Design of ZDF code using uniform shift enumerator

The fountain code is an erasure correcting code used for the packet erasure channel. ZDF codes (Zigzag Decodable Fountain codes) are a kind of fountain codes which are generalizations of Raptor codes. The distinguishing characteristic of ZDF codes is to apply bit shift operation to generate the encoded packets. The bit-wise peeling decoding (PA) is used based on the difference bit shift of the precoded packets to the encoded packets. To provide more start of bit-wise PA, we investigate the enumerator of the encoded packets' shift combinations. We found that the shift combination of all the degree of the encoded packet has the uniform enumerator, the packets can have an effective start for bit-wise PA. Thus, we propose a ZDF code with variable shift distribution based on shift combinations with a uniform enumerator. From the simulation results, we have shown that the decoding erasure rate per received packet is decreased compared with other methods by limiting the number of selection of each shift and suppressing the deviation of the shifts.