First, here are a few comments from this article, The Case for Non-Targeted Input (Krashen, 2013)
"For an item of grammar to be acquired, the language acquirer must be ready to acquire the item. It must, in other words, be at the acquirers' i+1, where i = aspects of grammar that were most recently acquired."
"An important corollary of the Comprehension Hypothesis is the "Net" Hypothesis: Given enough comprehensible input, i+1, all the vocabulary and structures the student is ready for, is automatically provided. In Krashen and Terrell (1983) this was referred to as the Net: "When someone talks to you in a language you have not yet completely acquired so that you understand what is said, the speaker "casts a net" of structure around your current level of competence, your "i". This net will include many instances of i+1, aspects of language you are ready to acquire" (p. 33)."
"Ray and Seely (2008) emphasize the importance of translation because they feel that students must understand every word of what is said in class and what they read. As noted earlier, this may indeed be very helpful at the very beginning, but the transparency requirement should give way to the requirement that students feel that they are understanding everything. If only the feeling of full comprehension is required, if input is allowed to contain some i+n, we are no longer restricted to translation as a means of making input comprehensible. We are free to use pictures and realia, as emphasized in Natural Approach (see also comments by Carol Gaab in Ray and Seely, p. 235), as well as other means of making input comprehensible that do not obviously provide a one-to-one mapping from form to meaning (e.g. background readings that provide a general context for a story). If, in fact, the input is truly compelling, it is likely that students will not even notice the "noise" or bits of incomprehensible and nontransparent elements in the input."
I believe there is a difference between "total translatability" and "total comprehensibility" (I dislike the word "transparency" because I think it is confusing and could apply to either case).
Total translatability - students have a one-to-one connection for each and every word. This limits what you can communicate to students as well as the intention of communicating it: the emphasis is on learning forms, not on understanding messages.
Total comprehensibility - I'm beginning to think that acceptable "noise" does not come in the form of incomprehensibility, but rather that the meaning of words that would be incomprehensible on their own are made clear through other methods. For instance, when Diane Neubauer told us the story about the Zodiac, there was a part where the rat jumped over the ox's head. Had she focused on us understanding the words in that part of the story, it would have been overwhelming as well as disrupted the flow of the story - we were right at the climax and focused on what was happening, so it would have been much less compelling (not to mention out of bounds) to sit and focus on the somewhat more-complex language involved in communicating that idea. However, we completely comprehended that very critical part and kept the "flow" of the language going thanks to her gestures. We learned plenty in the process - and she could still use that story for valuable input (as opposed to being "barred" from an otherwise comprehensible story because a key part would have been "out of bounds"). This still counts as noise, however, because I didn't make any connections with the actual target language and couldn't have told you what the words were, even just after hearing her say them. And, frankly, I didn't care - I understood the message and wanted to hear the rest of the story! They key is that the message was, in fact, 100% comprehensible even if it did include noise, which was important because it lowered my affective filter and kept me in "flow". In other words, I didn't get stressed about trying to achieve a deeper level of comprehension than I was ready for nor was I stressed that there were details I was missing, because I felt confident that I had comprehended the entire message.
With regard to i+1 - there have been a few that say if everything is "100% comprehensible", then it is not providing the "+1". However, this position confuses what is acquired with what can be understood. It is important to understand that "i" is NOT what can be understood - it is what is already acquired, meaning that it can be used by the student. The "+1" is the language that is not yet acquired but can be understood (and therefore has the potential to be acquired). This area of "+1" is very broad and flexible as it contains all of the language that can be made comprehensible. For instance, novice students who have never been exposed to the target language before, have zero "i"; thus, the entire first lesson (or series of lessons) are all within the "+1" range. As students acquire "i" from the "+1" input, their ability to comprehend additional "+1" expands, although much of the language that was "+1" will remain "+1". This is why I agree with Krashen (2013) that non-targeted language is ideal for differentiation - students convert the "+1" into "i" at different rates according to the natural order, but as long as students are provided with a "Net" of language that includes "+1" for all students, all students will be able to continue acquiring the language they are ready for at their own pace .
With regard to noise, I don't think that "noise" can be acquired - the grammar and vocabulary from the language used MUST be made comprehensible before acquisition of that particular form can occur. In my above example with the Zodiac story, I had no chance of acquiring the structure for "jump over" because I never really even wrapped my head around the target language words in the first place. However, that was not a bad thing - in fact, it enabled Diane to tell a compelling story while staying "in bounds" and keeping the affective filter low. I believe that teachers need to skillfully judge and plan how they will tell a story knowing that the majority should be comprehensible at an level which students can acquire it, but be able to bridge these sections with tiny bits of comprehensible noise (if that makes sense) in order to make up for bits of language that might be beyond the "+1" level yet are still necessary to be compelling.
So, to answer my initial questions:
YES, teachers MUST be 100% comprehensible - meaning that students feel that they are comprehending everything. Some misunderstandings will occur - that's fine. That is part of language development and their understandings will become refined as they receive more input (also noted in Krashen, 2013). This keeps the affective filter low as students become comfortable and confident about comprehending messages, forgetting to focus on individual words and whether they can translate them.
YES, there is room for noise, but it must be comprehensible noise that is strategically used only when necessary. In other words, the messages must remain comprehensible even if the language is not. Moreover, teachers need to use their best judgement in order to maximize the amount of "+1" at a level that is possible for students to acquire. Yet, they should not feel constrained to only providing input that is at the "+1" level - comprehensible noise can be used as a tool to help students access input opportunities that might be otherwise compelling and comprehensible for students.