Novel Degree Distribution Function for LT codes over Finite Field

TL;DR

This paper introduces a new degree distribution function for LT codes over finite fields, aiming to enhance decoding success rates while maintaining sparsity, with simulations demonstrating superior performance over existing functions as field size increases.

Contribution

A novel degree distribution function for LT codes over finite fields that improves decoding success rate and maintains sparsity, outperforming previous distributions in larger fields.

Findings

Improved decoding success rate with the new distribution.

Maintains sparsity of encoding matrix.

Performs better than existing distributions as field size increases.

Abstract

Luby Transform (LT) code over finite field is a recent research topic. In order to find out the properties of LT codes over finite field, a novel degree distribution function is proposed in this paper. The main thinking of our developed distribution function is to improve the decoding success rate with the same overhead, and still to keep the sparse property for the encoding matrix. Numerical simulations are used to show the general performance of our novel function. Various simulation results show that in the environment of LT codes over finite field, our new degree distribution function performs much better than the degree distribution functions proposed by Luby as the field size increasing. In conclusion, our novel degree distribution function is more suitable to be used in LT codes over finite field.