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‘CPYRGHT PUTHOFF AND TARG: PERCEPTUAL CHANNEL FOR INFORMATION TRANSFER TABLE X 5-Bir Cope FOR ALPHANUMERIC CHARACTERS rm Y G W v B ) 1 2 3 4 5 6 7 8 9 Favnormenrowwm ann Note: Alphabet characters listed in order of decreasing frequency in English text. See, for example, A. Sinkov [79]. (The low-fre- quency letters, X, Z, K, Q, and J, have been grouped with similar characters to provide space for numerics in a 5-bit code.) In consideration of the uneven dis- tribution of letter frequencies in English text, this code is chosen such that 0 and 1 have equal probability. dundancy. One efficient coding scheme for such a channel is obtained by application of a sequential sampling procedure of the type used in production-line quality control [80]. The adaptation of such a procedure to paranormal communication channels, which we now discuss, was considered first by Taetzsch [81]. The sequential method gives a rule of proce- dure for making one of three possible decisions following the receipt of each bit: accept 1 as the bit being transmitted; reject 1 as the bit being transmitted (i.e., accept 0); or continue transmission of the bit under consideration. The sequential sampling procedure differs from fixed-length coding in that the number of bits required to reach a final decision on a message bit is not fixed before transmission, but depends on the results accumulated with each transmission. The principal advantage of the sequential sampling procedure as compared with the other methods is that, on the average, fewer bits per final decision are required for an equivalent degree of reliability. Use of the sequential sampling procedure requires the speci- fication of parameters that are determined on the basis of the following considerations. Assume that a message bit (0 or 1) is being transmitted. In the absence of a priori knowledge, we may assume equal probability (p = 0.5) for the two possibili- ties (0,1). Therefore, from the standpoint of the receiver, the probability of correctly identifying the bit being transmitted is p=0.5 because of chance alone. An operative remote-sensing channel could then be expected to alter the probability of correct identification to a value p = 0.5 + W, where the param- eter W satisfies O<|Y|<0.5. (The quantity may be positive or negative depending on whether the paranormal channel results in so-called psi-hitting or psi-missing.) Good psi func- tioning on a repetitive task has been observed to result in p = 0.12, as reported by Ryzl [31]. Therefore, to indicate the design procedure, let us assume a baseline psi parameter [a Ea (, DECISION 1 Accept “1” as the Bit Being Transmitted DECISION 2 Accept “0” as the Bit Being Transmitted “1" TARGET MESSAGE SEQUENCE 40 50 60 70 80 NUMBER OF TRIALS CUMULATIVE NUMBER OF MATCHES AGAINST Fig. 18. Enhancement of signal-to-noise ratio by sequential sampling procedure (p, = 0.4, p, = 0.6, a = 0.01, 8 = 0.01). The question to be addressed is whether, after repeated transmission, a given message bit is labeled a ‘‘1” at a low rate Po commensurate with the hypothesis Ho that the bit in ques- tion is a “0,” or at a higher rate py commensurate with the hypothesis H, that the bit in question is indeed a “1.” The decision-making process requires the specification of four parameters. , Po The probability of labeling incorrectly a “0” message bit asa ‘1.’ The probability of labeling correctly a ‘‘0”’ as a “0” is p= 0.5 + W, = 0.6. Therefore, the probability of labeling incorrectly a “0” asa “1” is 1- p= 0.4 = Do. The probability of labeling correctly a “1” message bit asa “1,” is given by p; = 0.5 + Wy = 0.6. The probability of rejecting a correct identification for a “0” (Type Terror). We shall take a= 0.01. The probability of accepting an incorrect identification for a “1” (Type Il error). We shall take 6 = 0.01. With the parameters thus specified, the sequential sampling procedure provides for construction of a decision graph as shown in Fig. 18. The equations for the upper and lower limit lines are 2, =41 + SN 2, 740 t SN 1- Po log 1- py Pi 1~ Po log Po l- Pi in which S is the slope, N is the number of trials, and d, and do are the y-axis intercepts. A cumulative record of receiver- Vp = 0.1 and Bese Ra POP REIHSR BOOHGR/OS 'tin-RDPSE UA PIZRBGOSAdS BEGIN is complied unt either