Holographic dispersal and recovery of information

1123 consider N as a continuous variable and seek N* so that aF,/aN = 0. The result is 1-Mp 1-2 which implies N* > M + 1. Although these channels are simple, they constitute a useful model for comparison with the channels studied in the text, which are perhaps of greater practical interest. The special case of N* = M and p = r should be mentioned. The Gram matrix for this channel is given by (B.4) and the solution to the quantum detection problem is known [17]. The matrix elements qJ = (a,IpJ) are given by where g = (a,la,) = exp(-p') for all i, j. We easily obtain for the cutoff rate M FdM) =In 1 + 2(M-1) p q. Following the method established in Appendix I and based on the inversion of the matrix G as defined by (B.4), with a = g, we arrive at M &(") =In 1 + (M-1) g. Note that (C.7) is also the result given by (C.6) for g-+ 0. Analysis of (C.6) is most useful. In particular we can prove for p < p , with p o = ln2M/2, that