Bounds on the Pseudo-Weight of Minimal Pseudo-Codewords of Projective Geometry Codes

TL;DR

This paper establishes bounds on the pseudo-weight of minimal pseudo-codewords in type-I projective geometry LDPC codes, which are crucial for understanding their decoding performance.

Contribution

It provides new upper and lower bounds on the pseudo-weight of minimal pseudo-codewords in PG-LDPC codes, advancing the analysis of their decoding behavior.

Findings

Bounds on pseudo-weight are derived for minimal pseudo-codewords.

Results improve understanding of decoding performance for PG-LDPC codes.

The bounds help in assessing the error-correcting capabilities of these codes.

Abstract

In this paper we focus our attention on a family of finite geometry codes, called type-I projective geometry low-density parity-check (PG-LDPC) codes, that are constructed based on the projective planes PG{2,q). In particular, we study their minimal codewords and pseudo-codewords, as it is known that these vectors characterize completely the code performance under maximum-likelihood decoding and linear programming decoding, respectively. The main results of this paper consist of upper and lower bounds on the pseudo-weight of the minimal pseudo-codewords of type-I PG-LDPC codes.