Channel Codes Homepage

Channel coding, also called forward error correction (FEC) or error correction coding, is used in every digital communication system today. They detect and correct bit errors, that occur during transmission of data via noisy channels, e.g., radio channels.

Over the years different type of codes have been invented starting with classical codes, like Hamming, convolutional, BCH or Reed-Solomon codes to modern coding schemes like Turbo, LDPC or Polar codes. Nearly all utilized codes are linear blockcodes, that can be described by a parity check matrix. In some cases the parity check matrix is defined by mathematical definitions, in some cases they are standardized and in others they have been designed by heuristics and experience.

Here, we provide a database of various parity check matrices of different standardized and customly designed LDPC codes, LTE turbo codes, BCH, Reed-Solomon codes, non-binary LDPC codes and Polar codes:

To Channel Codes Database


To correct errors sophisticated decoding algorithms are applied at the receiver side to correct bit errors that occurduring transmission. These algorithms, however, are most often only suboptimal heuristics, meaning that they do not reach the theoretical error-correcting potential of the coding system, called maximum-likelihood performance.

In our research project we simulate channel codes under optimal, i.e., maximum-likelihood (ML) decoding. The results were obtained by modelling the decoding problem as an integer program (IP) and then solving that model by methods of mathematical optimization.

On this homepage we provide frame-error-rate (FER) curves for channel codes under ML decoding. The FER results can be used as a reference or bound for researchers that work on improving decoding algorithms towards ML performance. The results are available for free download.

To Maximum-Likelihood Decoding Results

How to Cite

If you use these results in your publication, please cite our website as:

Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft, Stefan Ruzika, and Norbert Wehn. Database of Channel Codes and ML Simulation Results., 2023.


A cooperation of RPTU and University Koblenz Landau

ML Simulation Results
Channel Codes Database
Matrix File Formats
Related Publications