Protograph-based LDPC codes with chordless short cycles and large minimum distance
- Resource Type
- Conference
- Authors
- Amirzade, Farzane; Sadeghi, Mohammad-Reza; Panario, Daniel
- Source
- 2022 17th Canadian Workshop on Information Theory (CWIT) Information Theory (CWIT), 2022 17th Canadian Workshop on. :16-20 Jun, 2022
- Subject
- Communication, Networking and Broadcast Technologies
Conferences
Parity check codes
Numerical models
LDPC codes
girth
Tanner graph
elementary trapping set
chordless cycles
minimum distance
- Language
Controlling small size trapping sets and short cycles can result in LDPC codes with large minimum distance $d_{\min}$. We prove that short cycles with a chord are the root of several trapping sets and eliminating these cycles increases $d_{\min}$. We show that the lower bounds on $d_{\min}$ of an LDPC code with chordless short cycles, girth 6 and column weights $\gamma$ is $2\gamma$. This is a significant improvement compared to the existing bounds $\gamma+1$ • Several exponent matrices of protograph-based LDPC codes with chordless short cycles are proposed for any type of pro-tographs, single-edge and multi-edge. These numerical results as well as simulations show that the removal of short cycles with a chord improves previous results in the literature.