|| Asymptotic Analysis of Factored LT codes for Distributed Matrix Multiplication
||Asit Kumar Pradhan, Anoosheh Heidarzadeh, Krishna Narayanan, Texas A & M University, United States|
||D4-S4-T1: Coded Distributed Matrix Multiplication II
||Thursday, 15 July, 23:00 - 23:20
||Thursday, 15 July, 23:20 - 23:40
This work considers the asymptotic analysis of factored LT (FLT) codes which we proposed previously for distributed matrix multiplication. We show that all nodes in the Tanner graph of a randomly sampled code have a tree-like neighborhood with high probability. This ensures that the density evolution analysis gives a reasonable estimate of the average error performance of FLT codes. In addition, using Azuma–Hoeffding inequality, we derive concentration results to show that the error performance of a randomly chosen FLT code is close to the ensemble average. Our simulation results indicate that the error performance concentrates around the ensemble average for moderate values of blocklength.