On channel dispersion per unit cost

The fundamental tradeoff of channel coding per unit cost in the fixed-error probability regime is investigated for discrete memoryless channels in the presence of a free input symbol. The speed of convergence to the capacity per unit cost in the absence of feedback is characterized in terms of a characteristic of the channel and cost function, which is referred to as ε-dispersion per unit cost. Further, a sufficient condition for feedback to improve this convergence speed is provided.