nnon limit. The question of how in practice one achieves this It is useful to give two simple models for discrete channels with performance is complex, one method being the use of orthogonal memory, before going onto ideas associated with capacity and signals. coding for these channels. The first model is due to Blackwell 4/10 Information theory Figure 4.4 Trapdoor channel (1961), and considers 'trapdoors' as shown in Figure 4.4. Initially a system stays in this state with probability .99, errors tend to occur ball labelled with 0 or 1 is placed in each of the two slots. One of in groups. the trapdoors is then opened, with each door having the same The models developed for the case of a discrete channel with probability of being opened. The ball then falls through the open memory are those for which the channel has a finite number of door, and the door then closes behind it. The empty compartment internal states, for which the present state of the channel represents then has another ball placed in it, and the whole process starts all a summary of its past history. The application of an input will result over again. This model defines a channel whose inputs correspond in a transition to another state, with the production of an output. The to the balls placed in the empty compartment and whose outputs resulting source channel matrix then determines a finite Markov correspond to the balls which fall through the trapdoors. If the chain with states where a are the states of the source and S symbol b, corresponds to the condition in which a ball labelled i are the states of the channel. If the chain associated with the source remains in an occupied slot, and time is started after one of the doors channel matrix has steady state probabilities, then given the pair (a., is opened, four states S for i,j = 0 or 1 may be defined as follows. one can determine the corresponding input f (a, = f(a) and The channel is in state S. at time t = n, if the condition b. holds at outputg,(a,s)=g(f(a),s). Thus the chain associated with t