When are erasure correcting block codes better than convolutional codes in a multi-hop network?

Abstract

In this paper we investigate the effect of imposing a maximum allowed delay on the symbol loss probability for a set of rate 1/2 erasure correcting codes. Given some maximum allowable delay, we define the effective symbol loss probability to be the probability that a symbol is received too late or not at all. Consider a network with three nodes; source, relay, and sink. The source encodes data using an erasure correcting code, the relay decodes, recodes, and finally the sink decodes using Gaussian elimination. We compare the effective symbol loss probability of systematic triangular block codes, dense block codes, and systematic convolutional codes. For a wide range of packet loss probabilities and allowable symbol delays, our results show that the systematic triangular block codes are superior. Our results also show that the field size does not affect the gain in effective symbol loss probability.