Interleaving for combating bursts of errors

To ensure data fidelity, a number of random error correction codes (ECCs) have been developed. ECC is, however, not efficient in combating bursts of errors, i.e., a group of consecutive (in one-dimensional (1-D) case) or connected (in two- and three- dimensional (2-D and 3-D) case) erroneous code symbols owing to the bursty nature of errors. Interleaving is a process to rearrange code symbols so as to spread bursts of errors over multiple code-words that can be corrected by ECCs. By converting bursts of errors into random-like errors, interleaving thus becomes an effective means to combat error bursts. In this article, we first illustrate the philosophy of interleaving by introducing a 1-D block interleaving technigue. Then multi-dimensional (M-D) bursts of errors and optimality of inter-leaving are defined. The fundamentals and algorithms of the state of the art of M-D interleaving-the t-interleaved array approach by Blaum, Bruck and Vardy and the successive packing approach by Shi and Zhang-are presented and analyzed. In essence, a t-interleaved array is constructed by closely tiling a building block, which is solely determined by the burst size t. Therefore the algorithm needs to be implemented each time for a different burst size in order to maintain either the error burst correction capability or optimality. Since the size of error bursts is usually not known in advance the application of the technique is somewhat limited. The successive packing algorithm, based on the concept of 2×2 basis array, only needs to be implemented once for a given square 2-D array, and yet it remains optimal for a set of bursts of errors having different sizes. The performance comparison between successive approaches is made. Future research on the applications packing approach is discussed. Finally, applications of 2-D/3-D successive packing interleaving in enhancing the robustness of image/video data hiding are presented as examples of practical utilization of interleaving.