Buffer asymptotics for coding over networks

• Authors: Sandeep Bhadra;Sanjay Shakkottai
• Venue: IEEE Transactions on Information Theory
• Year: 2010

Traditionally, network buffer resources have been used at routers to queue transient packets to prevent packet drops. In contrast, we propose a scheme for large multihop networks where intermediate routers have no buffers for queueing transient packets. In the proposed scheme, network storage resources (memory) are used only at source and destination nodes to encode/decode packets using random linear coding over time. Our scheme capitalizes on the common empirical observation that for large networks with many flows through each router, if packet loss occurs in a flow path, it will very likely occur only at only a very few links on the path. Unfortunately, the location of this congested link varies with time, thereby preventing prevailing static buffer allocation strategies from exploiting this observation. We propose source coding over packets at the session layer as a means of "sharing" memory across links along a flow path. We call this spatial buffer multiplexing--where buffering and coding implemented at the source compensates for packet loss at any downstream bufferless link. First, we consider large spatial multihop networks with N nodes (each with finite buffer space for coding/decoding) and Θ(N) flows; the number of flows through each link scales as Ω(Nα) for some α ∈(0,1). Using many-sources large deviations analysis, we show that to obtain comparable packet drop probabilities (QoS), spatial buffer multiplexing provides an order-wise buffer gain of Ω(Nα) per node over traditional static buffer allocation for queueing. Next we consider the complementary case of a network with a small number of flows through a buffer, but large source buffer. Here, we provide a sufficient condition under which the packet loss probability decreases exponentially in a function that is linear in the size of the input buffer, where the function is required to meet a predetermined negative slope -- δ. We express the loss effective bandwidth for coding and compare it against that for queueing.