An Analytical Model for Sparse Network Codes: Field Size Considerations

One of the by-products of Sparse Network Coding (SNC) is the ability to perform partial decoding, i.e., decoding some original packets prior to collecting all needed coded packets to decode the entire coded data. Due to this ability, SNC has been recently used as a technique for reducing the Average Decoding Delay (ADD) per packet in real-time multimedia applications. This study focuses on characterizing the ADD per packet for SNC considering the impact of finite field size. We present a Markov Chain model that allows us to determine lower bounds on the mean number of transmissions required to decode a fraction of a generation and the ADD per packet of the generation. We validate our model using simulations and show that the smaller finite fields, e.g., q = 2
⁴
, outperform large finite fields, e.g., q = 2
³²
, in regard to the ADD per packet and provide a better tradeoff between the ADD per packet and the overall number of transmissions to decode a generation.