Tutorial on Lempel-Ziv Data Compression Algorithm

In many scenario of digital communication and data processing, we may deal with strings of data which have certain structural regularities, making it possible for time-saving techniques of data compression. Given a discrete data source, the data compression problem is first to identify the limitations of the source, and second to devise a coding scheme which will best compress it subject to certain performance criteria. If the relevant source parameters have been identified, the problem reduces to one of minimumredundancy coding. When no a priori knowledge of the source characteristics is available, and if statistical estimation are either impossible or unreliable, one must resort to universal coding schemes whereby the coding process is interlaced with a learning process for the varying source characteristics. Therefore, such coding schemes inevitably require a larger working memory space. The Lempel-Ziv Data Compression Algorithm[1] (sometimes called LZ ’77) is one of universal coding scheme which can be applied to any discrete source and whose performance is comparable to certain optimal fixed code book schemes designed for completely specified sources. This compression algorithm is adapted from the concept of encoding future segments of the source-output by maximum-length copying from a buffer containing the recent past output. The transmitted codeword consists of the buffer address and the length of the copied segment. At the decoding end, the source data can readily be reconstructed with a predetermined initial load of the buffer and the information contained in the codewords. In Section II, this coding scheme will be described in detail. In Section III, we give bounds on the compression efficiency attainable with full a priori knowledge of the source by fixed code book schemes, and then show that the efficiency of LZ ’77 with no a priori knowledge of the source approaches those bounds. Then, in Section IV, we will provide some improvements on the original algorithm. Finally, in Section V, some applications of LZ ’77 will be demonstrated.