Allocating Redundancy Between Erasure Coding and Channel Coding When Fading Channel Diversity Grows With Codeword Length.

A transmitter sends a packetized message over a fading channel using packet-level erasure coding and physical-layer channel coding of each resultant packet. Given an overall code rate, this paper finds the optimal rates of the erasure code and the channel code to minimize the transmit power required for a certain message error probability. This paper considers a practically important fading model in which the number of block fades in a transmitted channel codeword increases with the codeword length. Such a model applies, for example, in a time-varying channel with a fixed coherence time. The rate at which diversity grows with codeword length plays an important role in the optimization problem. If the diversity growth factor is large enough, then the erasure code plays a minor role, having an optimal rate that is essentially nondecreasing with decreasing overall rate. We prove analytically that, on a channel with linear growth in diversity, as overall rate decreases, the optimal erasure code rate eventually increases to its maximum possible value (e.g., a rate of 1 for an erasure code with no overhead). Additionally, we also consider the optimization problem of minimizing the message error probability given a transmit power. Numerical results again show that erasure coding is not necessary when overall code rates are sufficiently low. [ABSTRACT FROM PUBLISHER]