On Sliding Window Approximation of Gilbert-Elliott Channel for Delay Constrained Setting
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In this paper, we first provide analytical expressions for the block erasure probability (BEP) of block codes that can recover erasures that are (1) random with weight atmost a or (2) burst with atmost b consecutive erasures when used over Gilbert-Elliott (GE) channel. The same approach is then used to come up with tractable upper and lower bounds for the BEP over the GE channel, of codes designed for the delay constrained sliding window (DCSW) channel model introduced by Badr et al. This channel model permits either a single burst of b erasures or else a random erasures within a sliding window of specified length and requires recovery within a strict decoding delay constraint. Using the upper bound for BEP, we show that the family of streaming codes developed for the DCSW channel offer better rates in comparison with MDS codes operating under the same conditions of delay and BEP.
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