DE10147482A1 - Error correction of data transmitted in optical data transmission systems involves using serially chained, three-dimensional Single Parity Check turbo-code - Google Patents

Abstract

The method involves generating a product code word, using an interleaver on the code word, generating a product code word from the code word from the interleaver, sending coded data over a transmission line, decoding the code word generated by the second encoder taking into account extrinsic information of a first decoder and decoding the code word generated by the first encoder taking into account extrinsic information of a second decoder. The method involves generating a three-dimensional Single Parity Check or SPC product code word with a first encoder (1), using an interleaver on the generated code word, generating a three-dimensional SPC product code word from the code word from the interleaver using a second encoder (2), sending coded data over a transmission line, decoding the code word generated by the second encoder with a second decoder (8) taking into account extrinsic information of a first decoder (7) and decoding the code word generated by the first encoder using the first decoder taking into account extrinsic information of the second decoder. AN Independent claim is also included for the following: an error correction system.

Description

The invention relates to an error correction method and a Corresponding system for the correction of digital data, which in a data transmission system, in particular an optical one Transmission system to be transmitted, according to the preamble of claims 1 and 9 respectively.

In a transmission system, data between one Transmitter and a receiver transmitted. The data originally coupled in the form of rectangular pulses on their way to the recipient through various influences distorted so that it is a faulty at the receiver Data recognition, that is, bit errors can occur.

In order to minimize such bit errors, it is known that Encode data before it is transmitted. In doing so additional bits (check bits) are generated from the information data, which are transmitted together with the information data. Out the additional information can be, depending on the type of Codes indicate the existence of one or more errors and deduce the position of the error (s).

After the data have been transferred, they must be received by the recipient be decoded. There are a number of decoding methods for this known. An effective way to decode data offer z. B. Turbo decoding method for product codes. Turbo- Decoding methods were first described by Pyndiah: R.M. Pyndiah, A. Glavieux, A. Picart, S. Yasq "Near-optimum decoding of product codes "in Proc. of IEEE Globecom 1994 Conference, Nov.-Dec. 1994, San Francisco, 1/3, pages 339-343, presented.

Product codes are multi-dimensional Block code with the parameters (n, k, d,) where n is the Code word length, k the number of information bits, and d the minimum Hamming distance is.

In Fig. 1, an example is a two-dimensional (n1, k1, d1) × (n2, k2, d2) product code shown. Field A contains the information bits, field B the check bits for each row of information bits, and field C the check bits for each column of information bits. Each row or column of the product code forms a code word.

The product code shown is otherwise a full one Product code, because also for the check bits (fields C, B) own Check bits are provided (field D).

In the above publication, Pyndiah used for both dimensions BCH codes. Using a special turbo decoding method (based on the chase Algorithm) will give good results in terms of Bit error rate reached. Despite the low bit error rate, the Chase algorithm but disadvantages because of its high complexity and is therefore for use in optical Transmission systems only suitable to a limited extent.

It is therefore an object of the present invention Error correction procedures and a corresponding system too create that is particularly simple and at the same time minimal Bit error rates enabled.

This problem is solved by the in claim 1 or 9 specified characteristics. Further refinements of the invention are the subject of subclaims.

The advantages of the invention result from a number of Measures that greatly improve overall Bit error rate (coding gain). First of all proposed that the data to be transmitted be linked using a chained three-dimensional SPC product codes (SPC: Single Parity Check) to code. A corresponding encoder comprises a first one Encoder for generating a three-dimensional SPC code word from the information data, an interleaver for regrouping of the data, and a second encoder for generating a three-dimensional SPC code word from that of the interleaver output code word.

The information data will eventually be shared with the generated parity bits transmitted over a transmission link and decoded on the receiver side. The decoding takes place using an iterative turbo decoding algorithm, which SPC code word generated by the second encoder by means of a second decoder and the SPC generated by the first encoder Code word is decoded by means of a first decoder. Thereby extrinsic information is added between the decoders replaced.

A decoder constructed according to the invention thus comprises a second decoder for decoding the second Encoder generated SPC code word, a first decoder for Decoding the SPC code word generated by the first encoder, as well as a deinterleaver.

Extrinsic information is additional Information based on probability considerations determined from the received code words and with their help the code word received at each iteration step is modified.

For a better understanding, the method is explained below using an example, a code C with a length n being assumed. A code word can be c _i = (c _i1 , c _i2 , _... , C _in ) i = 1, 2 _,. , , 2 represent ^n-1 , and c _ij ∈ {-1, +1}. Each code word of an SPC code has an even number of +1 bits. The SPC code words for n = 3 are e.g. B .:
C ₁ = (-1, -1, -1)
C ₂ = (-1, +1, +1)
C ₃ = (+1, -1, +1)
C ₄ = (+1, +1, -1)
where c _i1 and c _{i2 are} information bits and c _{i3 is} the parity bit. This code word c is sent to a receiver via an optical transmission system, for example, whereby it is distorted.

The distorted vector obtained at the receiver can be represented as x = (x ₁ , x ₂ ,... X _n ), x _j = c _j + n _j , where {n _j } independent Gaussian random variables with a zero mean and a Are standard deviation of σ ² . All code words have the same probability. The same applies to bits +1 and -1. Due to the distortion, the following code words are obtained, for example:
C ₁ = (-0.9 -0.2 0.4)
C ₂ = (0.2 1.3 0.8)
C ₃ = (0.5 -1 0.3)
C ₄ = (-0.1 0.7 -1.8)

The original data should now be returned from this code be recognized. One possibility for this is the so-called "hard decoding "(the direct decision for a value - here +1 or -1 - due to decision thresholds. This However, method is less of the present invention Importance.

The other decoding algorithm is called "soft decoding" designated. It is characterized by the fact that only after several iteration steps one decision (+1 or -1) is taken and until then analog values are expected which is used in each iteration step according to the Decoding algorithm can be modified.

To carry out the decoding process, so-called soft input soft output decoders are used which modify a supplied code word taking into account extrinsic information and which themselves provide extrinsic information. Various decoding algorithms can be used here. The optimal output value of a soft input soft output decoder can e.g. B. using a MAP algorithm (MAP: Maximum a posteriori) with evaluation of a probability ratio LLR (LLR: Log Likelihood Ratio), where:

Pr is the probability that a bit of a received code word x is +1 or -1. This relationship can also be represented as

The value x _jext represents the extrinsic information.

According to a preferred embodiment of the invention, a "Max-Log-Map" algorithm is used instead of the MAP algorithm, by means of which an additional reduction in the signal-to-noise ratio can be achieved. This "max log map" algorithm is also much easier to implement. The extrinsic information can be calculated using the following equation:

An encoder according to the invention preferably consists of several, in particular three concatenated individual encoders, the generate one SPC code word for each dimension.

A decoder according to the invention preferably comprises several, in particular three, serial-linked individual decoders. Each individual decoder of a decoder generates extrinsic information from others Individual decoders is taken into account in order to be fed to their input Modify code word.

According to a preferred embodiment of the invention a soft decoding method is used for the decoding. The individual decoders are therefore preferably SISO - (Softinput softoutput) decoder implemented.

The redundancy in the coding is preferably less than 25% especially less than 20%.

The invention is described below with reference to the accompanying Drawings explained in more detail by way of example. Show it:

FIG. 1 shows an example of a two-dimensional product code word;

FIG. 2 shows an example of a three-dimensional SPC product codeword;

Fig. 3 is a schematic representation of the generation of a three-dimensional concatenated SPC code word;

FIG. 4 shows the schematic structure of a data transmission system comprising an encoder for generating a three-dimensional concatenated SPC product codeword and a corresponding decoder; and

Fig. 5 shows a serial-concatenated decoder according to an embodiment of the invention.

With regard to FIG. 1, reference is made to the explanations given in the introduction to the description.

Fig. 2 shows a typical example of a three-dimensional SPC product codeword. The 3D code word comprises a block A with information bits, which contains a total of k1 × k2 × k3 bits. Each row (in the x or z direction) and column (in the y direction) represents a sub-code word which has a parity bit in its last position (n _i - k _i = 1). The parity bits are designated overall by P1.

A parity bit is e.g. B. 1 if the code word is an odd Number of 1 bits and 0 if the code word is one has an even number of 1 bits. The number of 1 bits in every row or column is therefore always even.

The number k _i of information bits in each dimension is preferably the same. The 3D code word shown is also a full product code.

FIG. 3 shows the generation of a three-dimensional SPC product code word by means of a serial-linked encoder. The serially concatenated encoder comprises a first encoder 1 and a second encoder 2 . The first encoder 1 generates a three-dimensional SPC product code word 4 with a code rate of z. B. (26/27) ³ . This corresponds to the 3D code word of FIG. 2 with a total number of information bits of 26 ³ = 17576.

The 3D code word 4 output at the output of the first coder 1 is fed to an interleaver 3 , which is a modification of an interleaver, as used, for. B. in an article by L. Ping, S. Chan, and KL Yiung, "Efficient soft-in-soft-out sub-optimal decoding rule for single parity check codes", Electron. lett., Vol. 33, No. 19, pages 1614-1615, 1997. The interleaver 3 rearranges the individual bits of the 3D code word 4 , whereby a new 3D code word 5 is created.

The code word 5 output by the interleaver 3 is finally encoded by the encoder 2 , which generates a three-dimensional SPC product code word with parity bits P2 and a code rate of (27/28) ³ . The code rate of the entire concatenated encoder is therefore (26/28) ³ = 0.8. The redundancy is thus 25%.

Fig. 4 shows the schematic structure of a data transmission system having a concatenated encoder, comprising the encoder 1 and 2, and a corresponding decoder comprising the decoder 7 and 8.

The first encoder 1 in turn comprises three individual encoders C11, C12 and C13, each of which generates an SPC code word for one dimension of the 3D product code word 4 . The second encoder 2 also comprises three individual encoders C21, C22, C23 for generating the three-dimensional SPC product code word 6 .

The SPC code word 4 generated by the first encoder 1 and the parity bits P2 of the SPC code words 6 generated by the second encoder 2 are transmitted via a transmission line L. Optionally, the SPC code word 4 generated by the first encoder 1 and the entire SPC code word 6 can also be transmitted.

The transmitted information is finally received by a decoder, which has a second decoder 7 for decoding the SPC code word 6 generated by the second encoder 2 , and a first decoder 8 for decoding the SPC code word 4 generated by the first encoder 1 . A deinterleaver 9 is arranged between the two decoders 7 , 8 and performs an inverse rearrangement of the individual bits.

The information data supplied to the decoders 7 , 8 are designated by u, extrinsic information by EXT. As can be seen, the second decoder 7 generates extrinsic information which is fed to the first decoder 8 via the deinterleaver 9 . The first decoder 8 takes this information into account and outputs extrinsic information itself, which in turn is fed to the second decoder 7 in the next iteration step via an interleaver 10 .

The decoders 7 , 8 each comprise three individual decoders D21, D22, D23 or D11, D12, D13, which are each responsible for decoding in one dimension.

FIG. 5 shows a more detailed view of the decoder from FIG. 4, the second decoder 7 being shown in the upper part and the first decoder 8 being shown in the lower part of the figure.

The individual decoders SISO21-23 and SISO11-13 of the first and second decoders 7 , 8 are each implemented as SISO decoders.

The information data are denoted by u and the parity bits by p. The superscript determines the decoder 7 , 8 from which the data originate or to which the relevant data are sent. The subscript denotes the individual decoder (SISO21-23 or SISO11-13) that generated the data. Extrinsic information generated by one of the decoders 7 , 8 and intended for the other one of the decoders 7 , 8 is identified by the index ext.

The turbo decoding algorithm is done in n iterative steps carried out. All are before the first iteration step extrinsic data is zero.

At the input of the second decoder 7 , the information bits u ² and the parity bits p ^{2 of} the SPC code word 6 are supplied. This data is also fed to the subsequent SISO22 and SISO23 individual decoders. Each of the individual decoders SISO21-23 generates modified pairs of information data u and parity bits p from the data supplied to it, more precisely a series of probability distributions which contain or represent extrinsic information. This extrinsic information is fed to the other two SISO21-23 individual decoders at their input.

So z. B. the second individual decoder SISO22 in addition to the parity bits p ^{2 of} the SPC code word 6, the extrinsic information of the individual decoders SISO21 and SISO23 (p ² ₂₁ , p ² ₂₃ ). The third individual decoder SISO23 receives e.g. B. at its input the information data u ² ₀ and the extrinsic information of the two other individual decoders SISO21, SISO22 (u ² ₂₁ , u ² ₂₂ ).

The decoder 7 also receives extrinsic information u ² _{ext from} the first decoder 8 and vice versa.

The information data u ² ₂₁ - u ² ₂₃ generated by the individual decoders SISO21-SISO23 are fed to a deinterleaver 9 . The deinterleaver 9 in turn forms information _data u ¹ _ext and parity bits p ¹ _ext for further processing by the first decoder 8 .

At the input of the first decoder 8 , the information data u ¹ and the parity bits p ¹ of the code word 4 generated by the first encoder 1 are supplied. For this purpose, the extrinsic data p ¹ _ext or u ¹ _ext generated by the second decoder 7 are added.

As in the example of the second decoder 7 , each individual decoder SISO11-SISO13 of the first decoder 8 also receives extrinsic information from the other two individual decoders. At the output of the last individual decoder SISO13, all extrinsic data, ie both the information data u ¹ ₁₁ -u ¹ ₁₃ and parity data p ¹ ₁₁ -p ¹ _{13 are} added and each fed to an interleaver 10 . This generates extrinsic information u ² _ext , which is fed to the second decoder 7 .

This starts a second iteration step. After n A decision is made in iteration steps.

With the presented concatenated, three-dimensional SPC turbo code, a great improvement in the bit error rate in an optical transmission system can be achieved. Since this coding method is fairly simple and can be implemented inexpensively, it is also suitable for wide-area optical transmission systems. The Q factor with almost error-free transmission (BER = 10 ^-15 ) is thus reduced to around 6.4 dB.

Claims (14)

1. Error correction method for correcting data which are transmitted in a data transmission system, in particular an optical transmission system, characterized by the following steps: - Generating a three-dimensional SPC product code word ( 4 ) by means of a first encoder ( 1 ); - Applying an interleaver ( 3 ) to the SPC code word ( 4 ) generated by the first encoder ( 1 ); - Generating a three-dimensional SPC product code word ( 6 ) from the code word ( 5 ) output by the interleaver ( 3 ) by means of a second encoder ( 2 ); - transmitting coded data over a transmission line (L); - Decoding the code word ( 6 ) generated by the second encoder ( 2 ) by means of a second decoder ( 7 ), taking into account extrinsic information (u ² _ext ) from a first decoder ( 8 ); and - Decoding the code word ( 4 ) generated by the first encoder ( 1 ) by means of the first decoder ( 8 ), taking into account extrinsic information (u ¹ _ext ) from the second decoder ( 7 ). 2. The method according to claim 1, characterized in that the first or second encoder ( 1 , 2 ) has a plurality of individual encoders (C11-C13; C21-C23). 3. The method according to claim 1 or 2, characterized in that the first or second decoder ( 7 , 8 ) has a plurality of individual decoders (D11-D13; D21-D23; SISO11-13, SISO21-23). 4. The method according to claim 3, characterized in that each individual decoder (D21-D23; D11-D13) one of the decoders ( 7 , 8 ) generates extrinsic information from the other individual decoders (D21-D23; D11-D13) of the decoder ( 7 , 8 ) is taken into account. 5. The method according to any one of the preceding claims, characterized in that the decoders ( 7 , 8 ) use a max log map algorithm. 6. The method according to any one of the preceding claims, characterized in that the decoders ( 7 , 8 ) are SISO decoders. 7. The method according to any one of the preceding claims, characterized in that the SPC code word ( 6 ) generated by the second encoder ( 2 ) has a redundancy of at most 25%. 8. The method according to any one of the preceding claims, characterized in that the extrinsic information generated by the second decoder ( 7 ) is fed to a deinterleaver ( 9 ). 9. An error correction system for digital data that is transmitted in a data transmission system, in particular an optical transmission system, comprising:
a first encoder ( 1 ) for generating a three-dimensional SPC product code word ( 4 );
an interleaver ( 3 ) for rearranging the SPC code word ( 4 );
a second encoder ( 2 ) for generating a second three-dimensional SPC product code word ( 6 ) from the code word ( 5 ) output by the interleaver ( 3 );
a transmission line (L) for transmitting the encoded data;
a second decoder ( 7 ) for decoding the SPC code word ( 6 ) generated by the second encoder ( 2 ); and
a first decoder ( 8 ) for decoding the SPC code word ( 4 ) generated by the first encoder ( 1 ), the first and second decoders ( 7 and 8 ) generating extrinsic information that the other decoder ( 8 and 7 ) is fed. 10. System according to claim 9, characterized in that the first and second encoder ( 1 and 2 ) each comprise three series-connected individual encoders (C11-C13; C21-C23). 11. System according to claim 9 or 10, characterized in that the first and second decoders ( 7 and 8 ) each comprise three series-connected individual decoders (D21-D23, D11-D13, SISO11-13, SISO21-23). 12. System according to one of claims 9 to 11, characterized, that each of the individual decoders (D11-D13; D21-D23, SISO11-13, SISO21-23) generates extrinsic information. 13. System according to claim 12, characterized, that the extrinsic information is one of the individual decoders (D21-D23; D11-D13) the other two Individual decoders (D21-D23; D11-D13, SISO11-13, SISO21-23) are fed. 14. System according to one of claims 9 to 13, characterized in that the decoders ( 7 , 8 ) operate according to a max log map algorithm.