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By G. Longo (eds.)

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Let us now consider those sequences y for which the MJ\11-decoder associated with & commits an error. By (13), every such y is contained in the set. &(x) of those sequences y for which there is another ~€ e' different from X with the property (19) I(x/\y);;:;. l(x/\y) .

We would therr like to set the retrarrsmissiorr probabilities so that T(k) approaches T* . By "listenirrg" to the channel, we carr distirrguish silerrt slots from the others arrd define the variable S(k) if S(k)= 0 T(k) = 0 otherwise k 2 Dividing the charrrrel time into "wirrdows" of L slots, we therr defirre Performance Analysis of Multi-User Communication Systems ... tionary then S'(k) is the maximum likelihood estimator of Pr[T(k)=O]and T(k) is an estimator of T(k). I be a sequence of random variables taking values in ]O,I[ and which will give the values of the retransmission probability in Let {fk}k ~ the adaptive control.

I. The broadcast channel is unstable for both the finite and infinite source models. Let us first consider the infinite source model. Let p (k) PROOF. denote the probability that N(k) = n. (k)c. + p 1 (k)g 1 (n+l)c + p (k)(l-g 1 (n))c n-J J n+ o n o + p (k)g (n)c 1 + p 1 (k)(l-g (n-l))c 1 . n o no E. Gelenbe 34 To illustrate the interpretation of the right-hand side, we note that the first term covers the cases where two or more packets have been transmitted by the active terminals during the kth slot and the second term covers the case in which exactly one blocked terminal has transmitted while no active terminal has done so.

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