DE102019200941B4 - Decoding method - Google Patents

Abstract

Method for decoding a data bit sequence û (i = 1, ..., k), in which a data signal encoded by means of a product code as a Reed-Muller subcode is received and a Reed-Muller decoder is used. The respective possibilities of the data bits ûbis û∈ {0, 1} P-paths are formed, each path p (p = 1, ..., P) having i-1 edges, each edge of a path p each having one Data bit û (i '= 1, ..., i-1) reproduces. For each of the existing paths p, soft decisions are determined by the decoder. Thus, each of the existing paths branches out so that 2P paths arise. When calculating the soft decisions m for the ith bit üi, all previous decisions within the respective path p are taken into account. This continues with the calculation of the soft decisions for the i + 1th data bit until the kth data bit is reached. The path p with the largest soft decision value is then accepted as the decoded data bit sequence.

Description

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

In known methods, a data bit sequence u _i (i = 1, ..., k) is first coded into a code word x _r (r = 1, ..., n) by an encoder. The codeword encoded 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 applies to all i, the data bit sequence was received correctly.

Due to the lossy transmission channel, however, it is necessary that individual errors during transmission can be corrected by the decoder. For this purpose, it is known to use a maximum likelihood method in which soft decisions are initially calculated. In the definition generally familiar to the person skilled in the art, the soft decision is a value that reflects 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 here is that the maximum likelihood method, in particular for longer code words, that is to say with large values for n, very quickly becomes computationally expensive and the decoding performance is thus reduced.

Dann wird die Generatormatrix G_RM(m,m) der m-ten Ordnung des Reed-Muller-Codes mit der Länge n = 2^m erzeugt mit $$G_{RM}\left(m,m\right)=G_2^{\otimes m},$$

wobei $"G_2^{\otimes m}"$

das Kronecker-Produkt m-ter Ordnung von G₂ bezeichnet. Bei der Erzeugung von Codewörtern mittels Reed-Muller-Code wird die Generatormatrix G r-ter Ordnung verwendet für einen Reed-Muller-Coder der Länge n=2^m, wobei G erzeugt wird aus G_RM, indem alle Reihen mit dem Hamming-Gewicht größer oder gleich 2^m-r. Sodann werden mittels x = uG die Codewörter erzeugt. Somit ergibt sich die Code-Dimension zu $k={\displaystyle {\sum }_{i=m-r}^m\left(\begin{array}{c}m\\ i\end{array}\right).}$

From the state of the Technik I. Reed, "A class of multiple-error-correcting codes and the decoding scheme," Transactions of the IRE Professional Group on Information Theory, vol. 4, no. 4, pp. 38-49, Sep. 1954 and DE Muller, "Application of boolean algebra to switching circuit design and to error detection," Transactions of the IRE Professional Group on Electronic Computers, vol. EC-3, no. 3, pp. 6-12, Sep. 1954 Reed-Muller codes are known. Here is $G_2\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right].$

Then the generator matrix G _RM (m, m) of the m-th order of the Reed-Muller code with the length n = 2 ^{m is} generated with $$G_{\mathrm{R.}\mathrm{M.}}\left(m,m\right)={\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="DE102019200941B4\_0021.png,DE102019200941B4\_0023.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\otimes m},$$

in which $"G_2^{\otimes m}"$

denotes the Kronecker product of the m-th order of G ₂ . When generating code words by means of Reed-Muller code, the generator matrix G r-th order is used for a Reed-Muller coder of length n = 2 ^m , where G is generated from G _RM by adding all rows with the Hamming weight greater than or equal to 2 ^mr . The code words are then generated using x = uG. Thus the code dimension arises too $k={\displaystyle {\sum }_{i=m-r}^m\left(\begin{array}{c}m\\ i\end{array}\right).}$

und

zwei binäre lineare Block-Codes mit den Parametern (n₁, k₁) und (n₂, k₂), dann ist ein PC gegeben mit den Parametern (n = n₁n₂, k=k₁k₂), wobei jedes Codewort ein n₂×n₁ Array bildet, wobei jede Reihe ein Codewort in und jede Spalte ein Codewort in darstellt. und werden als Komponenten-Codes bezeichnet. Die Generatormatrix des 2-dimensionalen PC wird dabei erzeugt durch das Kronecker-Produkt der Generatormatrizen der Komponenten-Codes selbst, so dass G = G₁ ⊗ G₂, mit G₁ und G₂ als Generatormatrizen von und . Dabei wird ein PC der Dimension d entsprechend gebildet mittels G = G₁ ⊗...⊗ G_d, wobei G_s die Gereatormatrix des s-ten Komponenten-Codes

bezeichnet.Furthermore, product codes (PC) are known from the prior art. Be

and

two binary linear block codes with the parameters (n ₁ , k ₁ ) and (n ₂ , k ₂ ), then a PC is given with the parameters (n = n ₁ n ₂ , k = k ₁ k ₂ ), where each code word forms an n ₂ × n ₁ array, each row representing a code word in and each column representing a code word in. and are called component codes. The generator matrix of the 2-dimensional PC is generated by the Kronecker product of the generator matrices of the component codes themselves, so that G = G ₁ ⊗ G ₂ , with G ₁ and G ₂ as generator matrices from and. A PC of dimension d is formed using G = G ₁ ⊗ ... ⊗ G _d , where G _{s is} the device matrix of the s-th component code

designated.

An iterative decoding method is usually used to decode the code words. The disadvantage of this, however, is that when the iterative coding method is used, no external check code, such as a CRC (cyclic redundancy check) code, can be used by means of which an improved decoding performance can be achieved.

WO 2018/113705 A1 discloses a polar encoder and a polar decoder, the decoder being designed as a Successive Cancellation List (SCL) decoder.

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

The object is achieved by the method of claim 1, the transmission method according to claim 4, the receiver according to claim 6 and the transmission device according to claim 7.

In the method according to the invention for decoding a data bit sequence û _i (i = 1, ..., k), a data signal y _r (r = 1, ..., n) is received, which is a product code (PC) acts, which is designed as a Reed-Muller subcode; then a Successive Cancellation List (SCL) decoder is used, the data bit sequence û ' _{i being able to} be determined by the decoder. According to the invention, the respective bit options 0 or 1 of the data bits û ' ₁ 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 particular path p a data bit û '_i' (i '= 1, ..., i-1) reproduces. For example, the data bit û ' _{1 can be} the possibilities 0 or 1 exhibit. Thus, if complete, there would be two paths, the first path (p = 1) representing û ' ₁ = 0 and the second path (p = 2) representing û' ₁ = 1. For each further data bit û '_i' , each of these paths branches according to the options {0,1}, so that a maximum of 2 ^(i-1) paths are present.

According to the invention, the soft decisions m _{i are} determined for each of the existing paths 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 as well as a reliability value or soft decision value, which indicates a starting point for the probability of the respective bit value. If, for example, m _i (û ' _i = 0) = -∞, there is a high probability that û' _i = 1. Since soft decisions are determined for both possibilities of û ' _i without one of these possibilities being rejected a priori becomes, each of the existing paths p branches, so that 2P paths arise. When calculating the soft decisions m _i for the i-th bit û ' _i, all previous decisions within the respective path p 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. The calculation of the soft decisions for the i + 1-th data bit û ' _{i + 1 is then continued} . A corresponding soft decision thus results for each edge of the paths p. When the k-th data bit û ' _k is reached, the soft decision of path p with the highest soft decision value, that is to say the greatest reliability, is then taken as the decoded data bit sequence û' _i = û _i . On the one hand, this results in an improved decoding performance compared to iterative decoding. At the same time, the previous decisions in the decoding process are taken into account on the basis of the determination of soft decisions initially made. This increases the ability to correct for incorrectly transmitted bits in the data signal y _r and reduces the block error rate. Thus, according to the invention, an SCL decoder is used for the PC.

A value L> 1 is preferably established. In the event that the number of existing paths becomes P> L, the paths p are selected which have the greatest soft decision value, that is to say the greatest reliability. Then as many paths are discarded until P ≤ L. The number of paths to be taken into account is thus reduced to L, in particular after each decoding of a further data bit û ' _i . If the soft decisions were determined for the data bit û ' _i , it is then checked whether P L is still met. Otherwise, a corresponding number of paths with a low soft decision value are rejected.

A cyclic redundancy check (CRC) code is preferably applied to the remaining options after the soft decision of the k-th data bit û _{k has been determined} . If more than one possible data bit sequence û _i then remains because more than one path represents a valid code word, then the path with the greatest soft decision values is selected from the remaining paths p.

The soft decisions are preferably calculated as follows I. Tal and A. Vardy, "List of decoding polar codes," IEEE Transactions of Information Theory, vol. 61, no. 5, pp. 2213-2226, May 2015 and E. Arikan, "Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels," IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051-3073, July 2009 known.

A complete rule for the soft decisions is thus given, taking the previous decisions λ into account. Thus, the reliability values of the i-th data bit û ' _{i are} determined for each existing possibility of the data bit sequence û' _i or for the most L-reliable variants according to the respective path.

According to the invention, the components of the product code used are a Reed-Muller subcode and / or an extended Hamming code and / or a single parity check code.

gewählt. Dann wird die Generatormatrix G_RM(m,m) der m-ten Ordnung des Reed-Muller-Codes mit der Länge n = 2^m erzeugt mit $$G_{RM}\left(m,m\right)=G_2^{\otimes m},$$

wobei $"G_2^{\otimes m}"$

das Kronecker-Produkt m-ter Ordnung von G₂ bezeichnet. Bei der Erzeugung von Codewörtern mittels Reed-Muller-Subcode wird die Generatormatrix G' r-ter Ordnung verwendet für einen Reed-Muller-Subcode der Länge n=2^m, wobei G' erzeugt wird aus G_RM, indem alle Reihen mit dem Hamming-Gewich t größer oder gleich 2^m-r ausgewählt werden. Somit ergibt sich die Code-Dimension zu $k={\displaystyle {\sum }_{i=m-r}^m\left(\begin{array}{c}m\\ i\end{array}\right).}$

Seien nun und Reed-Muller-Subcodes der Länge 2^m und 2ⁿ mit den Generatormatrizen G₁ und G₂ erzeugt wie vorstehend beschrieben, dann kann aus den Reed-Muller-Subcodes ein Product-Code (PC) erzeugt werden der Länge 2^m+n mit der Generatormatrix G = G₁ ⊕ G₂, wobei es sich dabei wiederum um einen Reed-Muller-Subcode handelt. Insbesondere ist dabei der Reed-Muller-Subcode ein Product-Code der Dimension d>2, so dass die Generatormatrix G erzeugt wird durch G = G₁ ⊕ G₂ ⊕ ... ⊕ G_d mit G₁ (i = 1,...,d) als Reed-Muller-Subcodes.Sodann werden mittels x = uG die Codewörter erzeugt.The invention also relates to a transmission method with a transmitter, the transmitter encoding a data bit sequence u = u ₁ , ..., u _k into the code word x = x ₁ , ..., x _n by means of a product code as Reed-Muller -Subcode. The generator matrix G by means of x = uG is used for coding the code word x. This is done $G_2\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$

elected. Then the generator matrix G _RM (m, m) of the m-th order of the Reed-Muller code with the length n = 2 ^{m is} generated with $$G_{\mathrm{R.}\mathrm{M.}}\left(m,m\right)=G_2^{\otimes m},$$

in which $"{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="DE102019200941B4\_0021.png,DE102019200941B4\_0023.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\otimes m}"$

denotes the Kronecker product of the m-th order of G ₂ . When generating code words by means of Reed-Muller subcodes, the generator matrix G 'r-th order is used for a Reed-Muller subcode of length n = 2 ^m , where G' is generated from G _RM by adding all rows with the Hamming -Weight t greater than or equal to 2 ^mr . Thus the code dimension arises too $k={\displaystyle {\sum }_{i=m-r}^m\left(\begin{array}{c}m\\ i\end{array}\right).}$

Let Reed-Muller subcodes of length 2 ^m and 2 ^{n be} generated with generator matrices G ₁ and G ₂ as described above, then a product code (PC) can be generated from the Reed-Muller subcodes with a length of 2 ^{m + n} with the generator matrix G = G ₁ ⊕ G ₂ , which in turn is a Reed-Muller subcode. In particular, the Reed-Muller subcode is a product code of dimension d> 2, so that the generator matrix G is generated by G = G ₁ ⊕ G ₂ ⊕ ... ⊕ G _d with G ₁ (i = 1 ,. .., d) as Reed-Muller subcodes. Then the code words are generated using x = uG.

In the transmission method according to the invention, the code word x is then transmitted over a transmission channel. This is particularly a disturbed transmission channel or a lossy transmission channel. In particular, it is a binary input discrete memoryless transmission channel (B-DMC). The code word x is disturbed by the transmission channel, so that the receiver receives a disturbed code word y = y ₁ , ..., y _n . If the transmission channel were a lossless ideal channel, the undisturbed code word y would correspond to the transmitted code word x.

In the transmission method according to the invention, the received code word y is decoded according to the method described above for decoding a data bit sequence û = û ₁ , ..., û _k , so that û is determined which corresponds to the original data bit sequence u with error-free decoding.

Before generating the code word x, a CRC encoder is preferably provided for generating a CRC checksum that is also transmitted.

The present invention also 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. The decoder is designed to carry out the method for decoding a data bit sequence û = û ₁ , ..., û _k , as described above.

The present invention also relates to a transmission device with a transmitter, the transmitter having a data source and an encoder. The encoder is designed to encode a data bit sequence u of the data data source using a product code as a Reed-Muller subcode into a code word x. The transmission device also has a transmission channel. In particular, it is a binary input discrete transmission channel (B-DMC) without memory. Furthermore, the transmission device has a receiver, a disturbed code word y being received by the receiver. The receiver is designed as described above.

A CRC encoder is preferably provided between the data source and the encoder for generating a CRC checksum which is also sent by the transmitter. The receiver also has a CRC decoder for checking the decoded data bit sequence.

The transmission channel is preferably a radio connection or a wired connection or an optical data transmission.

The invention is explained in more detail below on the basis of a preferred embodiment with reference to the accompanying drawings.

• 1 eine schematische Darstellung eines Encoders für einen Reed-Muller Subcode;
• 2 (a) bis 2 (d):
  • Entscheidungsschritte des Decodierverfahrens,
• 3 eine Ausführungsform des erfindungsgemäßen Übertragungsverfahrens.

Show it:

• 1 a schematic representation of an encoder for a Reed-Muller subcode;
• 2 (a) to 2 (d) :
  • Decision-making steps of the decoding process,
• 3 an embodiment of the transfer method according to the invention.

gewählt. Dann wird die Generatormatrix G_RM(m,m) der m-ten Ordnung des Reed-Muller-Codes mit der Länge n = 2^m erzeugt mit $$G_{RM}\left(m,m\right)=G_2^{\otimes m},$$

wobei $"G_2^{\otimes m}"$

das Kronecker-Produkt m-ter Ordnung von G₂ bezeichnet. Bei der Erzeugung von Codewörtern mittels Reed-Muller-Code wird die Generatormatrix G' r-ter Ordnung verwendet für einen Reed-Muller-Subcode der Länge n=2^m, welcher als RM(r,m) bezeichnet wird, wobei G' erzeugt wird aus G_RM, indem alle Reihen mit dem Hamming-Gewicht größer oder gleich 2^m-r ausgewählt werden. Somit ergibt sich die Code-Dimension zu $k={\displaystyle {\sum }_{i=m-r}^m\left(\begin{array}{c}m\\ i\end{array}\right).}$

Seien nun und Reed-Muller-Subcodes der Länge 2^m und 2ⁿ mit den Generatormatrizen G₁ und G₂ erzeugt wie vorstehend beschrieben, dann kann aus den Reed-Muller-Subcodes ein Product-Code (PC) erzeugt werden der Länge 2^m+n mit der Generatormatrix G = G₁ ⊕ G₂, wobei es sich dabei wiederum um einen Reed-Muller-Subcode handelt. Insbesondere ist dabei der Reed-Muller-Subcode ein Product-Code der Dimension d>2, so dass die Generatormatrix G erzeugt wird durch G = G₁ ⊕ G₂ ⊕ ... ⊕ G_d mit G₁ (i = 1,...,d) als Reed-Muller-Subcodes. Sodann werden mittels x = uG die Codewörter erzeugt.In the method according to the invention, a code word is first generated as a Reed-Muller subcode by means of a product code (PC), a data bit sequence u = u ₁ , ..., u _{k being} coded into the code word x = x ₁ , using the PC. ..., x _n . The generator matrix G by means of x = uG is used for coding the code word x. This is done $G_2\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$

elected. Then the generator matrix G _RM (m, m) of the m-th order of the Reed-Muller code with the length n = 2 ^{m is} generated with $$G_{\mathrm{R.}\mathrm{M.}}\left(m,m\right)=G_2^{\otimes m},$$

in which $"{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="DE102019200941B4\_0021.png,DE102019200941B4\_0023.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\otimes m}"$

denotes the Kronecker product of the m-th order of G ₂ . When generating code words using the Reed-Muller code, the generator matrix G 'r-th order is used for a Reed-Muller subcode of length n = 2 ^m , which is referred to as RM (r, m), where G' generates becomes G _RM by selecting all rows with the Hamming weight greater than or equal to 2 ^mr . Thus the code dimension arises too $k={\displaystyle {\sum }_{i=m-r}^m\left(\begin{array}{c}m\\ i\end{array}\right).}$

If Reed-Muller subcodes of length 2 ^m and 2 ^{n are} now generated with the generator matrices G ₁ and G ₂ as described above, then a Product codes (PC) with a length of 2 ^{m + n} are generated with the generator matrix G = G ₁ ⊕ G ₂ , which in turn is a Reed-Muller subcode. In particular, the Reed-Muller subcode is a product code of dimension d> 2, so that the generator matrix G is generated by G = G ₁ ⊕ G ₂ ⊕ ... ⊕ G _d with G ₁ (i = 1 ,. .., d) as Reed-Muller subcodes. The code words are then generated using x = uG.

$\mathcal{A}$

ist dabei die Menge aller Indizes der Reihen von G_RM(m,m) mit dem Hamming-Gewicht kleiner als 2^m-r. Die verbleibenden k Elemente von u' tragen dabei die Informationsbits. Bits deren Indizes zu $\mathcal{A}$

gehören, sind festgelegte Bits, wobei der Encoder den Wert dieser festgelegten Bits kennt. Die so gewonnene Genratormatrix wird genutzt als Komponenten-Code in der Erzeugung des Product-Codes. Encoding erfolgt somit mittels x = u'G_RM(m,m).Alternatively, the code word can be generated by means of the generator matrix G _RM (m, m) of the m-th order. For this, a 2 ^m -bit vector u 'must be defined, where u _i = 0 for all i ∈ $\text{I.}\in \mathcal{A}\text{.}$

$\mathcal{A}$

is the set of all indices of the series from G _RM (m, m) with the Hamming weight less than 2 ^mr . The remaining k elements of u 'carry the information bits. Bits to their indices $\mathcal{A}$

are fixed bits, and the encoder knows the value of these fixed bits. The generator matrix obtained in this way is used as a component code in the generation of the product code. Encoding is therefore carried out using x = u'G _RM (m, m).

1 shows a Tanner graph for the generation / encoding of a (4,3) Reed-Muller subcode, which is formed from (1,2) Reed-Muller codes as component codes and thus in turn represents a Reed-Muller subcode.

The code word x generated in this way is then transmitted to the receiver via a channel W as y. At the receiver the decoding takes place by means of an SCL decoder, whereby the data bit sequence û'i can be determined by the decoder. Due to the respective possibilities of the data bits û ' ₁ to û' _i-1 ∈ {0,1} P paths are formed, each path having p (p = 1, ..., P) i-1 edges, each edge of a path p each reproduces a data bit û '_i' (i '= i, ..., i-1). For each of the existing paths p, the decoder determines the soft decisions m _i for m _i (û ' _i = 0) and m _i (û' _i = 1). The previous decisions of the respective path are also taken into account.

Thus, according to 2 (a) two possibilities 0 and 1 with the calculated soft decisions m _{i = 1} (û ' ₁ = 0) and m _{i = 1} (û' ₁ = 1), whereby there is a path for each possibility and thus P = 2. The soft decisions m _{i are} calculated as follows I. Tal and A. Vardy, "List of decoding polar codes," IEEE Transactions of Information Theory, vol. 61, no. 5, pp. 2213-2226, May 2015 or E. Arikan, "Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels," IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051-3073, July 2009 known.

Then according to 2 B) continued with the decoding of the second data bit û ' ₂ . Here, for each of the existing paths p, both possibilities for the data bit û ' _{2 are again} taken into account and the corresponding soft decisions are determined so that four paths arise. 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.

According to the 2 (c) a further path is thus created for every further possibility, 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 selected, the number of paths P now exceeds the selected parameters, so that P> L. Then, according to the embodiment of the method described, the paths that have the highest reliability are selected, and then like this many paths with low reliability or lower soft decision value are crossed out until P ≤ L. This is in 2 (d) shown, with exactly four paths remaining due to the choice of L = 4. This ensures that no unnecessary especially for large block lengths are as improbable combinations of data bits û _'i still included.

so ist das Bit festgelegt und eine Verzweigung erfolgt nicht. Insbesondere ist die Unsicherheit für das bereits festgelegte Bit û'_i, i ∈ $\text{i}\in \mathcal{A}$

gleich Null.If one of the bits to be decoded is one of the previously defined bits with û ' _i , i ∈ $\text{i}\in \mathcal{A}$

so the bit is fixed and no branching takes place. In particular, the uncertainty for the already determined bit is û ' _i , i ∈ $\text{i}\in \mathcal{A}$

equals zero.

In a first alternative, after all soft decisions have been determined for each of the data bits û ' ₁ to û' _4, that path is selected with the highest soft decision value or with the highest reliability. The values corresponding to the path are then viewed as the transmitted code word û _i = û ' _i . Alternatively, as in 3 shown is between the information source 18th and the product code encoder 20th a CRC (Cyclic Redundancay Check) encoder 22 is provided, which creates a CRC check number, which is entered in the code word by the product code encoder 20th embedded and over the transmission channel 24 is also transmitted. By the Reed-Muller decoder 26th the data bits û _i , which contain the CRC checksum, are then decoded as described above. The possible paths that occur are then stored in a CRC decoder 28 The integrity of the CRC checksum is checked so that the decoder 26th determined possible paths the one that passes the CRC test is selected. If the checksum is correct for several of the possible paths through the decoder 26th have been determined, the one with the highest soft decision value or with the highest reliability is selected and viewed as the transmitted signal or data bit sequence u to be transmitted. Thus, in this variant, on the one hand, the fault-tolerant decoding method is implemented by means of soft decision, further errors being avoided by the downstream use of a CRC decoder. A decoding method is thus created with a high performance and a low block error rate or a high correction capability.

Claims (9)

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, the data signal being encoded by means of a product Codes, as Reed-Muller subcode; b) a Successive Cancellation List (SCL) decoder is used, the data bit sequence û ' _{i being able to} be determined by the decoder; c) P paths are formed by the respective possibilities of the data bits û ' ₁ to û' _i-1 ∈ {0,1}, each path having p (p = 1, ..., P) i-1 edges, where each edge of a path p represents a data bit û '_i' (i '= 1, ..., i-1); d) where for each of the existing paths p the decoder determines the soft decisions m _i for m _i (û ' _i = 0) and mi (' _i = 1), thus each of the paths branches off and thus 2P Paths arise; e) all previous decisions within the respective path p being taken into account when calculating the soft decisions m _i for the i-th bit û '_i; f) continuing with the calculation of the soft decisions for the i + 1-th data bit û ' _{i + 1} ; g) the soft decisions of the path p with the largest soft decision value being taken as the decoded data bit sequence û ' _i = û _i when the k-th data bit û' _k is reached, characterized in that the components of the Product codes are an extended Hamming code and / or a single parity check code. Procedure according to Claim 1 , for which a value L> 1 is specified and, in the event that the number of existing paths P> L, the paths p are selected with the largest soft decision value, with as many paths being discarded until P L . Procedure according to Claim 1 or 2 , in which a cyclic redundancy check (CRC) code is applied to the remaining options after determining the soft decisions of the k-th data bit û _k and then the path with the largest soft decision value is selected from the remaining paths . Transmission method with a transmitter, wherein the transmitter encodes a data bit sequence u using a product code in a code word x as a ReedMuller subcode, the code word x is transmitted via a transmission channel and a disturbed code word y is received by a receiver, with an undisturbed code word y would correspond to the transmitted code word x, the received code word being decoded by the receiver according to the method according to one of the Claims 1 to 3 so that û is determined which corresponds to the original data bit sequence u with error-free decoding. Transmission procedure according to Claim 4 , in which, before the code word x is generated, a CRC encoder is initially provided to generate a CRC checksum that is also transmitted. Receiver for receiving and decoding a data bit sequence u, with a receiving device for receiving a data signal and a decoder, the decoder being designed to carry out the method according to one of the Claims 1 to 3 . Transmission device, with a transmitter, the transmitter having a data source and an encoder, the encoder being designed to encode a data bit sequence u of the data source into a code word x by means of a product code as a Reed-Muller subcode, a transmission channel and a Receiver, wherein a disturbed code word y is received by the receiver, the receiver being designed according to a receiver Claim 6 . Transfer device according to Claim 7 , 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 according to Claim 7 or 8th , wherein the transmission channel is a radio link or a wired connection or an optical data transmission.

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