Minimum-Distance Codewords

Database of Minimum-Distance Codewords

This webpage provides lists of minimum-distance codewords for low-density parity-check (LDPC) codes adopted in various wireless communication standards, including 5G NR, IEEE 802.11n (Wi-Fi), IEEE 802.11ad (WiGig), IEEE 802.15.3c (mmWave WPAN), IEEE 802.16 (WiMAX), and IEEE 802.22 (Cognitive WRAN). The website will be updated to include minimum-distance codewords for additional standards.

The minimum-distance codewords listed on this webpage were obtained using techniques developed in our recent work, “A Branch-and-Cut Algorithm for Enumerating Minimum-Distance Codewords in Quasi-Cyclic LDPC Codes,” which is currently under review in IEEE Transactions on Communications. This work was contributed by Junseo Park, Eugene Ha, and Jeongseok Ha.

The minimum-distance data provided on this webpage may be freely used for academic purposes provided that this website and the related work are properly cited. For commercial use, prior permission from Jeongseok Ha is required; inquiries may be sent to jsha@kaist.edu. We are currently developing code-design tools based on minimum-distance enumeration techniques and welcome opportunities for research collaboration.

Requests for the enumeration of minimum-distance codewords of LDPC codes may be sent to jsha@kaist.edu. Each request will be considered subject to the availability of computational and human resources. Please include the following information:
1. The parity-check matrix in MATLAB sparse-matrix format
2. For QC-LDPC codes, the base matrix and lifting size

Database of minimum distance codewords

Notes

  • $d_{\min}$: Minimum distance of the code
  • $A_{d_{\min}}$: Number of minimum-distance codewords
  • $N$: Code length
  • $R$: Code rate
  • $Q$: Lifting size of the QC-LDPC codes
  • Codeword file format: Each file lists the positions of the 1s in a codeword, one codeword per line. The indices range from $1$ to $N$ (1-based indexing)