Redundancy estimates for the Lempel–Ziv algorithm of data compression Original Research Article

The problem of non-distorting compression (or coding) of sequences of symbols is considered. For sequences of asymptotically zero empirical entropy, a modification of the Lempel–Ziv coding rule is offered whose coding cost is at most a finite number of times worse than the optimum. A combinatorial proof is offered for the well-known redundancy estimate of the Lempel–Ziv coding algorithm for sequences having a positive entropy.