DE102012223040B3 - Method for restoring missing and/or damaged data transmitted from transmission device to receiving device in communication system, involves concatenating LDPC code with repetition code such that code word is multiplied with coefficient - Google Patents

Abstract

The method involves coding data by using an encoder connected with a transmission device, and transmitting the data from the transmission device to a receiving device over a transmission channel. The data is decoded by a decoder, where missing and/or damaged data is restored during the decoding. The data is coded by using non-binary LDPC code with values from Galois-field. The LDPC code is concatenated with multiplicative repetition code such that code word represented by a variable node in Tanner-graph-representation of LDPC code is multiplied with coefficient provided by the field.

Description

The invention relates to a method for restoring lost and / or damaged data.

For this purpose, it is known to use an LDPC code for encoding and decoding the data. Furthermore, it is known to concatenate an LDPC code with a multiplicative repetition code (MR). Such codes are referred to as MR LDPC codes for short. Standard decoding of MR codes leads to considerable losses, as the constant phase on the channel is not exploited over several code symbols. However, MR codes are z. B. useful in dealing with non-coherent additive White Gaussian Noise (AWGN) channels.

Noncoherent detection is commonly used in communication scenarios where recovery of the carrier phase is very problematic, e.g. Due to overlapping of superimposed signals in CDMA systems, random phase variations in multipath environments, frequency instabilities of oscillators or simply due to hardware complexity limitations. The blockwise non-coherent Additive White Gaussian Noise (AWGN) channel is a simple channel model that provides useful insights into the design of channel codes for channels of unknown phase. A particular example in which the blockwise non-coherent AWGN channel has been shown to be an accurate description of the actual channel behavior is that of (Fast) Frequency Hopping (FH) systems. LDPC codes on non-binary GFs have been proposed in M. Davey and D. MacKay in "Low density parity check codes over GF (q)," IEEE Commun. Lett., Vol. 2, no. 6, pp. 70-71, Jun. 1998, and rate-compatible constructions were introduced by K. Kasai, D. Declercq, C. Poulliat, and K. Sakaniwa in "Rate-compatible non-binary LDPC codes concatenated with multiplicative repetition codes," in Proc. 2010 IEEE Int. Symp. On Information Theory, Austin, Texas, USA, Jun. 2010 (abbreviated as MR Code). Compared to binary codes, non-binary LDPC codes show notable performance gains, especially for large block lengths on the order of a few hundred bits. As with LDPC binary codes, decoding is based on Belief Propagation (BP), that is on Message Passing (MP) along the edges of the Tanner Graph. MR codes are based on the idea that every variable Node of the mother code is repeated r times. In order to achieve a coding gain due to repetitions, the values of the mother variable node are not only repeated but also multiplied by non-zero elements of the Galois Field (GF). 1 shows the Tanner graph of an MR code with a repetition length of 2. The mother code consists of the check nodes (CNs) and variable nodes (VNs) in the upper part of the figure, while the repeated 18 symbols are arranged in the bottom part.

wobei y_t der empfangene Vektor der Länge t ist, x_t der modulierte gesendete Vektor der Länge t und n_t der Gaussian noise vector mit der Länge t samples ist. Es ist zu beachten, dass x_t erlangt wird aus dem nicht binären Codewortsymbol, indem dieses einer binären Sequenz zugeordnet und moduliert wird. Die Rauschsamples sind zirkulär symmetrische Gaußsche Zufallsvariablen mit einer Varianz von 2σ² und Mittelwert null. Die Phase θ_t ist für Blöcke von m Bits konstant.When transmitting over the blockwise coherent AWGN channel, the received signal is given by

where y _{t is} the received vector of length t, x _{t is} the modulated transmitted vector of length t and n _{t is} the Gaussian noise vector of length t samples. It should be noted that x _{t is} obtained from the non-binary codeword symbol by assigning it to a binary sequence and modulating it. The noise samples are circular symmetric Gaussian random variables with a variance of 2σ ² and zero mean. The phase θ _t is constant for blocks of m bits.

Each non-binary symbol of the Galois field of order q is assigned to a sequence of p = log ₂ (q) bits, using its polynomial representation. These bits are then modulated and sent on the channel. The vector x _t of length t bits contains the binary representation of t / p Galois field symbols, wherein in the following it is assumed for the sake of simplicity that t is a multiple of p.

The decoding of the MR codes is performed as follows. For each VN, the q-dimensional PMF P (β) is calculated, where β is a generic field element of the Galois field of order q.

Here I _{0 is} the modified Bessel function of the first kind and the order zero. The PMF serves as an initial channel message to begin decoding the Tanner graph of the code.

In order to reduce the complexity, it is possible to perform the first decoding step instead of BP on the entire Tanner graph as follows. In each degree, a VN (repeat of the VNs in the mother code) transmits its channel message (probabilities) to its root (VN of the mother code) where a new probability is calculated (new virtual channel message). Then, the decoding of the mother code is performed using the new channel message. This can be done with the same performance as decoding across the entire graph, because VNs with a degree of 1 do not transmit any probabilities other than their own.

Rate-compatible non-binary LDPC codes concatenated with multiplicative repetition codes exhibit excellent performance for various code rates on Gaussian channels. However, when considering blockwise non-coherent AWGN channels - which are actually of interest to a number of communication systems - they experience a notable loss in terms of channel capacity. The reason for this is that they do not exploit the fact that the channel phase remains constant over a block of modulation symbols.

The publication GORGOGLIONE, M .; SAVIN, V .; DECLERQ, D .: Full Diversity NB-LDPC Coding with Non-Binary Repetition Symbols over the Block Fading Channel. In: International Symposium on Wireless Communication Systems, August 2012, pp. 969-973. ISSN 2154-0217 describes a method for recovering corrupted data where the data is encoded using a non-binary LDPC code and sent to a receiver over a lossy transmission channel. The data is decoded using the LDPC code. A non-binary LDPC code is used here. The transmission channel is a non-coherent channel.

It is an object of the present invention to provide a method for recovering lost and / or corrupted data transmitted through a non-coherent channel, the method allowing for improved data throughput.

This object is achieved by the features of claim 1 of the invention.

In the method according to the invention, data is transmitted from a transmitting device to a receiving device. Prior to transmission, the data is encoded using an encoder connected to the transmitting device. Data is transmitted over a non-coherent transmission channel and then decoded using a decoder connected to the receiving device. This will restore lost and / or corrupted data during decoding.

The coding is performed using a non-binary LDPC code with values taken from a Galois field (GF) and defining the decode decoding matrix of the code.

According to the invention, the transmission channel is a noncoherent channel, which means that the phase of the sinusoidal carrier signal of the transmitted signal changes over time, but is partially constant at certain times, as is the case for frequency hopping systems, for example.

The LDPC code used for coding and decoding is concatenated with a multiplicative repetition code, which means that a codeword represented by a variable Node of the Tanner-Graph representation of the mother LDPC code is multiplied by a coefficient which is taken from the Galois field (GF) of the non-binary LDPC code and transmitted again to the receiving device to increase the redundancy of the transmitted data.

The invention is characterized in that the probability that a variable Node (VN) m of the mother LDPC code has a certain value from the Galois field (GF) is calculated block by block for variable nodes having a constant phase.

In simple terms, the inventive method uses the fact that the channel phase is constant for some of the corresponding variable nodes (ie, the phase does not change between these variable nodes). This information is used to calculate, in blocks, the probability that a variable Node has a particular value, which means that this probability is not individual is calculated for each variable Node, but for more than one variable Node. It is preferable to calculate this probability block by block for all variable nodes having the same phase.

In the following, an algorithm which can be used for the method according to the invention will be described in more detail. For simplicity, symmetric modulation constellations are considered. Then, for a given SNR and a particular VN, the first two terms (anything except the Bessel function) in (1) can be considered scaling factors that are equal for each field element β and thus negligible. It should be noted that the probabilities in the BP decoder are always normalized to 1. As a result, we consider the Bessel function, ie P (β) α I ₀ (1 / σ² | (x _p ^(β) , y _p ) |) (2)

The inner product in the argument of the Bessel function in (2) corresponds to a (complex) correlation calculation between y _p and x _p . This calculation is performed separately for each VN. Since t / p symbols have the same channel phase, the calculation in (2) does not take into account the information resulting from the constant channel phase over t / p symbols.

The idea in the present patent application is to modify the calculation of the correlations over several symbols. For this, the decoding of the multiplicative repetition LDPC code is divided into two steps. In the first, the correlations are determined over several symbols and from these the probability function for the variable Nodes in the mother graph is determined. In a second step BP is executed on the mother graph.

It takes into account a VN m in the parent code and its r repetitions, where r represents the repetition length. For the purpose of illustration only, it is assumed that the mother VN is not transmitted (punctured) but only his / her replica. It should be noted that if VN m is not to be punctured, it can be made identical to one of the replicas. From these r VNs, the VNs V _{i are} identified which have the same channel phase θ _j . They form the set S _j . Since the phase may vary within r code symbols, multiple sets S _{j may} exist, each of which is associated with a different phase. They form the set S. For every β of the Galois field the q dimensional correlation is calculated f _i (β): = (x _p ^(β) , y _p ⁽ⁱ⁾ ) for i, so that V _i in S _j . Here, the vector x _p ^(β) of length p denotes the modulated sequence associated with the Galois field code symbol β and y _p ⁽ⁱ⁾ denotes the received sequence for the VN V _i .

The non-binary coefficients of the Parity Check Matrix result in a permutation of the Graphnachrichten, which go to the r repetitions. The permutation of these repetitions is defined as ω = π _i (β) and their inverse as β = π _i ^-1 (ω). Then, the cumulative correlation is obtained for all y _p ⁽ⁱ⁾ such that V _{i is} in S _j

Furthermore, the probability function assigned to S _j is defined as P _j (β) α I ₀ (1 / σ 2 | F _j (β) |), where the total probability function for the parent VN is m:

The above multiplication includes all probability functions P _{j associated} with the different sets S _j in S. Now it is possible to continue with standard BP over the mother graph, assuming P (β) as new (virtual) channel messages at mother VN m.

As will be shown later, the method of the invention provides a significant improvement in performance.

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

1 Shows the basic concept of an MR LDPC code.

2 Shows the performance of the method according to the invention in comparison to the prior art.

1 has already been described in connection with the prior art.

To illustrate the performance gain from the described invention, the limits for iterative decoding of MR codes were calculated via block-wise correlated Gaussian channels with BPSK modulation. The results are presented for Galois fields of order 256, both for standard decoding of MR codes and for the improved. Decoding approach. It is assumed that the channel phase is constant over the r repetitions, where r is the repetition length. The considered mother code is a non-binary regular (2,3) LDPC code. The non-zero coefficients of the parity-check matrix were chosen randomly from GF (q) \ {0}. The repetition rate is varied between 1 and 6, which means that the results include code rates between 1/3 and 1/18.

As in 2 For R = 1/3, both decoding algorithms offer the same performance, since the channel phase is constant only over one symbol. There is a repetition length of 1. For R = 1/6, there is a repetition length of 2 and the phase is chosen to be constant over 2 symbols. Here, the improved decoding algorithm may benefit from the joint computation of the correlation, whereas the original decoding algorithm of K. Kasai, D. Declercq, C. Poulliat, and K. Sakaniwa, "Rate-compatible non-binary LDPC codes concatenated with multiplicative repetition codes," in proc. 2010 IEEE Int. Symp. At Information Theory, Austin, Texas, USA, Jun. 2010 does not do this. Therefore, the gap in capacity for the latter increases with increasing repetition length. Considering the improved decoding algorithm, the iterative decoding limits for the LDPC code ensembles are always close to the channel capacity and show clear advantages compared to standard decoding. For example. For example, for a code rate of 0.11, the improvement due to the proposed approach is nearly 2 dB in E _s / N ₀ .

The proposed method can be used in all types of wireless and wired transmission systems. All systems that require particularly efficient channel codes over blockwise non-coherent AWGN channels can take advantage of the proposed method.

Claims (3)

A method of restoring lost and / or corrupted data transmitted from a sending device to a receiving device, the method comprising the steps of: encoding said data using an encoder connected to the sending device, transmitting that data from the sending device to the receiving device via a transmission channel and decoding this data using a decoder connected to the receiving device, recovering lost and / or corrupted data during decoding, the encoding being performed using a non-binary LDPC code having values from a Galois field (GF) and the decoding is performed by solving the system of equations defined by the decoding matrix of the code, the transmission channel being a noncoherent channel, which means that the phase of the sinusoidal carrier signal of the transmitted signal changes over time, but is constant at certain time intervals, the LDPC code used for coding and decoding being concatenated with a multiplicative repetition code, in that a codeword generated by a variable Node in the Tanner graph Representation of the parent LDPC code is multiplied by a coefficient taken from the Galois field (GF) of the LDPC non-binary code and retransmitted to the receiving device to increase the redundancy of the transmitted data. characterized in that the probability that a variable Node (VN) m of the mother LDPC code has a certain value from the Galois field (GF) is calculated block by block for all variable nodes having a constant phase. Method according to claim 1, characterized by the following method steps: selecting the r replicas of a parent VN m or alternatively VNm in the mother code and its r - 1 repeats, where r represents the repetition length, identifying between these r VN's VN's V _j , which have the same channel phase θ _j , so that they form a set S _j , where for each β of the Galois field the q-dimensional correlation is calculated according to: f _i (β): = (x _p ^(β) , y _p ⁽ⁱ⁾ ) for i such that V _j in S _j , which means that all V _{j have the} same phase, where the vector x _p ^(β) of length p denotes the modulated sequence associated with the Galois field code symbol β and y _p ⁽ⁱ⁾ denotes the received sequence for the VN V _i , wherein the non-binary coefficients of the parity check matrix cause a permutation of the graph messages which go to the repetitions, the permutation of the repetitions being defined as ω = π _i (β) and its inverse as β = π _i ^-1 (ω) and the permutation for the nut variable Node in the non-punctured case β = π _i (β), determining the cumulative correlation for all y _p ⁽ⁱ⁾ , so that V _{i is} in S _j

Define the probability function associated with S _j as P _j (β) α I ₀ (1 / σ 2 | F _j (β) |), where the total probability function for the mother is variable Node m

the above multiplication being carried out over all the P _{j associated} with the sets S _j in S. Process according to claim 2, characterized by the following additional process step: Continue with a belief propagation algorithm over the parent LDPC graph, assuming P (β) as new channel messages.

Images