On the maximum redundancy of CSE for I.I.D. sources

Dubé and Beaudoin proposed a new technique of lossless data compression called compression via substring enumeration (CSE) in 2010. We present an upper bound of the amount of bits used by lossless compression via the CSE technique to encode any given binary string from the class of independent and identically distributed (i.i.d.) sources. We compare the worst case maximum redundancy obtained by the CSE technique with the least possible value of the worst case maximum redundancy obtained by the best fixed-to-variable length code satisfying the Kraft inequality. We also consider the optimality of the CSE code from the view point of overflow and underflow probabilities.