Bidirectional Hu man Coding

Under what conditions can Huuman codes be eeciently decoded in both directions? The usual decoding procedure works also for backward decoding only if the code has the aax property, i.e., both preex and suux properties. Some aax Huuman codes are exhibited, and necessary conditions for the existence of such codes are given. An algorithm is presented which, for a given set of codeword lengths, constructs an aax code, if there exists one. Since for many distributions there is no aax code giving the same compression as the Huuman code, a new algorithm for backward decoding of non-aax Huuman codes is presented, and its worst case complexity is proved to be linear in the length of the encoded text.