Combined error correcting and compressing codes

Traditionally the two encoding operations of compression and error detection/correction are at odds with one another. In the cases where these two encoding operations are combined, they are generally done as two separate encoding steps. Error correcting and compression coding (ECCC) explores the possibility of performing both compression and error correction in a single coding step. ECCC encodes using codewords of varying lengths, but selects codewords such that a minimum Hamming (1980) distance between codewords is maintained, enabling error detection and correction. Four results are presented. First, a motivating example of ECCC is shown. Second, a generalization of the Kraft-McMillen inequality bounding the existence of ECCC codes is presented. Third, preliminary techniques for generating ECCC codes are explored. Finally, a construction is presented which allows more complex ECCC codes to be built from simple codes