DE102015006173B4 - Method for transmitting data - Google Patents

Abstract

A method for transmitting data from a transmitter to a receiver, the data being encoded before transmission over a lossy transmission channel by an encoder connected to the transmitter, the data being decoded after its transmission over the transmission channel by a decoder connected to the receiving device where data is encoded and decoded using a Forward Error Correction Code, using a feedback channel from the receiving device to the transmitting device, and the amount and / or type of redundant data generated by the encoder in response to the feedback from the receiving device on the feedback Channel is requested, characterized in that a retransmission of those codeword symbols is requested via the feedback channel having the highest entropy, wherein a codeword symbol has a high entropy when there is a high uncertainty whether the codeword -S ymbol has a certain value.

Description

The invention relates to a method for transmitting data.

Forward error correction methods are known in the art for sending data from a transmitting device to a receiving device via a lossy transmission channel.

Furthermore, the use of a feedback channel from the transmitting device to the receiving device is known from the prior art: for example. It is generally known that due to the feedback codes with a short length can reach the performance of longer codes. However, in practice there is a need for error correction codes capable of achieving this result. For example. Turbo codes or LDPC codes achieve their highest performance only with a block size of several 1000 bits.

1. [1] C. Berrou, A. Glavieux, and P. Thitimajshima, „Near Shannon limit errorcorrecting coding and decoding: Turbo-codes,“ in Proc. IEEE International Conference on Communications, Geneva, Switzerland, May 1993.
2. [2] C. Douillard and C. Berrou, „Turbo codes with rate-m/(m+1) constituent convolutional codes,“ IEEE Transactions on Communications, vol. 53, no. 10, pp. 1630-1638, 2005 .

Prior art information can be found in the following publications:

1. [1] C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error correcting coding and decoding: turbo codes," in Proc. IEEE International Conference on Communications, Geneva, Switzerland, May 1993.
2. [2] C. Douillard and C. Berrou, "Turbo codes with rate-m / (m + 1) constituent convolutional codes," IEEE Transactions on Communications, vol. 53, no. 10, pp. 1630-1638, 2005 ,

US 2014/0133848 A1 describes a method of transmitting data from a transmitter to a receiver using an adaptive coding technique in which channel statistics are fed back to the transmitter so that it can adjust its forward error correction coding.

The object of the invention is to provide a method for transmitting data over a lossy transmission channel using a forward error correction code having an improved performance.

The object is achieved according to the invention by the features of claim 1.

The method according to the invention serves to transmit data via a lossy transmission channel. The data is in this case sent by a transmitting device and received by a receiving device. Before transfer, the data is encoded by an encoder. After transmission, the data is decoded by a decoder. The data is encoded and decoded using a Forward Error Correction Code.

According to the invention, a feedback channel from the receiving device to the transmitting device is used. This can be used in particular to signal which data was not received correctly by the receiving device and thus has to be retransmitted. According to the invention, the amount and / or type of redundant data is adjusted in response to the feedback signal transmitted via the feedback channel.

It is preferred that the adaptation of the amount and / or type of data to be retransmitted is adjusted as a function of the signal-to-noise voltage ratio of the transmission channel.

According to the invention, a retransmission of those data having the highest entropy is requested via the feedback channel. A codeword has a high entropy if there is a high degree of uncertainty about the codeword symbol having a certain value.

The method according to the invention makes it possible to achieve a performance with regard to the error correction of significantly longer and more complex error correction codes. For example. For example, it is possible to use a 40-bit block length with the same error-correction capability as the CCSDS deep-space LDPC code of the CCSDS standard with a block size of 2048 bits.

It is preferred that encoding and decoding be done by a non-binary LDPC code, in particular an LDPC code, from a> 64 Galois field.

In the following, preferred embodiments of the invention will be explained with reference to figures.

• 1 eine schematische Darstellung des erfindungsgemäßen Kommunikationsschemas,
• 2 eine beispielhafte Darstellung eines Constellation Designs,
• 3 eine Darstellung der Leistungsfähigkeit gegenüber dem Stand der Technik
• 4 eine Darstellung der Codeword-Error-Rate in Abhängigkeit vom Signal-Rausch-Spannungsverhältnis.

Show it:

• 1 a schematic representation of the communication scheme according to the invention,
• 2 an exemplary representation of a Constellation Design,
• 3 a representation of the performance over the prior art
• 4 a representation of the code word error rate as a function of the signal-to-noise voltage ratio.

kodiert. Als (N,K) werden die Parameter von C ausgedrückt als Feldsymbole bezeichnet. Es ergibt sich: k = K x m. Das Ausgangs-Codeword am Ausgang des Encoders wird durch c bezeichnet. 1 shows in a simplified manner the communication scheme according to the invention. A transmitting device generates a message u having k bits. The message u is passed through a linear block code from c ${\mathbb{F}}_{q.}q=2^m$

coded. As (N, K), the parameters of C are expressed as field symbols. The result is: k = K x m. The output code word at the output of the encoder is denoted by c.

ist invertierbar.Each codeword symbol in c is assigned to a Constellation symbol. The Constellation is called X and has a cardinality of | X | - q up. The assignment function $\mathrm{\Phi }(\cdot ):\mathbb{F}\to \mathcal{X}$

is invertible.

The modulated sequence x is N constellation symbols long and is transmitted over an AWGN channel with a signal to noise voltage ratio E _s / N ₀ = 1 / 2σ ² . It was assumed that the average transmission power 1 while σ ^{2 is} the noise variance per dimension.

The channel output is denoted by y and N has complex values. For the generic ith value, the soft demodulator calculates the Probability Mass Function $$\begin{array}{cc}{W}_i\left(\beta \right)\dot{=}\text{pr}\left\{C_i=\beta |y_i\right\}.& \forall \beta \in {\mathbb{F}}_q\end{array}$$

Here, C _i denotes the random variable associated with the ith codeword symbol.

ist. In diesem Fall basiert der Kanal-Decoder auf den nicht-binären Belief Propagation Algorithmus.The vector W = (W ₁ W ₂ ... W _N ) of the N probability density functions is the input of the channel decoder. It is assumed that C is a (N, K) cyclic code over ${\mathbb{F}}_q$

is. In this case, the channel decoder is based on the non-binary belief propagation algorithm.

If an error is detected after channel coding (i.e., if the output of the channel decoder does not satisfy the conditions of the code's parity equations), then a request for re-polling is sent via the feedback channel to the transmitting device. It is assumed that an ideal feedback channel. The retransmission request contains the index of the codeword symbol to be retransmitted. On the contrary, if the decoded word satisfies the parity equations, the estimated word û is fed to the receiver. In the case of a renewed data transfer, the encoder behaves as follows:

(die zyklische multiplikative Gruppe von ${\mathbb{F}}_q$

). Das neu erzeugte Symbol, das durch c̃_t (multiplikative Wiederholung von c_t. wird dann einem Konstellations-Symbol x̃_t zugeordnet und übertragen.Starting from the required symbol index t, the encoder calculates a scaled version of the codeword symbol c _t by multiplying c _t by a randomly chosen symbol γ in ${\mathbb{F}}_q^{*}$

(the cyclic multiplicative group of ${\mathbb{F}}_q$

). The newly generated symbol, represented by c _t (multiplicative repetition of c _t ., Is then assigned to a constellation symbol x _t and transmitted.

On the receiver side, given a channel output ỹ _t, a probability density function is calculated $$\begin{array}{cc}{\tilde{W}}_t\left(\beta \right)\dot{=}\text{pr}\left\{{\tilde{C}}_t=\beta |{\tilde{y}}_t\right\}.& \forall \beta \in {\mathbb{F}}_q\end{array}$$

Assuming that the scaling coefficient γ is known, a permuted version of the density function W _{t is} calculated: $${\tilde{W}}_t^{\text{'}}\left(\beta \right)={\tilde{W}}_t\left(\gamma \beta \right)$$

Die resultierende Dichtefunktion wird dann dem Kanal-Decoder zugeführt durch Ersetzen der t-ten Dichtefunktion in W. Es wird ein neuer Decodierversuch durchgeführt. Wenn ein gültiges Wort am Ausgang des Decoders erkannt wurde, wird die Nachricht dem Empfänger übermittelt. Andernfalls wird eine neue Anforderung auf eine erneute Datenübertragung produziert.An updated version of the t-th probability density function is therefore calculated by multiplying the previous density function (element by element) $W_t\text{With}{\tilde{W}}_t^{\text{'}},$

The resulting density function is then fed to the channel decoder by replacing the t-th density function in W. A new decode attempt is made. If a valid word has been detected at the output of the decoder, the message is transmitted to the receiver. Otherwise, a new request for a new data transmission is produced.

The following describes a strategy that can be used to determine the data to be retransmitted by the receiver.

In this case, those codeword symbols with the highest entropy are retransmitted. A codeword symbol has a high entropy if there is a high degree of uncertainty that the codeword symbol has a certain value.

(hier ist r_i die Gesamtanzahl der erneuten Datenübertragungen,die für das i-te Codeword-Symbol durchgeführt werden, und ỹ_i,l bezeichnet den Kanalausgang, der der I-ten erneuten Datenübertragung von c_i zugeordnet wird. Es gilt: $$H\left(C_i|y_i\right)=-{\displaystyle \sum _{\beta \in {\mathbb{F}}_q}{\tilde{W}}_i\left(\beta \right){\text{log}}_2{\tilde{W}}_i\left(\beta \right)}$$

The uncertainty with respect to the ith codeword symbol is denoted by H (C _i | y _i ). It is assumed that the set of the associated channel output is y _i and the set of retransmissions $y_i=\left\{y_i\right\}\cup {\left\{{\tilde{y}}_{i.l}\right\}}_{l=1}^{r_i}$

(Here, r _{i is} the total number of retransmissions performed on the ith codeword symbol, and ỹ _{i, l} denotes the channel output assigned to the ith re-transmission of c _i . $$H\left(C_i|y_i\right)=-{\displaystyle \underset{\beta \in {\mathbb{F}}_q}{\Sigma }{\tilde{W}}_i\left(\beta \right){\text{log}}_2{\tilde{W}}_i\left(\beta \right)}$$

The receiver requests a new data transmission of the symbol c _t , with $$\text{t}=\underset{i\in \left[\mathrm{1,}N\right]}{\text{arg max}}H\left(C_i|y_i\right)$$

The algorithm thus aims to determine the value of the least reliable codeword symbol.

The constellation design is described in more detail below. As a reference, q-type QAM modulations are taken into account. To avoid losses, APSK-like constellations are used in which the constellation points are optimized with respect to the input-limited channel symmetric information rate. An example of a 4096-point constellation obtained by differential evolution is in 2 shown.

basieren. Im ersten Fall ist die maximal erzielbare Spektral-Effizienz log₂ 256 = 8 b/s/Hz., während im zweiten Fall die maximal erzielbare Spektral-Effizienz log₂ 4096 = 12 b/s/Hz. 3 represents the measured spectral efficiencies of different schemes based on ${\mathbb{<figure-callout\; id="256"\; label="F"\; filenames="DE102015006173B4\_0017.png"\; state="\{\{state\}\}">F</figure-callout>}}_{256}\text{and}{\mathbb{F}}_{4096}$

based. In the first case, the maximum achievable spectral efficiency log ₂ 256 = 8 b / s / Hz., While in the second case, the maximum achievable spectral efficiency log ₂ 4096 = 12 b / s / Hz.

• - ein A N = 6, K = 2 zyklischer Code, bezeichnet als Tetra Code
• - ein A N = 15, K = 5 zyklischer Code, bezeichnet als Petersen Code
• - ein A N = 48, k = 16 zyklischer Code;

The used channel codes are:

• an AN = 6, K = 2 cyclic code, called Tetra Code
• an AN = 15, K = 5 cyclic code, referred to as Petersen code
• an AN = 48, k = 16 cyclic code;

For this code, the code dimension is in bits $(\text{k}=128\text{For}{\mathbb{<figure-callout\; id="256"\; label="F"\; filenames="DE102015006173B4\_0017.png"\; state="\{\{state\}\}">F</figure-callout>}}_{256}\text{and k}=192\text{For}{\mathbb{F}}_{\text{4096}})$

In all cases, each decode attempt consists of a maximum of 50 iterations. The maximum entropy strategy described above is used to determine the data to be retransmitted. To extend the code rate to higher rates, the three codes described above were punctured to achieve a rate of 2/3, allowing the range of spectral efficiency to be increased towards higher noise-to-voltage ratios.

Despite the very small code dimensions (from 192 down to 16 bits), all schemes work close to the Shannon limit (black solid line, R = log ₂ (1 + E _s / N ₀ ).) For medium to low noise voltage ratios while for large noise voltage ratios, codes with the code dimensions k = 128 and k = 192 bits will work within 2dB of the Shannon limit.

In 4 the codeword error rate (CER) versus signal-to-noise voltage ratio is shown in the form of E _b / N ₀ for the Peterson code with 256 APSK modulation. The performance of the code was shown assuming preliminary puncturing to achieve a higher mother code rate. In this case, five iterations were performed. Unless puncturing is used, ie the mother code rate is 1/3, 5, 4, and 3 iterations were used.

The puncturing leads to a high CER. This is justified by the fact that when operated at very high code rates, the decoder tends to produce many undetected errors, since the mother code is very weak.

The more iterations are used, the more the final code rate (spectral efficiency) is improved. However, the decoder will often fail due to the convergence to erroneous codewords. As the number of iterations is reduced, the decoder will less likely converge at high code rates, resulting in fewer undetected errors.

It is noteworthy that due to the feedback in the context of the method according to the invention at E _b / N ₀ ~ 2 dB, a CER of approximately 10 ^-4 can be achieved. This corresponds to the performance achieved by the (2048,1024) CCDS LDPC code with 50 iterations. It should be noted that the Peterson code is much shorter (K = 40 bits).

Claims (4)

A method for transmitting data from a transmitter to a receiver, the data being encoded before transmission over a lossy transmission channel by an encoder connected to the transmitter, the data being decoded after its transmission over the transmission channel by a decoder connected to the receiving device wherein data is encoded and decoded using a Forward Error Correction Code using a feedback channel from the receiving device to the transmitting device, and the amount and / or type of redundant data generated by the encoder is adjusted in response to the feedback of the receiving device on the feedback channel, characterized in that a retransmission of those codeword symbols via the feedback channel is requested, which is the highest Entropy, wherein a codeword symbol has a high entropy, if there is a high uncertainty about whether the codeword symbol has a certain value. Method according to Claim 1 characterized in that the amount and / or type of data to be retransmitted is adjusted in response to the signal to noise voltage ratio of the transmission channel based on the feedback feedback signal. Method according to one of Claims 1 to 2 , characterized in that the coding and decoding is performed using a non-binary LDPC code from a> 64 Galois field. Method according to one of Claims 1 to 3 , characterized in that the codeword symbol to be retransmitted is denoted by a symbol index t, starting from the required symbol index t of the encoder a scaled version of the codeword symbol c _t by multiplication of c _t by a randomly chosen symbol γ in ${\mathbb{F}}_q^{*}$

calculated, wherein the newly generated symbol is transmitted to the receiver.

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