Recent studies have shown that retransmissions can cause heavy-tailedtransmission delays even when packet sizes are light-tailed. Moreover, theimpact of heavy-tailed delays persists even when packets size are upperbounded. The key question we study in this paper is how the use of codingtechniques to transmit information, together with different systemconfigurations, would affect the distribution of delay. To investigate thisproblem, we model the underlying channel as a Markov modulated binary erasurechannel, where transmitted bits are either received successfully or erased.Erasure codes are used to encode information prior to transmission, whichensures that a fixed fraction of the bits in the codeword can lead tosuccessful decoding. We use incremental redundancy codes, where the codeword isdivided into codeword trunks and these trunks are transmitted one at a time toprovide incremental redundancies to the receiver until the information isrecovered. We characterize the distribution of delay under two differentscenarios: (I) Decoder uses memory to cache all previously successfullyreceived bits. (II) Decoder does not use memory, where received bits arediscarded if the corresponding information cannot be decoded. In both cases, weconsider codeword length with infinite and finite support. From a theoreticalperspective, our results provide a benchmark to quantify the tradeoff betweensystem complexity and the distribution of delay.
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