The Explicit Decoding Delay Probability Distribution Based on Random Linear Coding Scheme

Xubo ZHAO  Hang ZHOU  Xiaoping LI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A    No.11    pp.2299-2301
Publication Date: 2013/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.2299
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Coding Theory
random linear coding,  lossy channel,  decoding delay,  

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Under random linear coding (RLC) scheme, we present a simple expression of the probability distribution p(D=K) for decoding delay D incurred by the lossy channel, where K is a positive integer. In contrast with the previous contribution, our focus is firstly on deriving the cumulative distribution function of the discrete random variable D over a perfect channel. One benefit of such dispose is that, from the overall viewpoint, computing the cumulative distribution function of delay D can be related with calculating the cardinalities of sets of some special matrices, so that the former can be obtained from the latter. Moreover, our expression of the probability distribution is an explicit form, and is valid for any number of packets M, freewill field size q and arbitrary channel loss rate ε.