p\left(0\right)+{\displaystyle \underset{i\text{'}=1}{\overset{i-1}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^{\left(\mathcal{l}\right)p}\left({\lambda }_{\mathcal{l}.j.i\text{'}}^p\right)}\\ +\underset{c_{i+1}....c_{n_{\mathcal{l}}}}{{\displaystyle \text{Max}}}*\left[1\left({\lambda }_{\mathcal{l}.j\mathrm{,1}}^p\oplus \cdots \oplus {\lambda }_{\mathcal{l}.j.i-1}^p\oplus 1\oplus c_{i+1}\oplus \cdots \oplus c_{n_{\mathcal{l}}}=0\right){\displaystyle \underset{i\text{'}=i+1}{\overset{n_{\mathcal{l}}}{\Sigma }}{P}_{\mathcal{l}.j.i\text{'}}^p\left(c_{i\text{'}}\right)}\right]\end{array}$$

for the path p, where l denotes the level of the local decoder j, P ^P _{l, j, i '} corresponds to the determined soft decision values of the previous decisions, λ corresponds to the previous decisions, and c _{i + 1} , ..., c _nl ∈ {0,1} are chosen such that a codeword arises with nl of the block length of the jth local decoder in the level l. Method according to Claim 6 in which the forwarding of the ascertained soft decisions from one local decoder j to the next local decoder j 'is effected by m ^P _{1, j, i} (0) → P ^P _{l + 1, j', i '} (0), and m ^P _{l, j, i} (1) → P ^P _{l + 1, j ', i'} (1). Transmission method with a transmitter, wherein the transmitter is a data bit sequence u coded by means of a SPC-PC code in a codeword x, the codeword x is transmitted via a transmission channel and a disturbed codeword y is received by a receiver, wherein an undisturbed codeword y the sent Code word x, wherein the received codeword is decoded by the receiver according to the method of one of Claims 1 to 7 so that û is determined which corresponds to the original data bit sequence u in error-free decoding. Transmission procedure according to Claim 8 in which, prior to the generation of the code word x, a CRC encoder is initially provided for generating a co-transmitted CRC checksum. A receiver for receiving and decoding a data bit sequence u, comprising a receiving device for receiving a data signal and a decoder, wherein the decoder is designed to carry out the method according to one of Claims 1 to 7 , Transmission device comprising a transmitter, the transmitter having a data source and an encoder, the encoder being adapted to code a data bit sequence u of the data source by means of an SPC-PC code into a codeword x, a transmission channel and a receiver, wherein a disturbed one Codeword y is received by the receiver, wherein the receiver is formed according to a receiver Claim 10 , Transfer device after Claim 11 in which a CRC encoder is provided between the data source and the encoder for generating a CRC checksum and the receiver has a CRC decoder for checking the decoded data bit sequence. Transfer device after Claim 11 or 12 , wherein the transmission channel is a radio link or a wired connection or an optical data transmission.

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