Simplification of Packet-Symbol Decoding With Errors, Deletions, Misordering of Packets, and No Sequence Numbers

In this paper, a new method is described which builds on Mitzenmacher's idea of adding a different pseudorandom number to each packet to help decode packet-symbol low-density codes, with deletions, errors, and out-of-order reception, without sequence numbers. The new method has lower decoding complexity than the original method. The most basic form of the new method applies to any parity-check code structure, but is limited to a rather small number of packets in the code. Decoding success is slightly inferior to an ideal erasure channel, which would require sequence numbering and error detection in each packet. Error detection is needed only for the whole code, amounting to usually less than one bit per packet symbol. Moreover, if error detection can resolve one of a small number of alternatives, the ordered case performs almost as well as the ideal erasure channel. Ways are shown to modify the basic algorithm for use with long codes, possibly approaching the erasure channel capacity limit.