New Upper and Lower Bounds on Exponentially Weighted Average Length of Optimal Binary Prefix Codes

Abstract

In this paper, we consider the exponentially weighted average codeword length introduced by Campbell as a performance measure for source codes. This criterion assumes that the cost is an exponential function of the codeword length and includes the usual expected codeword length criterion as a special case. Such situations could arise when the cost for encoding and decoding is significant, or if the buffer overflow caused by long codewords is a serious issue. Under Campbell's average codeword length criterion, we derive new upper and lower bounds on the exponentiated expected length of optimal binary prefix codes when partial information about the source symbol probabilities is available.