Simplification of Packet-symbol Decoding with Deletions, Mis-ordering of Packets, and No Sequence Numbers

A new method is described which builds on Mitzenmacher’s idea of adding a different pseudo-random number to each packet to help in verification-based decoding low density codes with packet deletions or errors, or out-of-order receptions, and no sequence numbers. The new method has less decoding complexity and is applicable to any parity check code structure, not just low density codes. Performance depends on the weight distribution of the code. For deletions with ordered reception, the method tolerates, roughly, up to only one more deletion, or packet error, than an erasure channel that knows the positions of all packet errors or deletions. With out-of-order reception, it tolerates, roughly, up to only two more deletions than the erasure channel. Also, it is shown how convolutional codes can further simplify decoding through a partition of the verification search. Moreover, with a modest amount of error detection built into the data, most of the deficiency relative to the erasure channel can be overcome by using error detection to choose from a small list of possibilities.