A novel evaluation function for LT codes degree distribution optimization

Luby transform (LT) codes implements an important property called ratelessness, meaning a fixed code rate is unnecessary and LT codes can complete the transmission without channel status. The property is advantageous to transmit over certain environments such as broadcasting in heterogeneous networks or transmitting data over unknown channels. For this reason, improving LT codes is a crucial research issue in recent years. The performance of LT codes is decided by the code length and a probability mass function, called degree distribution, used in the encoding process. To improve the performance of LT codes, many studies proposed to optimize the degree distribution by using methods in evolutionary computation. One of the key steps in the evolutionary process is to evaluate decision variables for comparing the fitness of each individual. In the optimization of LT codes, it needs to repeatedly simulate the encoding/decoding process with a given distribution and evaluate the performance over a sufficient number of runs. Hence, a lot of computational resource is necessary for the optimization of LT codes. In this paper, we propose a heuristic function to evaluate the performance of LT codes. The evaluation function estimates the expected fraction of unsolved symbols with the specified code length, reception overhead, and degree distribution. Based on the proposed function, a huge number of evaluations is possible for searching for better degree distributions. We first verify the practicality of the proposed function and then employ it in a multi-objective evolutionary algorithm to investigate the tradeoff of LT codes between the computational cost and decoding performance.