Some Results on Update Complexity of a Linear Code Ensemble

Alan Jule (1) , Iryna Andriyanova (1)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes

In this paper, the update complexity of a linear code ensemble (binary or nonbinary) is considered. The update complexity has been proposed in [1] as a measure of the number of updates needed to be done within the bits of a codeword, if one of information bits, encoded in this codeword, has been changed. The update efficiency is a performance measure of distributed storage applications, that naturally use erasure-correction coding. The ensemble maximum complexity and the average complexity are distinguished in this paper. We first propose a simple lower bound on the average update complexity γavg of a code ensemble and further evaluate a general expression for γavg. Finally, it has been shown that one can upper bound the average update complexity for binary LDPC codes, by using the computation tree approach. We show that the code ensembles with polynomial minimum distance growth are not update-efficient, i.e. they have a high update complexity. It seems that only code families with sub- polynomial minimum distance (i.e. logarithmic) are update- efficient.

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Alan Jule, Iryna Andriyanova. Some Results on Update Complexity of a Linear Code Ensemble. Network Coding (NetCod), 2011 International Symposium on, Jul 2011, China. pp.1-5, ⟨10.1109/ISNETCOD.2011.5979095⟩. ⟨hal-00671664⟩