Generalized product constructions

Talk by Ghid Maatouk

Date: 21.10.13  Time: 11.00 - 12.00  Room:

Abstract: We present two generalizations of product codes. First, we introduce and analyze irregular product codes, a generalization where rows and columns of codeword matrices are not restricted to a single row and column code but can come from a distribution of component codes of varying rates. We characterize the rate of these codes and give families of irregular product codes based on MDS component codes that achieve rate 1 - epsilon on erasure channels of parameter epsilon (at the cost of a growing field size). We also exhibit finite-length irregular product codes that outperform all regular product codes of similar rate on erasure channels. Second, we discuss staircase codes, a product-like construction introduced by Smith et al. that combines a short component code in two dimensions in a "continuous" fashion. Motivated by the improvement that these codes present over their component code, we seek to push this improvement further by going to higher dimensions still. We abstract out the properties of staircase codes that allow them to be generalized to higher dimensions and present a three-dimensional staircase code construction.