Pseudocodeword weights for non-binary LDPC codes

TL;DR

This paper investigates pseudocodewords in non-binary LDPC codes, defining their weights on various channels and establishing lower bounds on their minimum pseudocodeword weights for different modulation schemes.

Contribution

It extends the weight definitions of pseudocodewords to q-ary LDPC codes and channels, providing theoretical bounds applicable to multiple modulation formats.

Findings

Defined pseudocodeword weights for q-ary LDPC codes on symmetric and AWGN channels

Extended weight definitions to q-PAM and q-PSK modulations

Established tree-based lower bounds on minimum pseudocodeword weight

Abstract

Pseudocodewords of q-ary LDPC codes are examined and the weight of a pseudocodeword on the q-ary symmetric channel is defined. The weight definition of a pseudocodeword on the AWGN channel is also extended to two-dimensional q-ary modulation such as q-PAM and q-PSK. The tree-based lower bounds on the minimum pseudocodeword weight are shown to also hold for q-ary LDPC codes on these channels.