On the derivation of the optimal payload size for packet based transmission over a binary symmetrical communication channel

A criterion function for selecting the optimal payload size in data transmission over a binary symmetrical communication channel is presented. The work assumes that the packets comprise a fixed size header and variable length payload. The conventional criterion function is based on the ratio between payload size and mean number of transmitted bits per packet, which includes re-transmissions of corrupted packets. Applying a logarithm to the inverse of this criterion function makes the resulting function very suitable for mathematical analysis. This also facilitates parameter sensitivity studies without recourse to numerical methods. As such, this helps to visualise and understand the problem of optimal payload length selection when teaching courses in signal processing for communications and multimedia.