Veri cation Codes

Most work in low-density parity-check codes focuses on bit-level errors. In this paper, we introduce and analyze veri cation codes, which are simple low-density parity-check codes speci cally designed to manipulate data in packet-sized units. Veri cation codes require only linear time for both encoding and decoding and succeed with high probability under random errors. We describe how to utilize code scrambling to extend our results to channels with errors controlled by an oblivious adversary. Although veri cation codes over n packets require (log n) bits per packet, in practice they function well for packet sizes as small as thirty-two bits.