A Study On Fast Multi-erasure Correcting Codes For Large Data Blocks

Erasure-corrected coding technique is one of forward error correction tech-nologies aiming at erasure channel, that used to ensure efficient, reliable trans-mission and storage. With the developments of the P2P network, multicast, etc., the transmission and storage of mass data based on blocks or packages had been paid more and more attentions and been widely required. Most of the existing codes were designed for bit or symbol oriented applications which focus on binary symmetric channel, that are unfit to cope with error-controlling of this system because of the restriction of encoding/decoding complexity. The construction of blocks oriented multi-erasure-correcting codes with strong erasure correcting abil-ity (more than 2 erasures) and low complexity of encoding/decoding has become a focal point of research in channel coding field.Aiming at mass data reliable transmission and storage system based on blocks or packages, this dissertation has studied large block oriented inter-block multi-erasure correcting method based on the research of single parity-checking codes. We have made some achievements and proposed a fast multi-erasure correcting codes for large data blocks, that has:●Strong erasure correcting ability, the codes can correct at most any 4 blocks erasure;●Large blocks or packages oriented inter-blocks erasure-correcting codes with any size, and draw a conclusion that the codes can encode with at most 27 continuous blocks;●Fast encoding/decoding computation, the complexity is O(n) (n is the size of the block by byte);●Belong to MDS codes, the codes can reconstruct at most any 4 failed blocks with only 4 redundant blocks. It means that the codes achieves the optimal erasure-correcting ability at the same condition. This dissertation introduces in detail the constructing method of the multi-erasure correcting codes and theoretical proof, the optimization of the encod-ing/decoding which meet the real-time requirements. Finally, We have analyzed the application of the multi-erasure correcting codes in practical system, gave a brief summarization and put forward on future researches.