My aim is to try out the 5G LDPC codes by using the aff3ct library. This library needs the parity check matrix loaded from a .alist or a .gc file to create the LDPC encoder. I've been looking how to generate a parity check matrix that is compliant with the 5G specs, can someone orientate me on this topic?

Thanks a lot

  • $\begingroup$ many 5G codes are actually delivered with aff3ct, did you check its website? Other than that, the Kaiserslautern LDPC codes listing has a-list files, pretty-good-codes.org (which sadly is currently down) has alists, so do a lot of other websites. You really don't have to write down the alist file from the standards specifications yourself. Other people have done that for you. $\endgroup$ Commented May 12, 2023 at 15:48
  • $\begingroup$ also, quick google: (26112,17664) 5G NR alist (no warranties) $\endgroup$ Commented May 12, 2023 at 15:53
  • $\begingroup$ (other than that, IIRC those are quasicyclic (QC) LDPC codes, so reading up on how these are represented in a base matrix probably makes a lot of things clearer. ETSI TS 138 212 specifies the base matrices for these QC codes. The thing is, if you have a QC LDPC matrix, you usually don't want to use a naive representation of the code (i.e., you don't want to use an alist) to feed your decoder, as that would lead to very inefficient decoder structure. I don't know whether aff3ct has support for QC. $\endgroup$ Commented May 12, 2023 at 15:59
  • $\begingroup$ ah, I looked that up. It does. $\endgroup$ Commented May 12, 2023 at 16:02

1 Answer 1


Aff3ct directly supports quasicyclic matrix definitions, so you don't need to expand the base matrix and generate an alist to parameterize your encoder.

See the documentation of the --dec-h-path parameter, and the --enc-type (esp. LDPC_QC) parameter.

You can thus directly use tables 5.3.2-2 and 5.3.2-3 from ETSI TS 138 212 in a .qc file as explained in the --dec-h-path documentation.

So, no need for an alist. If you, for some other purpose, need an alist, you'll have to implement the quasi-cyclic expansion. That's pretty straightforward, and even ETS TS 138 212 describes the process in 5.3.2 step 3):

The elements in $\mathbf H_{BG}$ with row and column indices given in Table 5.3.2-2 (for LDPC base graph 1) and Table 5.3.2-3 (for LDPC base graph 2) are of value 1, and all other elements in $\mathbf H_{BG}$ are of value 0.

The matrix $\mathbf H$ is obtained by replacing each element of $\mathbf H_{BG}$ with a $Z_c\times Z_c$ matrix, according to the following:

  • Each element of value 0 in $\mathbf H_{BG}$ is replaced by an all zero matrix 0 of size $Z_c \times Z_c$;
  • Each element of value 1 in $\mathbf H_{BG}$ is replaced by a circular permutation matrix $\mathbf I(P_{i , j})$ of size $Z_c\times Z_c$, where $i$ and $j$ are the row and column indices of the element, and $\mathbf I(P_{i , j})$ is obtained by circularly shifting the identity matrix $\mathbf I$ of size … to the right $P_{i , j}$ times. > The value of $P_{i , j}$ is given by $P_{i , j} =V_{i , j} \mod Z_c $ . The value of $V_{i , j}$ is given by Tables 5.3.2-2 and 5.3.2-3 according to the set index $i_{LS}$ and LDPC base graph.
  • $\begingroup$ Thanks! I thought I had to expand the matrix from the BG myself. So where can I find the .qc file of BG1 and BG2 of the standard? I don't know how to construct the .bg from the Tables you listed. $\endgroup$
    – JonPC
    Commented May 15, 2023 at 6:50
  • $\begingroup$ The documentation of aff3ct I referred to describes the QC format. You literally just have to put the content of these tables into that. $\endgroup$ Commented May 15, 2023 at 6:53
  • $\begingroup$ Oh I get it thanks! But this are very large matrices, are these base matrices available somewhere already in this format? $\endgroup$
    – JonPC
    Commented May 15, 2023 at 7:04
  • $\begingroup$ I managed to construct the matrices and parse them to the QC format. So if I want to try to encode and decode using QC_LDPC, should I give that same H matrix to both the encoder and decoder? $\endgroup$
    – JonPC
    Commented May 15, 2023 at 9:27

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