TECHNICAL FIELD The present invention relates to the field of channel coding. More specifically, the invention relates to devices and methods for generating a code for a communication apparatus as well as a communication apparatus using such a code, in particular in the context of a hybrid automatic repeat request (HARQ) scheme. BACKGROUND

Hybrid automatic repeat request (HARQ) schemes are used in communication systems to provide both efficient and reliable data transmissions. Incremental Redundancy (IR) is a HARQ method for combining the payloads from different retransmissions. A fixed retransmitted payload is currently used in the LTE system as a baseline.

Some known HARQ schemes are based on matrix-based low density parity check (LDPC). US 201 10239075 discloses a channel coding, modulating and mapping method for a HARQ scheme based on a LDPC. A uniform matrix H is considered for different code lengths. Modular or floor lifting is used to obtain a matrix with a new size of the circulant. Moreover, a constellation rearrangement strategy is disclosed, where high- order bits are mapped to reliable points in the constellation.

US 201 1 138260 discloses a row-splitting scheme to obtain the matrix for the second retransmission of the HARQ scheme. Some rows are split and some new columns are added. The splitting degree may be different for different rows.

Using low-rate codes and transmitting different sets of parity bits at different transmissions is disclosed, for instance, in US 20071 13147, US 2010192037 and US 2007220399. US 2007113147 proposes arranging transmitted parity bits at regular intervals. In US 2010192037 the transmission order of parity bits is based on their column degree. In US 2007220399 the order of transmission is based on the notion of k-step recoverable nodes. Although the conventional approaches described above already provide some improvements compared to other prior art approaches, there is still a need for improved devices and methods for generating a code for a HARQ communication apparatus. SUMMARY

It is an object of the invention to provide improved devices and methods for generating a code for a HARQ communication apparatus. The foregoing and other objects are achieved by the subject matter of the independent claims. Further implementation forms are apparent from the dependent claims, the description and the figures.

According to a first aspect the invention relates to a device for generating on the basis of a first protograph matrix P of size (m ^χ n), wherein the first protograph matrix P defines a first code H, a second protograph matrix P' of size (m + d ^χ n + d), wherein the second protograph matrix P' defines a second code H', wherein the device comprises a processor configured to generate the second protograph matrix P' by: (i) setting the elements (l :m, l :n) of the second protograph matrix P' equal to the corresponding elements (l :m, l :n) of the first protograph matrix P; (ii) setting the elements (l :m, n+l :n+d) of the second protograph matrix P' equal to -1 ; (iii) presetting the elements (m+1 :m+d, 1 :n+d) of the second protograph matrix P' equal to -1 ; (iv) setting selected elements of the elements (m+l :m+d, l :n+d) of the second protograph matrix P' to a value different from -1 ; and (v) setting the diagonal elements of the submatrix defined by the elements (m+l :m+d, n+l :n+d) of the second protograph matrix P' equal to 0. In a first possible implementation form of the device according to the first aspect, the processor is configured to set the selected elements of the elements (m+l :m+d, l :n+d) of the second protograph matrix P' equal to 0. In a second possible implementation form of the device according to the first aspect, the processor is configured to set the selected elements of the elements (m+l :m+d, 1 :n+d) of the second protograph matrix P' equal to p.

In a third possible implementation form of the device according to the first aspect, the first protograph matrix has a circulant size z and the processor is configured to set the selected elements of the elements (m+l :m+d, l :n+d) of the second protograph matrix P' equal to (-1-zero block circulant).

In a fourth possible implementation form of the device according to the first aspect as such or any one of the first to third implementation form thereof, a parameter D is associated with the number of diagonals of the first protograph matrix P and the processor is configured to set the selected elements of the elements (m+l :m+d, l :n+d) of the second protograph matrix P' to a value different from -1 by (i) determining a (1 x n) vector ColWeigWit such that ColWeig Q) is equal to the number of elements of the y ^' -th column of the first protograph matrix P, which are not equal to -1, (ii) determining a sequence i ₁ , i ₂ , ... , i _n such that ColWeigUlti )≤ ColWeigU\t[i ₂ ) ...≤ ColWeigWt[i _n ), and (iii) generating for each value of the index from 1 to d a set of indices i _ _D+2 , including all indices with k > 0 and setting for the respective value of the index j for each k being element ol the set of indices {i _ _D+1 , i _; _ _D+2 , i _j } the respective element of the second protograph matrix identified by j and k to a value different from -1.

In a fifth possible implementation form of the device according to the fourth implementation form of the first aspect, the following relation holds between the parameter D and the values d and n: D≤ d≤ n. In a sixth possible implementation form of the device according to the first aspect as such or any one of the first to fifth implementation form thereof, the first protograph matrix P and the second protograph matrix P' have the same circulant size z. In a seventh possible implementation form of the device according to the first aspect as such or any one of the first to sixth implementation form thereof, the first protograph matrix P and the second protograph matrix P' are repeat accumulate matrices.

According to a second aspect the invention relates to a communication apparatus comprising a channel encoder comprising a device for generating a protograph matrix according to the first aspect of the invention.

According to a third aspect the invention relates to a communication apparatus comprising a channel encoder comprising a first protograph matrix P or a corresponding first code H and a second protograph matrix P' or a corresponding second code H', wherein the channel encoder is configured to use the first code H for a first transmission of a HARQ scheme and the second code H' for a retransmission of the HARQ scheme and wherein the first protograph matrix P or the corresponding first code H and the second protograph matrix P' or the corresponding second code H' have been provided by a device for generating a protograph matrix according to the first aspect of the invention.

In a first possible implementation form of the communication apparatus according to the second aspect as such or the communication apparatus according to the third aspect as such, the channel encoder is configured to use the first code H for a first transmission of the HARQ scheme and the second code H' for a retransmission of the HARQ scheme for code rates smaller than a code rate threshold and to use a third code H* for a retransmission of the HARQ scheme for code rates larger than a code rate threshold, wherein the third code H* is based on a third protograph matrix, which has been derived from the first protograph matrix using a row splitting scheme. In an implementation form, the code rate threshold has a value of 0.6. According to a fourth aspect the invention relates to a method for generating on the basis of a first protograph matrix P of size (m ^χ n), wherein the first protograph matrix P defines a first code H, a second protograph matrix P' of size (m + d χ n + d), wherein the second protograph matrix P' defines a second code H', wherein the method comprises: setting the elements (l :m, l :n) of the second protograph matrix P' equal to the corresponding elements (1 :m, 1 :n) of the first protograph matrix P; setting the elements (1 :m, n+1 :n+d) of the second protograph matrix P' equal to -1 ; pre-setting the elements (m+l :m+d, l :n+d) of the second protograph matrix P' equal to -1 ; setting selected elements of the elements (m+l :m+d, l :n+d) of the second protograph matrix P' to a value different from -1 ; and setting the diagonal elements of the submatrix defined by the elements (m+1 :m+d, n+1 :n+d) of the second protograph matrix P' equal to 0.

In a first possible implementation form of the method according to the fourth aspect of the invention as such, a parameter D is associated with the number of diagonals of the first protograph matrix P and the step of setting selected elements of the elements (m+l :m+d, l :n+d) of the second protograph matrix P' to a value different from -1 comprises the following steps: (i) determining a (1 ^χ n) vector ColWeig t such that ColWeig it(j) is equal to the number of elements of the j-t column of the first protograph matrix P, which are not equal to -1 ; (ii) determining a sequence i _lt i _2l — , i _n such that ColWeig ^) < ColWeigmt{i ₂ ) ... < ColWeigU\t[i _n ); and (iii) generating for each value of the index j from 1 to d a set of indices i _j -D+2>— including all indices with k > 0 and setting for the respective value of the index j for each k being element of the set of indices {i _j -D+i _> i _j -D+2>— _> i _j } ^me respective element of the second protograph matrix identified by j and k to a value different from -1.

The method according to the fourth aspect of the invention can be performed by the device according to the first aspect of the invention. Further features and implementation forms of the method according to the fourth aspect of the invention result directly from the functionality of the device according to the first aspect of the invention and its different implementation forms. According to a fifth aspect the invention relates to a computer program comprising program code for performing the method according to the fourth aspect when executed on a computer.

The invention can be implemented in hardware and/or software.

BRIEF DESCRIPTION OF THE DRAWINGS Further embodiments of the invention will be described with respect to the following figures, wherein:

Fig. 1 shows a schematic diagram illustrating an apparatus for generating a code for a HAQR communication apparatus according to an embodiment;

Fig. 2 shows a schematic diagram illustrating a communication system comprising a HARQ communication apparatus according to an embodiment;

Fig. 3 shows a schematic diagram illustrating the performance of a HARQ communication apparatus according to an embodiment;

Fig. 4 shows a schematic diagram illustrating the performance of a HARQ communication apparatus according to an embodiment; Fig. 5 shows a schematic diagram illustrating a first matrix and a second matrix generated by an apparatus for generating a code according to an embodiment;

Fig. 6 shows a schematic diagram illustrating the performance of a HARQ communication apparatus according to an embodiment;

Fig. 7 shows a schematic diagram illustrating the performance of a HARQ communication apparatus according to an embodiment; and Fig. 8 shows a schematic diagram illustrating a method for generating a code for a HARQ communication apparatus according to an embodiment. In the various figures, identical reference signs will be used for identical or at least functionally equivalent features.

DETAILED DESCRIPTION OF EMBODIMENTS In the following description, reference is made to the accompanying drawings, which form part of the disclosure, and in which are shown, by way of illustration, specific aspects in which the present invention may be placed. It is understood that other aspects may be utilized and structural or logical changes may be made without departing from the scope of the invention. The following detailed description, therefore, is not to be taken in a limiting sense, as the scope of the invention is defined be the appended claims.

For instance, it is understood that a disclosure in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa. For example, if a specific method step is described, a corresponding device may include a unit to perform the described method step, even if such unit is not explicitly described or illustrated in the figures. Further, it is understood that the features of the various exemplary aspects described herein may be combined with each other, unless specifically noted otherwise.

Figure 1 shows a schematic diagram illustrating a device 100 for generating a code for a HARQ communication apparatus, for instance, the HARQ communication apparatus 210 of the communication system 200 shown in figure 2. Before describing the device 100 shown in figure 1 and the HARQ communication apparatus 210 shown in figure 2 in more detail, the following definitions and notation will be introduced. Let P be a (m ^χ n) protograph matrix and z is a circulant size, that is,

such that - 1 < ρ _έ · < z - 1.

The LDPC code, in particular QC-LDPC code, of length n ^■ z corresponding to protograph matrix P is defined by the (m ^■ z ^χ n · z) parity-check base matrix H

H = H(P) =

where the circulant permutation matrix (CPM) Ai represents either the [z ^χ z ) zero matrix Z if py = - 1, or the (z ^χ z ) circulant permutation matrix /(p ) obtained by cyclically right-shifting the (z ^χ z ) identity matrix 7(0) by p; _j positions. In embodiments of the invention, H represents a first LDPC code, in particular a first QC-LDPC code, which is used for the first transmission of a HARQ scheme, in particular an incremental redundancy (IR) HARQ scheme. In embodiments of the invention, the protograph matrix P is a repeat accumulate (RA) protograph matrix, which can be beneficial in communication systems, because the corresponding parity- check matrix has easy-encoding properties: P =

the above exemplary representation of the protograph matrix P the first row has been included for clarity to indicate which bits are either information bits or parity bits. The first column has been included to identify the row. As already described above, each (m 1 ) column of P corresponds to (m ^■ z ^χ z ) submatrix of H(P), that is, i _j corresponds to a group of z information bits as well as p _j .

The device 100 for generating a code for a HA Q communication apparatus comprises a processor 101. The processor 101 of the device 100 is configured to generate on the basis of a first protograph matrix P corresponding to first code H a second protograph matrix P' corresponding to a second code H'. In an embodiment, the first code is based on a first protograph matrix P having m rows and n columns, i.e. a (m ^χ n) matrix. In an embodiment, the first protograph matrix P has a circulant size z. Herein the first protograph matrix will be denoted as P or P _l5 whereas the second protograph matrix will be denoted as P* or P ₂ . Further protograph matrices will be denoted as Pj with i > 2.

In an embodiment, the second protograph matrix P' is a matrix of dimensions (m + d n + d) and also has a circulant size z. Thus, the parameter d defines the number of additional rows and columns of the second protograph matrix P' in comparison to the first protograph matrix P.

The additional parameter D is related to the number of diagonals of the first protograph matrix P. In an embodiment, the following relation holds: D≤ d≤ n. 01

10

In a first stage, the processor 101 of the device 100 is configured to determine a (1 x n) vector CoiWeig t such that ColWeig®t(j) is equal to the number of Pi ≠ - 1, 1 < i < n. In a second stage, the processor 101 of the device 100 is configured to find a sequence i _t , i ₂ , ... , i _n such that ColWeig®t{i- \≤ ColWeig®t[i ₂ ) ... < ColWeig®t{i _n }.

In a third stage, the processor 101 of the device 100 is configured to predetermine the upper part of the second protograph matrix P' as a (m ^χ n + d) matrix of -l's. Moreover, the processor 101 of the device 100 is configured to set the first n columns of the upper part of the second protograph matrix P' equal to the corresponding columns of the first protograph matrix, i.e. UpPart(l :m, 1 :n) = P.

In a fourth stage, the processor 101 of the device 100 is configured to predetermine the lower part of the second protograph matrix P' as a (d ^χ n + d) matrix of -l 's. Moreover, the processor 101 of the device 100 is configured to set selected elements of the lower part of the second protograph matrix P' to values different from -1. In an embodiment, the processor 101 of the device 100 is configured to set the selected elements of the lower part of the second protograph matrix P' to one of the following values: 0, p or (-1 - zero block circulant).

In an embodiment, the processer 101 of the device 100 is configured to select the elements of the lower part of the second protograph matrix P' to be set to values different from -1 in the following manner. For each value of the index j from 1 to d the processor 101 is configured to generate the set of indices { ij_ _D+1 , ij_ _D+2 , ... , ij} including all indices with k > 0 and to set for the respective value of the index j for each k being element of the set of indices {i _; _ _D+1 , i _ _D+2 , ... , i } LowPart(j, k) to a value different from -1. Put differently, the processor 101 of the device 100 is configured to perform the steps defined by the following pseudo code: For j = l :d

Indices = {t _; _ _D+1 , i _p+ ₂ ,— (at most D indices, i.e. we include i _k if k > 0); For k £ Indices LowPart(j, k)≠ -1;

End For

End

In a fifth stage, the processor 101 of the device 100 is configured to insert in the portion (l:d, n+l:n+d) of the lower part of the second protograph matrix P', i.e. LowPart (l:d, n+l:n+d), a zero-diagonal matrix.

The above-described stages 1 to 5 for generating the second protograph matrix P' on the basis of the first protograph matrix P can be considered as a generalized repeat accumulate (GRA) approach or algorithm. As already described above, the GRA algorithm according to embodiments of the invention takes as input the first protograph matrix P as well as the parameters d and D and generates as output the second protograph matrix P', i.e. P' = GRA (P, d, D).

In the following, an example for the above embodiments will be provided for the following first protograph matrix P having a circulant size z = 5:

For this example, D is equal to 2 and d has been selected to be equal to 4. Thus, the vector ColWeig t has the following components: ColWeigUit = (3,2,3,2,2,1)- The corresponding sequence of indices is given by (6, 2, 4, 5, 1, 3). The additional steps can be taken from the resulting second protograph matrix P' given below:

2 4 1 0 -1 -1 -1 -1 - ¹ - ¹

1 -1 3 0 0 -1 -1 -1 - ¹ - ¹

3 1 2 -1 0 0 -1 -1 - ¹ - ¹

-1 -1 -1 -1 -1 0 0 -1 - ¹ - ¹

-1 0 -1 -1 -1 0 -1 0 - ¹ - ¹

-1 0 -1 0 -1 -1 -1 -1 0 - ¹

-1 -1 -1 0 0 -1 -1 -1 -1 0 As already mentioned above, in an embodiment the selected elements can be set to a value of p. This allows to avoid short cycles of length 4 made of already assigned entries. This is generally possible, if the circulant size is at least (D-l)*m, since the number of such cycles is at most (D-l)*m.

Because of the specific structure of the obtained second protograph matrix P', easy (linear time) encoding can be performed. Indeed, the upper submatrix P(l :m,l :n+d) has a RA part and the lower submatrix P(m+1 :m+d, 1 :n+d) has a diagonal part.

As already mentioned above, in an embodiment the processor 101 is configured to set the selected elements of the lower part of the protograph matrix P' to a value of (-1 - zero block circulant), which helps to avoid harmful cycles creating a trapping set. This is important to improve decoding. In an embodiment, lifting can be performed by using the whole protograph after masking GRA circulants, which add a harmful trapping set.

This is exemplified on the basis of the following first protograph matrix P:

In this example the following mask matrix M is used

¹ 1 1 1 ^{1 1 1 1 1 1}

¹ 1 1 1 ^{1 1 1 1 1 1}

¹ 1 0 1 ^{1 1 1 1 1 1}

¹ 1 0 1 ^{1 1 1 1 1 1}

¹ 1 1 1 ^{1 1 1 1 1 1} Then the resulting second protograph matrix P' is given by the Hadamard product of the matrix P and the mask matrix M, namely

A first protograph matrix P and/or a corresponding first code H and a second protograph matrix P' and/or a corresponding second code H' as described above can be beneficially used in a HARQ scheme. In an embodiment, the first protograph matrix P and/or the corresponding first code H and the second protograph matrix P' and/or the corresponding second code H' are implemented in the communication apparatus 210 of the communication system 200 shown in figure 2.

More specifically, in an embodiment the first protograph matrix P and/or the corresponding first code H and the second protograph matrix P' and/or the corresponding second code H' can be stored in a channel encoder 213 of the communication apparatus 210, for instance, in a memory of the channel encoder 213. In such a scenario, the first protograph matrix P and/or the corresponding first code H and the second protograph matrix P' and/or the corresponding second code H' could be generated offline by the device 100 shown in figure 1 and provided to the channel encoder 213 of the communication apparatus 201. In another embodiment, the channel encoder 213 itself could comprise the device 100 shown in figure 1 for generating the second protograph matrix P' and/or the corresponding second code H' online on the basis of the first protograph matrix P. In an embodiment, the communication system 200 shown in figure 2 implements a RB-HARQ scheme. The communication system 200 comprises the transmitting communication apparatus 210 and the receiving communication apparatus 220. In an embodiment, the transmitting communication apparatus 210 and the receiving communication apparatus 220 could be a base station, a user equipment or the like.

A binary information sequence with attached Cyclic Redundancy Check code bits of overall length K denoted as u = (u(l), w(2), ... , u(/f)) is provided by a source 21 1 of the communication apparatus 210. After channel encoding by the channel encoder 213 for transmission I one obtains a binary code sequence = (c ^l (V) , c ^l (2) , ... , c ^l (N )^, wherein N denotes the number of code bits for the l-t transmission. The modulator 215 maps this sequence to a M-QAM modulated sequence x^ ^l After passing through the communication channel 220, e.g. a fully interleaved Rayleigh channel, one obtains i.e. the vector of received complex symbols:

where 0■ denotes the Rayleigh fading channel coefficient with zero mean and unit

CO . . . . o variance and n denotes the complex Gaussian noise with variance 2 · af .

The M-QAM demodulator 235 of the communication apparatus 230 can calculate channel log-likelihood ratios (LLRs) and can be implemented in Max-Log MAP fashion, so

L¾ = maxe _/eA0 log (r °, ¾°, ⁽ ¾, 0, ^■ ) ,

where

where and cf; ² are estimations of fading coefficient and noise variance respectively, A- constellation points of M-QAM, k - 1 ... , log ₂ M. Thereafter, the HARQ combiner 233 follows, where input LLRs are summed at code positions that were previously sent (Chase combining) and LLRs for new parity bits are just concatenated to form one codeword (Incremental Redundancy). This codeword is provided to the Soft Input Soft Output (SISO) channel decoder 231 of the communication apparatus 230. This channel decoder 231 can be implemented as a Turbo, LDPC or convolutional code decoders. So L corresponds to input LLRs of the SISO decoder 231 at the -th transmission and L^ _t - soft output LLRs of the decoder 231. Generally, RB-HARQ algorithms take L^ _T and in case of decoding failure (CRC fails) try to determine which bits should be retransmitted and signal it in the feedback channel 240.

In an embodiment, the communication system 200 shown in figure 2 can be implemented to perform the following steps defining a first stage of a HARQ scheme with K≥ 2 possible steps. Denote by number of columns of protograph matrix Pi, n = n^ rii+ _! > rij for case of incremental redundancy η _έ = i - n.

Take information bits with attached CRC denoted by u. Encode it using LDPC code H(P) and get codeword C _\ of length n _x · z. After modulation of the codeword, passing through the communication 220 channel, demodulation of the received signal one obtains soft information consisting of LLR's corresponding to bits of C _\ . Using parity-check matrix H(P) one can decode L _\ . After decoding the CRC can be checked. If the information is confirmed, then the correct information bits have been received. Otherwise the next stage with iter = 2 can be performed. As will be described in more detail further below, in an embodiment depending on the code rate one of the different approaches to construct the protograph P' can be used, including the GRA approach described above. On the basis thereof the following steps defining a second stage can be performed: Encode u using LDPC code H{P') and get codeword c ₂ of length n _ter · z. Since c ₂ contains j _ter _i as a subword, only the remaining part of c ₂ is transmitted, that is is transmitted. After modulation of the codeword, passing through the channel 220, demodulation of the received signal one gets soft information L' _iter consisting of LLR's corresponding to bits of CiterXCfter-.! . Then the soft information Li _ter -\ and L' _iter can be combined into Liter ( ^{m an} embodiment, this is just a concatenation into vector of length n; _ter · z). Using parity-check matrix H(P') L _iter can be decoded. After decoding the CRC can be checked. If the information is confirmed, then the correct information bits have been received. Otherwise, if iter < K the above second stage with iter = iter + 1 can be repeated.

In an embodiment, the device 100 shown in figure 1 and/or the communication apparatus 210 shown in figure 2 are configured to generate or implement different second codes based on the code rate. In an embodiment, the processor 101 of the device 100 can be configured to generate a set of K protograph matrices P ₂ , ... , P _K on the basis of a first protograph matrix Ρ _α of size m ^χ n and the number Kof maximum HARQ iterations.

In an embodiment, the proposed rate-adaption algorithms could be used for the HARQ scheme. In an embodiment, the code rate R of the first code / (Pi) can be determined

Til

as R - 1 -— . In an embodiment, for constructing P; ₊₁ based on Pi with adding di new rows and columns, one can take Q ₁ = Pi as well as any set of numbers 0 < a.j, bj,j 6 {1, + bj = d _{i s} any set of 7) G {A, B} , any set of numbers Dj < n and repeat the following procedure times:

Q _2j = RS{Q ₂ j_ ₁ , aj _j ) wherein RS( ) denotes a row-splitting algorithm for constructing a protograph matrix, which will be described in more detail further below.

The above algorithm leads to the result P; ₊₁ = Q ₂ n +i ^an d can be repeated for each i up to K - 1. For incremental redundancy di = n can be chosen, which gives rate P _j = Y for protograph matrix Pj. In an embodiment, for R > 0.6, rij = l, di = n, a _x = n, b ₁ = Ο, Τ^ = A, a single time RS approach can be used to generate the second protograph matrix.

In an embodiment, for R < 0.6, = l, dj = n, _x = 0, b _x = 0, D _t = 2, a single time GRA approach can be used to generate the second protograph matrix.

One can see that the rate of the code H[P ₂ ) corresponding to the second protograph matrix P ₂ is R/2. In other embodiments, combinations of the RS approach and the GRA approach can be used to generate the second protograph matrix P ₂ .

In an embodiment, the first protograph matrix is a repeat accumulate (RA) protograph matrix.

As already described above, in embodiments of the invention the RS approach or algorithm can be used by the device 100 to generate the second protograph matrix P'. In an embodiment, the processor 101 of the device 100 is configured to generate the second protograph matrix P' of size (m + d * n + d) with circulant size z on the basis of the first protograph matrix P of size (m ^χ n) with circulant size z using the following RS algorithm. In an embodiment, the first protograph matrix P and/or the second protograph matrix P' are RA matrices. In an embodiment, further input parameters for the RS algorithm are d - integer, option 0 6 [A, B}. In a first step of the RS algorithm a (m ^χ 1) vector RowWeig is defined, such that RowWeig i) is equal to the number of pi _j ≠ - 1, 1≤ j≤ n - m.

In a further step of the RS algorithm an integer Weight = RowWeig^ltix) is defined.

In a further step of the RS algorithm it is checked whether Weight < m + d, and, if this is the case, the RS algorithm will be terminated. If 0 = A , then the (m ^χ 1) vector splittingFactors is defined, such that splittingFactors(i) < RowWeigUlt(i), and all values of splittingFactors are close (may be equal) to each other, and∑ splittingFactors(i) = m + d.

If 0 = B, then the (m ^χ 1) vector splittingFactors is defined, such that splittingFactorsfi) < RowWeiqWt[i) and all values of ^s P ^llttin g ^Factors (0 _{are c} \ _ose & RowWeight{i)

(may be equal) to each other, and∑ splittingFactors(i) = m + d.

The vector splittingFactors(i) determines how many rows will appear in the second protograph matrix P' instead of i-th row of P. Options A and B allow to control regularity or irregularity of obtained QC-LDPC code H(P').

The Matrix P' consists of m submatrices P'[i)

P'(l)

P'(2)

P'

P'(m)

The submatrix P'(i) is obtained by splitting the i-th row of the first protograph matrix P and adding some new columns in the way, as expressed by the following pseudo code.

P'(i) is predetermined as a (splittingFactor(i) ^χ n + d) matrix of -1 's

Residue = 0;

For any j E [n - m]

lf P(i,j) = = - 1

Continue;

End If

Residue = Residue + 1 ;

Residue = mod(Residue, splittingFactor(i)); P'(i, Residue ) = P(i,y);

End For

begPos i = n - m + ∑ _¾ = splittingFactor(k) ;

Insert in P'(i, begPos(j + 1: begPos{i) + splittingFactor(i)) a (splittingFactor(i)) ^χ splittingFactor(i)) ) matrix representing a RA part of LDPC code;

End For

The second protograph matrix P' generated in the way described above has an RA part, so that easy (linear-time) encoding can be performed.

The general RS approach described above will be further illustrated on the basis of the following exemplary first protograph matrix P with circulant size 5:

Input: P and d = 4;

1) RowWeig st = (3, 2, 3) ^r ;

2) Weig t = 3 + 3 + 3 = 8;

3) Check 8 > 7;

4) A) splittingFactor = (2, 2, 3)

B) splittingFactor = (3, 1, 3)

For option A:

Rows r and r ₁₂ of the matrix P' are based on row r _x of the matrix P. Rows r ₂₁ and r ₂₂ of the matrix P' are based on row r ₂ of the matrix P. Rows r ₃₁ , r ₃₂ and r ₃₃ of the matrix P' are based on row r ₃ of the matrix P.

For option B:

Rows r _n , r ₁₂ and r ₁₃ of the matrix P' are based on row r _a of the matrix P. Row r ₂₁ of the matrix P' is based on row r ₂ of the matrix P. Rows r ₃₁ and r ₃₂ of the matrix P' are based on row r ₃ of the matrix P.

P" =

The RS approach described above leads to coherent matrices P and P' as well as the corresponding LDPC codes. Indeed, = ∑- r _i -, thus rows in each layer of P' (using the rule (- 1+k) = k and (k+k) = - 1) can be summed and the matrix P". which could be the same as P, can be obtained, if columns with zero weight, i.e. columns consist of - 1 's only, are excluded. In other words, if information bits i ₂ , i ₃ ) are encoded with the LDPC code corresponding to the protograph matrix P' resulting in a codeword i ₂ , i ₃ , p _lt p ₂ , p ₃ , P , Vs _> Ve _> P7), then a subword (i _lf i ₂ , i ₃ , p ₃ , p ₄ , p ₇ ) is a codeword of the LDPC code corresponding to the protograph matrix P with the same information bits (ί _α , i ₂ , i ₃ ) .

Embodiments of the invention allow getting a better performance (BLER and throughput) than conventional LTE HARQ systems for moderate and high code rates. In the following the performance of embodiments of the invention are illustrated for different channel conditions.

In the following, an LTE turbo code with 8 iterations and scaled Max Log MAP decoding (scale factor = 0.75 for all iterations) will be used as a comparison. By way of example, a CRC of length 24 is chosen. For the following examples the maximal number of transmissions is restricted to 2 (in case of a wrong decoding after the first transmission, the second transmission is used). Moreover, a SC-LDPC code with 30 iterations and Layered Min Sum decoding is used. Also in this case a CRC of length 24 is chosen. Two algorithms are compared. As a baseline algorithm the currently used LTE system is used.

Figures 3 and 4 show the results of simulations for the specific standard case for the downlink channel. The modulation coding scheme (MCS) index is 8, modulation is 4- QAM, data size K is 1408, coding rate (CRj) for the first transmission is 0.51, the number of resource blocks (RB) is 10, the total length of codeword is 2760.

In this case the rate of the first transmission is moderate. As consequence, according to an embodiment of the invention, the GRA approach described above will be chosen for constructing the LDPC matrix for the second transmission in such a way that at the second transmission only new parity-check bits are transmitted, i.e. the input parameter in this case is d = n. For this case, if for the first transmission a first m ^χ n protograph matrix P is used, then for the second transmission a second protograph matrix P' of size (m + n x 2n) is used. Figure 5 shows the first and second LDPC matrices for the first transmission and for the second transmission. In this example, the RA part of LDPC code is moved from the right side to the left side, as described above for the RS algorithm.

In Figure 3 the block error rate is shown for each transmission. In Figure 4 the throughput for IR-HARQ LTE protocol and IR-HARQ LDPC protocol is shown.

Figures 6 and 7 show the results for simulations for the specific standard case for the downlink channel: modulation coding scheme (MCS) index is 25, modulation is 64- QAM, data size K is 17016, coding rate (CRi) for the first transmission is 0.685, the number of resource blocks (RB) is 30, the total length of codeword is 24840. In this case the rate of the first transmission is moderate. As consequence, the RS approach is chosen for generating the LDPC matrix for the second transmission in such a way that at the second transmission only new parity-check bits are transmitted. In Figure 6 the lock error rate for each transmission is shown. In Figure 7 the throughput for IR- HARQ LTE protocol and IR-HARQ LDPC protocol is shown.

Figure 8 shows a schematic diagram of a method 800 for generating on the basis of a first protograph matrix P of size (m n), wherein the first protograph matrix P defines a first code H, a second protograph matrix P' of size (m + d ^χ n + d), wherein the second protograph matrix P' defines a second code Ή. The method 800 comprises the steps of: setting 801 the elements (l :m, l :n) of the second protograph matrix P' equal to the corresponding elements (l :m, l :n) of the first protograph matrix P; setting 803 the elements (l :m, n+l :n+d) of the second protograph matrix P' equal to -1 ; pre-setting 805 the elements (m+l :m+d, l :n+d) of the second protograph matrix P' equal to -1 ; setting 807 selected elements of the elements (m+l :m+d, l :n+d) of the second protograph matrix P' to a value different from -1 ; and setting 809 the diagonal elements of the submatrix defined by the elements (m+l :m+d, n+l :n+d) of the second protograph matrix P' equal to 0. Embodiments of the invention allow constructing an extended low-density parity check (LDPC) code H ₂ with a lower code rate (CR) from an LDPC code H ₁ with a higher CR. Embodiments of the invention can be used in an IR HARQ scheme. Embodiments of the invention address shortcomings of known methods and the performance thereof was verified in a communication system with an Additive White Gauss Noise (AWGN) channel.

Embodiments of the invention propose a beneficial alternative to the HARQ protocol currently used in LTE systems. Embodiments of the invention provide two exact algorithms which can be used to design QC-LDPC code H ₂ of dimension (m + d)z ^χ (n + d]z from the QC-LDPC code H of dimension mz ^χ nz such that the code H _t is a subcode of H ₂ . In embodiments of the invention the first algorithm is used in case H ₁ has either low or moderate rate, while the second algorithm is appropriate in case H ₁ has either moderate or high rate.

Embodiments of the invention outperform currently used in LTE systems in terms of block error rate (BLER) for each transmission and, as a consequence, in terms of throughput. Embodiments of the invention can be easily implemented and can work online. Additional overhead in complexity of decoding of the second transmission does not exceed complexity of decoding of the first transmission.

While a particular feature or aspect of the disclosure may have been disclosed with respect to only one of several implementations or embodiments, such feature or aspect may be combined with one or more other features or aspects of the other implementations or embodiments as may be desired and advantageous for any given or particular application. Furthermore, to the extent that the terms "include", "have", "with", or other variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term "comprise". Also, the terms "exemplary", "for example" and "e.g." are merely meant as an example, rather than the best or optimal. The terms "coupled" and "connected", along with derivatives may have been used. It should be understood that these terms may have been used to indicate that two elements cooperate or interact with each other regardless whether they are in direct physical or electrical contact, or they are not in direct contact with each other.

Although specific aspects have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations may be substituted for the specific aspects shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific aspects discussed herein.

Although the elements in the following claims are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence.

Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teachings. Of course, those skilled in the art readily recognize that there are numerous applications of the invention beyond those described herein. While the invention has been described with reference to one or more particular embodiments, those skilled in the art recognize that many changes may be made thereto without departing from the scope of the invention. It is therefore to be understood that within the scope of the appended claims and their equivalents, the invention may be practiced otherwise than as specifically described herein.