.lb:14 ========================================================================= BOOK 1 ...FUTURE SYSTEMS by Mark T. Nadir... PAGE $$$ ========================================================================= CHAPTER 13 MORE ON GAMMA MODES INTRODUCTION 1 In Chapter 3 we were introduced to B Modes SysTems. These SysTems are characterized ÿby the employment of ForMat containing ÿtwo ÿsections. The ÿGamma Modes SysTems as we know also have two ÿsimilar ÿsections, the Address Section and the Data Section - with one difference. Beta Modes have Address Sections which are always comprised of exactly one Address Nest and no more. 2 The uniqueness of the B mode SysTems is a consequence of the the fact that ÿthis ÿmode's Address Section is comprised of only ÿONE ÿAddress Nest. ÿThis ÿallows B Modes SysTems to be employed as ÿwas previously described, i.e. it allows a single user to employed the entire chan nel, or a succession of single users to occupy each ForMat. This per mits [1] point to point and [2] broadcast communications. ÿThis qual ity is lost in G modes SysTems because these latter are always multi user Mass-Access SysTems, ÿÿas the result of having multi-Address Ad dress Sections. This was described previously. 3 There are many G Modes SysTems. Each has its own set of characterist ics. ÿOne of these important ÿcharacteristics ÿis ÿthe mere number of subscribers who can co-share each ForMat. ÿAnother is the ÿparticular type of DTP (Data Transfer ProGram) that is employed. Both effect the behavior and efficiency of the mode. ÿ(The number of Address Nests in an Address Section is specified by a numerical superscript used thus ly:- Gx where the subscript x is the number of Address Nests.) 4 The first (and smallest) mode that we will examine is the G3 Mode. As the subscript states, the G3 ÿmode has three Address Nests in its Ad dress Section. This tells us nothing about the rest of the ForMat. It only ÿstates ÿthat since there are three Address Nests not more ÿthan three ÿsubscribers can co-share all the nests of that Format. This is because a subscriber, ÿin order to enter that ForMat, ÿmust [1] seize an ÿempty ÿAddress ÿNest and [2] enter a receptor's address ÿtherein. Therefore, a maximum of three subscribers can co-share that ForMAt. 5 [NOTE:Numbers like 3, 7,15, 31, etc. ,etc. frequently appear in the dis cussions. These numbers are described by: (2n-1). The (-1) represents the fact that the all zero case represents an empty nest and, therefore, cannot be employed for any other purpose.] 6 The method of creating Identifiers was detailed in a previous chapter and ÿneed not be repeated here. ÿTo refresh the reader's ÿmemory ÿthe block diagram of figure 27 can be reviewed. 7 There are several Data transfer ProGrams (DTPs) which can be employed with the G3 ÿmode alone. ÿThese relate to (A) ÿthe number of ÿAddress Nests in the Address Section, ÿ(B) ÿthe choice of character-sets (em ployed in the Data Section, and (C) ÿthe value of "Q", (the number of times the character-set is repeated in a Data Section). ÿThe value of Q is generally (but indirectly) ÿdetermined by the system designer(s) who ÿdecides number of bits in a ForMat. ÿThis indirectly ÿdetermines the number of character-sets which can exist in ÿa ForMat. ÿThis also determines (indirectly) ÿwhat value Q will have. The specification of this ÿparameter is, ÿtherefore, ÿpartially system designer ÿdependent which puts it outside the scope of this book, i.e. Book 1. 8 The selection of the character-sets is another matter. ÿWe will start with a two character character-set. ÿThe characters which are ÿchosen are the characters "one" ÿand "zero", ÿnot the bits "1" and "0". ÿThe "one" and "zero" are to thought of as characters and not as bits. The difference ÿbetween bits and characters are that bits are voltages or currents ÿthat appear on the transmission path while ÿcharacters ÿare any symbol or information these ÿbits ÿthese ÿbits are made to repre sent. ÿTherefore, ÿif a nest conveys (i.e. represents) ÿa ÿ"one" that "one" ÿis a character, ÿditto for a "zero". ÿThe distinction must ÿbe comprehended ÿand ÿremembered or nothing will be comprehensible ÿfrom here on! Do not read further until the foregoing distinction is cry stal clear to you. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º 1- 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 º º 2- 00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00- º º º º FIGURE 29. Row 1 represents the character-sets being sent. º º Row 2 represents the empty digital data stream. º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 9 In the illustration of figue 29 above two lines of numbers are shown. The upper line, ÿrow 1, represents the characters (to be sent) ÿwhile the lower line, ÿrow 2, ÿrepresents the digital data stream which ÿis comprised ÿof nests that are two bits long. ÿThe digital data stream, as shown, is empty (all zeros) ÿand is therefore presented as 0s. The dashes (-) ÿseparate one nest from another (and of course, do not ap pear in the physical ÿsystem). ÿÿ[Alternate character-sets are under lined for clarity.] 10 The character-set(s) in the G3 Mode is used by all three subscribers. Each subscriber's uniplexer enters as many Identifiers as is possible into the nests of the ÿData Section (through its ÿshift register, ÿof course). ÿThe first subscriber ÿis ÿthe one who is the first to enter data ÿ(Identifiers) ÿinto the Data Section. ÿ[The first subscriber is the one who is the first to seize and enter a receptor's address into an ÿAddress ÿNest and consequently acquires ÿAddress Nest number one. That Address Nest is necessarily the first of the three Address Nests but only in a SysTem ÿthat is first starting up. ÿ(In a SysTem ÿwhich has been operating for even a short time this last is not necessarily true.) 11 The mode of entry is the one that you are familiar with:- Each time a empty ÿnest occurs that represents the character that is to be ÿsent; the ÿuniplexer enters an Identifier therein. ÿThe first ÿsubscriber's uniplexer has first access to the ForMat passing through the uniplex er's shift register. ÿThe ForMat is then passed ÿon ÿto the next sub scriber on the transmission path. ÿThe presence of the shift register in ÿeach ÿuniplexer delays the nest long enough for the uniplexer ÿto [1] read, [2] write, and/or [3] erase data. This means that the first subscriber APPARENTLY ÿhas ÿa better chance of entering data than ÿdo the subscribers who enter later. 12 The above might be true immediately after the SysTem has been turned on but is no longer true even one second later. ÿThe reason is simple enough:- ÿOne ÿsecond later the ForMat has gyrated around the ÿclosed loop ÿmany times. During that time many subscribers have entered data almost all of which has been removed by the receptors. ÿTherefore, we start must consider only ForMats which have been in use for some time and ÿwhen ÿthere is an excellent chance that one or more subscriber's Identifiers are already present. There is also a good chance that one or more subscribers' ÿIdentifiers will be removed (erased) before the next subscriber will ÿenter ÿdata (Identifiers) into the ForMat. ÿThe conditions ÿprevailing at ÿthe ÿmoment when our description starts is entirely aleatory. 13 The PROBABILITY OF ENTRY* (P of E) is a statistical number which man ifests the expected number of times ÿeach ÿsubscriber ÿmight enter an Identifier ÿinto a character-set. ÿ[It is given as "X charecters ÿper character-set or merely X characters.] In our case this number is 1.5 characters per character-set for our two character character-set when the character-sets are empty. ÿAfter one subscriber ÿhas entered data (Identifiers) ÿthe P of E therefore becomes less than 1.5 (characters per character-set) ÿsince fewer Data Nests are available to the ÿnext subscriber to enter Identifiers 14 The second and third subscribers might also enter Identifiers in the manner described. The result is that most of the nests will be filled by the three subscribers. (This might surprise you!) ÿThe Identifier (in ÿthis case) ÿis two bits long so each entered nest can contain ÿa two bit long Identifier. Now, it takes two digital bits to transfer a one bit character. The SysTem when used with the described DTP is ap parently only one ÿhalf ÿas efficient as a code system. ÿThat the ex plained ÿData transfer ProGram is not very efficient is self-evident. Still, the foregoing is not the whole story. 15 The statistical distance each Identifier will travel is always equal to one-half the of the total distance that comprises ÿthe distance a round the closed loop. After that, it will be removed and the vacated (erased) nests can be used by other subscribers to convey their data. The result is that the nest will ÿbe used ÿ(approximately) ÿtwice for each ÿcircuit that the ForMat makes - when the SysTem is busy. ÿÿThis changes the discussed efficiency to its more nearly real efficiency - which ÿis twice as great. ÿNOW the efficency starts to look (and ÿis) much better. ÿTherefore, while the preceding Data transfer ProGram is not recommended neither is its efficiency as poor as it first appear ed. The SysTem Efficiency is greater than code! [The discussion will continue by ignoring SysTem Efficiency.] 16 [To see how we came to the conclusion that the distance traveled by a nest is equal to one half a closed loop consider this:- ÿ"A" is talk ing to be "B". ÿThe distance from "A" ÿto "B" ÿplus the distance from "B" ÿto "A" ÿis exactly equal to the distance around the closed loop. Therefore, the mean distance from any "A" to any "B" ÿis equal to one half the total distance. ÿThe distance [«(A+B)] is the expected dist ance between any two subscribers regardless of the Mode employed.] 17 There are (very) many more efficient Data Transfer ProGrams than the one just presented. ÿÿWe will now look at one such. ÿThis new DTP em ploys a four character character-set. ÿThe character-set that will be used (to illustrate) ÿis comprised of the following FOUR characters:- 00, 01, 10, and 11. They are shown in figure 30 below. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º1- 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 º º2- 00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00- º º º º FIGURE 30 Row 1 represents the character-sets being employed. º º Row 2 represents the empty digital data stream. º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 18 When the second Data Transfer ProGram is employed one Identifier will transfer a two (binary) bit character to the receptor. The P of E is such that one can expect that most of the nests will be filled by the three subscribers. ÿThe result is that the eight bits (which comprise one character-set) ÿwill cause the transfer of close to eight digital bits - and do it twice in each circuit of the ForMAt around the loop. Since ÿthe four character character-set requires nests which are ÿtwo bits long it is comprised of eight bits. So, this method employs bits to transfer eight bits, ÿtwice per loop circuit. It is therefore more efficiently than code. 19 A third example of a DTP for a G3 mode is now specified. In this Data Transfer ÿProGram character-sets eight characters long are ÿutilized. These characters are:- ÿ000, ÿ001, 010, 011, 100, 101, 110, ÿand 111. Therefore, each nest will convey three bits of data for each Identif ier is entered therein. Figure 31 (below) illustrates this. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º1- 000 001 010 011 100 101 110 111 000 001 010 011 100 101º º2- 00 - 00 - 00 - 00 - 00 - 00 - 00 - 00 - 00 - 00 - 00 - 00 - 00 - 00 º º º º FIGURE 31 Rows 1 & 2 are as previously described. º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 20 The character-set, shown above, is comprised of eight three bit char acters. But, the Data Nests are comprised of two bits. The P of E for three subscribers is about five Identifiers per character-Set. ÿThese five Identifiers use 16 ÿbits to transfer 5 x 3 bits of data. ÿSo the efficiency of transfer is about the same as was shown previously. The G3 mode is capable of much higher data transfer efficiency. ÿSee the Sheet for futher information. THE G7 MODE 21 From the title we (should) know that there are seven Address Nests in this ÿmode. ÿThe reason there are seven Address Nests in this mode is because (A = 23-1). There are not eight nests because the eighth case is the all zeros case. [The -1 represents that case.] And an all zero Identifier ÿappearing ÿin a nest, ÿwould be read by the SysTem as ÿan empty ÿnest. ÿAnd so, ÿonly seven unique Identifiers are possible ÿin this instance. 22 It takes three bits to specfy one of the seven different Identifiers. Therefore, ÿthe Data Nests are three bits long. ÿThe simplest example is the one previously given (where the character-set is ÿcomprised of the eight characters previously employed.) ÿThe nests would all ÿtend to ÿbe filled (entered) ÿwith the result that the transfer efficiency is unaltered from before. 23 However, a slightly more efficient Data Transfer ProGram is now given. This Data Transfer ProGram employs a sixteen character character-set. These characters are: 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, ÿ1101, ÿ1110, and 1111. Thus, the char acters ÿare ÿcomprised of four bits while the Identifiers (as well as the data Nests) ÿare comprised of three bits. ÿThe statistical number of ÿtimes ÿall seven ÿsubscribers can enter Identifiers into ÿsuch ÿa character-set ÿis ÿslightly greater than 12. ÿThe result is ÿthat ÿit takes slightly less than four binary ÿbits to convey a four bit char acter. This is slightly better than the previous case. No illustrat ion ÿof this case is shown since there is nothing really new to illu strate. 24 The point of these examples is to demonstrate that Positional Trans duction Methodology can transfer data more efficiently than ÿcan code systems operating at their theoretical maximum efficiency. ÿThat ÿis, PTM ÿSysTems can (under the right conditions) ÿemploy fewer ÿbits ÿto send ÿthe same amount of ÿdata than can be done using code. ÿThis (so far) ÿoccurs only when the optimum character-sets are utilized. ÿ(The examples selected are not high efficiency examples. ÿThose might come later.) ÿBut - since fewer bits are required by PTM SysTems (than the theoretical minimum ÿcalled ÿfor by Code SysTems) ÿPTM SysTems can be made ÿmore efficient than can code systems when "efficiency" ÿis mea sured by the number of bits it takes to send or transfer a ÿcharacter This is demonstrated ÿhere in order to prove that PTM can be more ef ficient ÿthan code. ÿThe fact that the differences so far illustrated differ from code only by a fraction of a bit does not invalidate this statement. Also, ÿthe fact that the numbers presented are statistical does not changes anything. ÿNotice that the efficiency under discuss ion is not SysTem Efficiency. ÿIf SysTem Efficiency is the item being considered than PTM is definitely more efficiency than code! 25 There will be the "hue and cry" that "Shannon's Laws" are being vio lated. ÿ[When you hear this cry you can be sure the speaker knows not whereof (s)he speaks.] No such "laws" ÿare being violated. Such LAWS cannot be violated. ÿThey are laws of nature. The information that is transmitted by PTM SysTems is ÿcomprised ÿof Tags and not of charact ers. Such data is being transferred. The Shannon's laws (being refer red to) apply only to that which is transmitted, i.e. to overt or ex plicit data ÿand not to inplicit data which is being transferred. PTM messages ARE transferred ÿand ÿnot transmitted. ÿTherefore, Shannon's laws do apply. ÿThey do ÿapply to the explicit Tags which is the only information transmitted. over PTM SysTems. 26 The Tags employed by PTM SysTems are generally more amiable to (soft ware) manipulations and modifications than are codes. (Codes are very resistant ÿto genuine modification (although one six bit code can ÿbe changed to another six bit code there is little else that can be done to them. [ÿBasically one arbitrary configuration is ÿused in place of another ÿarbitrary ÿconfiguration.]) ÿIn PTM Tag SysTems the only Tag that is fixed is the subscribers' SysTem address. ÿBut, ÿthat Tag oc curs ÿonly once in a ForMat and does not, ÿtherefore, ÿextract a high price (measured in bits). ÿFrom the SysTem's viewpoint those bits are "overhead", ÿi.e. ÿbits which are essential (and have to be paid for) but which do not convey data. 27 Let us now look at Data Transfer ProGrams which do not transfer codes for ÿthe receptor's uniplexer to convert into characters) as has been the case in the previous illustrations). ÿIn what ÿfollows characters (letters, ÿsymbols, etc.) are sent as letters, ÿcharacters, ÿsymbols, etc. 28 The simplest character-set that comes to mind is a G7 Mode characters set comprised of the following numbers and symbols:- 1, 2, 3, 4, 5, 6, ÿ7, ÿ8, 9, 0, {,}, {.}, -, +, /, *, & @, ÿwhere ÿ@ ÿis the "space" character. ÿÿThese ÿcharacters comprise a character-set of ÿseventeen characters. . A ÿnest is assigned to represent each character ÿ(as is usual in PTM SysTems). ÿSuch Data Nests ÿare ÿthree bits long because seven subscribers wilI employ seven Identifiers in this ForMat. ÿÿThe full character-set is, therefore, ÿ(17 ÿx ÿ3 ÿ=) ÿ51 bits long. Stat istically, ÿabout 13 ÿIdentifiers can be entered into this character- -set. ÿTherefore, the statistical number of bits required to transfer a character is (approximately) 51 ö 13 = 3.9 bits/char. This is again slightly better than the theoretic minimum (number of ÿbits) required by code. ÿAlso, ÿa ÿ17 ÿcharacter character-set is being ÿtransferred rather than the 15 ÿcharacter character-set that code would transmit. (13% greater.) 29 The improvement in efficiency of data transfer is not very great. The purpose of the above is to introduce the reader to the new concept of sending ÿcharacters without the use of code. ÿAs we shall see (later) this solves some problems and brings up others. THE G15 MODE 30 The next mode to be examined has, as the title indicates, 15 ÿAddress Nests ÿin its Address Section. ÿThis means that the Identifiers ÿ(and the Data Section nests) ÿare four bits long. ÿThis is as (should ÿbe) expected. 31 One Data Transfer ProGram which can be employed with this mode is the use ÿof ÿcharacters and punctuation in a manner similar ÿto ÿthe ÿone illustrated ÿabove except that the entire alpabet is employed ÿrather than just numbers and symbols. ÿThe Data Section will appear as shown in figure 32 below. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º º º1- A B C D E F G H I J K L M N O P Q R S T U V W X Y Z @ , . # ; : A B º º2- 4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4- º º º º FIGURE 32. Row 1 shows the characters which the Data Nests represent º º The 4s in row 2 represent the number of bits in a nest. º º The "space character" is represented by @. The character º º # represents the "shift character". º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 32 The characters, shown in figure 32, ÿare in alphabetic order which is both a random and a familiar order. The character-set is comprised of 33 characters but without any "nul" character. The space character is represented by @. The symbol # is the shift character. The characters shown are upper case characters. ÿThese are shown in row 1. ÿRow 2 is comprised of 4s. Each 4 represents four ÿzeros in the digital data stream, ÿin keeping with the previous illustrations. (This is only to save space.) 33 This Data Transfer ProGram has a problem which becomes acute when the Data ÿTransfer ProGram is used in the G15 ÿmode. ÿThe problem is ÿnot unique to the G15 ÿmode but might be troublesome in almost all ÿmodes except ÿpossibly in the Beta and the Omega modes.(The latter is found only in the SHEETS.) Luckily the problem seems insurmountable, so, it can, therefore, be expected to be fairly easily surmounted. 34 The problem might be observed on examination of Table 1, ÿ"The Ranked Frequency of Letters in the English Language". In this table the non- uniform use ÿof letters in english text can be easily observed. ÿThis gives rise to the ÿfollowing condition:- ÿThose nests which represent frequently ÿused ÿletters are quickly seized and Identifiers ÿentered therein. Now, once an Identifier has been entered no other Identifier can be entered therein until after some receptor uniplexer erases its Identifier. This, ÿof course, ÿis expected to occur to any Identifier entered into any nest - sooner or later. 35 A difficulty arises when all the nests which represent frequently em ployed letters ÿhave been filled. ÿ(This occurs ÿrelatively quickly.) Since ÿless than eight characters occur more than 50 ÿpercent of ÿthe time ÿthese character occur very frequently. ÿ(If the space character is ÿincluded then a mere five characters occur more than 50% ÿof ÿthe time.) ÿBecause of this the nests which represent less frequently em ployed letters are left more or less empty. (Mostly more rather than less.) But, no more Identifiers can now be entered because the frequ ently ÿused nests are filled and the next character to be entered ÿis very probably another frequently employed letter. ÿThe result is that the entry of further ÿIdentifiers is blocked - yet more than half the nests may be empty! This is a form of contention that the Send Memory cannot cure. 36 The above is another "insurmountable" problem. However, the "cure" is relatively simple and is given immediately below. But, first a remark or two. ÿÿThe P of E given earlier are for random numbers ÿor ÿrandom letters. It is obvious that the letters (of any language) do not have a random distribution and, therefore, the P of E for them is differ ent and much lower). The earlier assumption appears invalid and would be ÿif things were allowed to take their course. ÿBut the ÿassumption that the character appear random can be made true (from the mathemat ical viewpoint). 37 The solution which is given appears, ÿat first sight, ÿhighly ridicu lous! - And impossible to carry out. But, the insurmountable can (ap parently) ÿÿalways be surmounted. ÿOne solution is to MAKE ALL OF THE NESTS APPARENTLY REPRESENT "RAMDOM" CHARACTERS, i.e. to make the Data Nests ÿall have an equal probablity of being entered and used. ÿDon't repeat ÿthe words "ridiculous" ÿand "impossible"; ÿthey have ÿalready been said. 38 Let us say that the first letter (and all the letters that follow it) is ÿas ÿshown on line 1 in figure 33 ÿ- ÿbut only for the ÿsubscriber whose address occurs in the first nest in the Address Section. If the first ÿletter ÿis next displaced to the left for the next ÿsubscriber who enters the ForMAt as shown on line 2 of figure 33, these two sub scribers ÿwill have no nests that represent the ÿsame ÿcharacter ÿfor both ÿof them. ÿ(The last character is now represented by ÿthe ÿfirst nest, ÿfor the second subscriber.) ÿThe result is that the first nest which represents "A" for the first subscriber represents "B:" for the subscriber who entered the second Address Nest. Now, as shown on line 3, let the same thing be done for the third subscriber, i.e. the sub scriber ÿwho entered the third Address Nest. ÿFor this subscriber the letter "A" is represented by the third nest and the letter "E" by the sixth nest. Now, ÿnone of three have a nest which represents the same character ÿfor ÿall three. ÿIf ÿthe same action is repeated for each subscriber that enters the ForMat, as shown on lines 4, 5, 6.. N none of ÿof ÿthe subscribers will have a nest that ÿrepresents ÿthe ÿsame character to all of them! ÿÿThe use of ALL ÿOF THE NESTS [as a group] has been "randomized". 39 Not "in effect" but, in ACTUALLITY, the allocation of ALL of the Data Nests has been randomized! The particular manner of allocation cannot be carried out in the exact manner described above. ÿBut the same re sults ÿcan be obtained and mechanized by the slight rearrangement ÿof the circuits that already exist as described below. 40 The above can be accomplished as follows: We know from before that at the same moment, when an Address Nest is seized, its number is enter ed into the Identifier Memory. (The method of doing this was describ ed earlier.) ÿIn order to cause each Data Nest to represent a differ ent character to ÿevery subscriber who enters the ForMat the circuits must now be modified thusly: ÿAt the same moment that the number from the Address Nest Counter is entered into the Identifier Memory it ÿis also entered into the Data Nest Counter AS A "PRESET" VALUE* ÿor pre set ÿnumber. ÿÿ(This counter is the last counter in the counter chain and is the one that drives the ROM.) The number entered into the Data Nest Counter of each uniplexer serves to PRESET ÿTHE COUNTER (OF EACH UNIPLEXER CO-SHARING ONE FORMAT) ÿTO A DIFFERENT NUMBER. Each counter now starts counting ÿfrom ÿthe number it is preset to rather than from zero. The result is that each subscriber's ÿData Nests are assigned a different number (from the ROM). Because of the foregoing preset each nest in the ForMat ÿrepresents ÿa ÿdifferent ÿcharacter to every sub scriber's uniplexer. 41 Since reach subscriber receives an unique Identifier (which is a num ber) ÿeach subscriber's counter (and the associated receptor's count er) ÿreceives a unique preset number. ÿThe final result ÿis that each subscriber is assigned a unique character-set! Now, no two originat ing subscribers ÿhave a nest which represents the same ÿcharacter ÿto both originators (or ÿtheir receptors). ÿÿEach nest represents a dif ferent character to each originating and receveiving subscriber pair. THE EMPLOYMENT OF THE NESTS HAVE BEEN ACTUALLY "RANDOMIZED"! 42 Both the receptor's and originator's uniplexer is the same uniplexer. That is, ÿthe same uniplexer is employed for both sending and receiv ing. In order to properly send (transfer) data the uniplexer is mod ified as described above. The same preset modification makes it poss ible for the same uniplexer to receive the preset modified character- set. ÿOnce this ÿhas been done correct transference and reception oc curs as a matter of course. 43 Figure 24, ÿbelow shows the effect of the preset on the character-set that is transferred. ÿEach nest forms a straight verticle line, ÿi.e. each nest ÿappears as a column. ÿNote that in any selected column all the characters ÿare different from each other. ÿThis is the result of the preset and is called herein NEST REPRESENTATION RANDOMIZATION. 44 The observant must have noticed that using the Identifier (number) to preset ÿthe ÿAddress Nest Counter results in each communicating ÿpair employing ÿa ÿunique character-set. As a result each subscriber pair has its own unique character-set. 45 The character-set shown in figure 33 ÿis an arbitrary (even if famil iar) character-set. Properly designed character-sets produce more eff icient transfer of data. ÿThe characters in a preferred character-set are arranged in such a fashion that maximum data transfer will occur. Such a set cannot be " just thrown together" ÿby just anyone. ÿTables detailing character frequencies, character sequences, etc. are requ ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º1- A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ü , . © ; : A Bº º2- : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ü , . © ; : Aº º3- ; : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ü , . © ; :º º4- © ; : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ü , . © ;º º5- . © ; : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ü , . ©º º6- , . © ; : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ü , .º º7- ü , . © ; : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ü ,º º8- Z ü , . © ; : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z üº º9- Y Z ü , . © ; : A B C D E F G H I J K L M N O P Q R S T U V W X Y Zº º10- X Y Z ü , . © ; : A B C D E F G H I J K L M N O P Q R S T U V W X Yº º11- W X Y Z ü , . © ; : A B C D E F G H I J K L M N O P Q R S T U V W Xº º12- V W X Y Z ü , . © ; : A B C D E F G H I J K L M N O P Q R S T U V Wº º13- U V W X Y Z ü , . © ; : A B C D E F G H I J K L M N O P Q R S T U Vº º14- T U V W X Y Z ü , . © ; : A B C D E F G H I J K L M N O P Q R S T Uº º15- S T U V W X Y Z ü , . © ; : A B C D E F G H I J K L M N O P Q R S Tº º16- R S T U V W X Y Z ü , . © ; : A B C D E F G H I J K L M N O P Q R Sº º º º FIGURE 33 THE EFFECT OF THE PRESET ON THE CHARACTER-SET. º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ired. Characters must be arranged in such a manner that they are most likely to be employed. When such sets are employed, the P ÿof ÿE will increase to a number greater than "2" possibly even greater than "3". If ÿsuch ÿsets ÿare employed fewer empty nests will ÿoccur ÿwith ÿthe attendant ÿresults that fewer bits per character ÿwill be employed to send a message. G15 MODE EFFICIENCY 46 The (bit) transfer efficiency of the Data Transfer ProGram illustrat ed in figure 32 ÿis not particularily high. ÿThe 15 subscribers will, statisticly, be able to enter about 25 ÿIdentifiers into the 32 nests of the character-set. ÿThe character-set is 4 x 32 ÿ= 128 ÿbits long. The ÿdata ÿtransferred ÿis a baudot code set comprised ÿof ÿfive ÿbit characters. ÿWhen data is transferred in G modes 128/25 = ÿ5.12 ÿb/ch are required. ÿAgain there is no increase ÿin the transfer (bit/char) efficiency. (But, there is a slight decrease.) 47 ONE of the reasons that the transfer efficiency showns no improvement is because the Data ÿTransfer ProGram are geared to transfer charact er-sets which were designed as ideal character-sets for codes. ÿ[Sets of ÿthe type ÿN = 2n are ideal designs for efficient transmission ÿof codes.] ÿCode ÿhardware ÿwas then designed around these ÿideal ÿcode sets. ÿÿBut, there is no reason why they should fit PTM SysTems. ÿPTM SysTems have their ÿown ÿideal ÿcharacter-sets and how they should be employed. 48 Most typewriter keyboards are comprised of 44 letter/symbol character keys. ÿIf "control ÿcharacters" ÿsuch as line feed, ÿcarriage return, etc. are included, the character-set required is increased to 48 low er ÿcase characters. ÿIf such a character-set is transmitted by ÿcode each character must be comprised of seven bits. But, using PTM such a character-set can be sent in the G31 Mode. 49 The G31 ÿmode, in this case, employs a Data Transfer ProGram slightly different ÿfrom ÿthe Data Transfer ProGram that was employed ÿbefore. The character-set is comprised of 48 ÿcharacters. Andthere will be 31 subscribers to this character-set. So, each Identifier will be 5 bits long, ÿwhich means that the Data Nests must also ÿbe five ÿbits long. About 42 ÿIdentifiers can be entered into the Data Section of such ÿa ForMAt. ÿThe 48 ÿnests are equal to, in this case, 48x5 or 240 ÿbits. Because only forty-two of the nests are entered so, each ÿIdentifier is 240/42 ÿor 5.71 ÿbits long. ÿThis is slightly better than the six bits required by code. 50 Readers should make note of the fact that these code ÿcharacters have neither start nor stop bits. But, stop and start bits are required by many machines. ÿIf these bits are added to the code characters, ÿthey will become ÿthey ÿwill be ÿthree bits longer than they are stated to be. Thus, the characters said to be five bits long are actually eight bits long. ÿBut PTM ÿSysTems ÿstill send the characters with the pre viously stated (statistical) 5.71 bits - and still send the start and stop bits. ÿThis is an increase of 140%. ÿNote that there has been no increase in the uniplexer's hardware. 51 In the PTM SysTems this problem does not arise because the ROM can be designed so that the start and stop bits will be erased from the code characters before transfer. ÿThe ROM at the receptor's site will then add the start and stop bits to the characters automatically. They are neither sent nor recreated. ÿConsidered in this light the PTM SysTems are ÿ140% ÿmore efficient than are code systems when stop ÿand ÿstart bits are required. 52 In the Sheets many things are discussed and described which cannot be printed in this book. Methods of transferring data with less than one half ÿthe number of bit required by code are detailed. Also described are methods for tailoring the Data Transfer ProGram to any character- set size. Even methods for sending messages without running into con tention described there. It must not be forgotten that the mean dist ance ÿa ÿmessage travels is « the distance around the loop ÿand ÿthat when ÿthis is taken into account the "bit efficiency" ÿis greatly in creased. 53 A discussion of other G Modes will only reveal that more nests can be added ÿto the Address Section - fact we already know. ÿThe manner ÿof using ÿthese ÿmodes are substantial the same as the ÿmethods ÿalready described. Rather than beating a dead horse by describing G63, G127, etc. Modes. we will proceed with our explanations. CHARACTER TRANSFER 54 When letters, symbols, etc. are sent, as was done in the last few in stances ÿthe ÿtreatment ÿof the character-sets is slightly ÿdifferent from ÿthe ÿmethods ÿthat were first presented. ÿThe technique may be only slightly different but the this difference is entirely justified by the results. 55 A very important characteristic of PTM systems is now noted and exam ined. ÿA nest which represents a letter (or other symbol) ÿrepresents that letter and not the code for that letter. ÿThe difference must be clearly understood, ÿand remembered. ÿThe point might seem trivial ÿ- but it is not. ÿThe fact that codes are ÿaccepted ÿas inputs and sup plied ÿas outputs does not change the fact that the Data Nests repre sent letters, ÿsymbols, punctuation, etc. ÿand not the code for these characters. 56 At the time of transference, the code for the character (generated by the subscriber's terminal equipment), ÿis received by the ÿuniplexer. Now the ROM also generates character codes. These ROM generated codes are compared with ÿthe code character received ÿfrom the subscriber's terminal equipment. Both are fed into a comparitor. ÿWhen both inputs are identical this is detected by the comparitor. ÿThe comparitor re sponds to an identity by causing an Identifier to be entered into the nest present ÿin the shift register at that moment. ÿThe nest entered represents the letter generated in code by ÿthe subscriber's terminal equipment. (To repeat: the nest does not represents the code for that letter; it represents the letter itself.) 57 The ROM's output, ÿin any uniplexer, is tailored to be an exact match for the code(s) that the local subscriber's terminal equipment gener ates. ÿThe code for each particular letter must match, ÿas a consequ ence, the locally generated code for that letter. ÿAlso, when the ROM is ÿmanufactured ÿit is made in such a fashion that for ÿeach ÿunique input number a ÿunique code character is generated. ÿÿThe code is de signed ÿto be an exact match to the locally generated code ÿfor ÿeach letter. ÿAll the ROMs are made to generate the code for the SAME LET TER when the SAME NUMBER is presented to the ROM's input. As a result the nest represents a letter. ÿNote ÿthat ÿthe code that represents a fixed letter can vary from one terminal equipment ÿto another and the codes generated will vary accordingly ÿ- ÿbut the character generated is unaltered. 58 The above may seem trivial. It is not. The consequences are important to ÿthe system and its subscribers. ÿThe flexiblity of the system ÿis seriously effected by this as is the cost of the subscriber's termin al equipments. ÿThe illustration which follows will (hopefully) ÿmake this comprehensible to the reader. 59 Let us assume that an originating subscriber wishes to send a message to a receptor. ÿBoth are equipped with an electric typewriter. ÿTheir keyboards are identical but the code that each generates when a given letter ÿkey ÿis depressed is different. ÿ[A not uncommon occurrence.] But, ÿÿas a consequence of the foregoing when the originator sends ÿa letter ÿan ÿIdentifier ÿis entered into a nest ÿthat ÿrepresents ÿthe letter, ÿnot the code for that letter. ÿOn reception of that Identif ier, the receptor's ROM turns the received letter into the local code for ÿTHAT letter. ÿThe typewriter, ÿtherefore, ÿtypes the letter ÿwas sent. ÿThis permits subscribers employing DISSIMILAR CODES to commun icate. And that is no trivial matter. 60 A very common problem in many systems is the non-compatibility of the terminal equipments. One of the reasons for this is the fact that the termnial equipments are ÿdesigned ÿto ÿgenerate and receive different codes and/or differant variants of a code. ÿThey then cannot directly communicate with each ÿother. ÿThis problem does not have to exist in PTM SysTems because of the foregoing SysTem behavior. ROMs are easily installed and are very flexible. ÿAnd their cost (compared to a term inal equipment) is negligible. 61 There is another problem which the disssimilarity of their keyboards. This ÿcannot ÿcured ÿby any non-mechanical approach ÿbut ÿit ÿcan ÿbe helped. We will come back to this later, but, in the next book. This is system's problem and Book 2 deals with systems. SIMULATION OF PTM SYSTEM 62 It was originally planned to include a Positional Transduction Method ology SIMULATION PROGRAM as part of Book 1. This idea had to be aband oned when it was "discovered" that such a program would require a very large amount of either memory or disk space. 63 In order to properly simulate the behavior of a Positional Transduct ion Methodology SysTem data from ÿ up to 250 ÿsubscribers, at the very least, ÿÿwould have to be simulated. ÿThis would require a very ÿlarge amount of data storage space (or disk storage space). ÿ[The simulation should permit a reasonable amount of ÿdata from ÿeach of the simulated subscribers to be stored, say several hundred word (at least) per each simulated subscriber.] 64 The Positional Transduction Methodology simulation program should per mit [1] ÿdata to be read into the simulated operating system from ÿone or more of the reader files. The same program must [2] permit the re covery of the data to another file, or files, ÿso that the ÿreader [3] can compare the recovered data with the original input data. ÿThe sim ulation program should [4] also permit the stored data to be examined. Item [4] is necessary so that the reader should be able to examine for himself or herself the number of nests which are used (or unused); the number of bits required of per character, and any other characteristic which might be interesting or important to the reader; etc., etc. 65 The Positional Transduction Methodology simulation program should also enable the (knowedgeable) reader to evaluate the program as a possible means of encrypting data. [Even the simple simulation cannot be DEcry pted unless the method of writing in data is foreknown!] 66 Two approached to the Positional Transduction Methodology SIMULATION PROGRAM are being presently considered. They are [1] to include dir ections for writing such a program - in Book 2 and [2] issuing a disk with such a program on it. No decision has as yet been made. Both ap proaches have their own advantages and disadvantages. Ideally the Pos itional Transduction Methodology simulation program should be able to either transferred to, or written directly into, a hard disk. This ap proach would permit simulation programs of millions of bits. 67 As of this data, ÿonly one firm decision has been made and that is not to ÿinclude ÿany such Positional Transduction ÿMethodology ÿsimulation program as part of Book 1.