Sequential coding of Gauss-Markov sources with packet erasures and feedback

We consider the problem of sequential transmission of Gauss-Markov sources. We show that in the limit of large spatial block lengths, greedy compression with respect to the squared error distortion is optimal; that is, there is no tension between optimizing the distortion of the source in the current time instant and that of future times. We then extend this result to the case where at time t a random compression rate rt is allocated independently of the rate at other time instants. This, in turn, allows us to derive the optimal performance of sequential coding over packet-erasure channels with instantaneous feedback. For the case of packet erasures with delayed feedback, we connect the problem to that of compression with side information that is known at the encoder and may be known at the decoder — where the most recent packets serve as side information that may have been erased, and demonstrate that the loss due to a delay by one time unit is rather small

From Instantly Decodable to Random Linear Network Coding

Our primary goal in this paper is to traverse the performance gap between two linear network coding schemes: random linear network coding (RLNC) and instantly decodable network coding (IDNC) in terms of throughput and decoding delay. We first redefine the concept of packet generation and use it to partition a block of partially-received data packets in a novel way, based on the coding sets in an IDNC solution. By varying the generation size, we obtain a general coding framework which consists of a series of coding schemes, with RLNC and IDNC identified as two extreme cases. We then prove that the throughput and decoding delay performance of all coding schemes in this coding framework are bounded between the performance of RLNC and IDNC and hence throughput-delay tradeoff becomes possible. We also propose implementations of this coding framework to further improve its throughput and decoding delay performance, to manage feedback frequency and coding complexity, or to achieve in-block performance adaption. Extensive simulations are then provided to verify the performance of the proposed coding schemes and their implementations.Comment: 30 pages with double space, 14 color figure