This comes down to where someone decided to break up the Pali, but I say this is not 'the ending of perception and experience' or 'the ending of perception of experience' but 'sense-experience-sense-perception-ending'. A compound.
It must make sense as one word. This is the situation where the meditator is bringing the last contact with the world to an end, not a case where either all perception or all experience is being brought to an end. Both perception and experience are used as terms describing what is going on in the state of arahantship. It is what is being perceived and experienced through the senses that is seen as ending in this jhāna.
It will not destroy the meaning if this term is translated "The ending of sense-perception and sense experience" but put as a compound it is more forceful, and in English at least we must distinguish between 'experience' and 'sense-experience' and 'perception' and 'sense-perception' where the Pali uses one word for each, or we encounter an unsolvable mystery.
In [SN 4.36.11] The Buddha explains his statement that whatsoever is sense-experience, that is of the nature of pain. Then he describes three progressions leading to Arahantship: that of a progression of endings; that of a progresion of masterings; and that of a progression of calmings-down.
The idea here is that the attaining of arahantship is gradual. There is a school of Zen Buddhism out there that speaks of sudden Awakening. This is another case where the subjective is ignored in the face of a perception which counts the subjective as insignificant, unreal. Like the struggle of an individual in a dream to wake up relative to his waking up. After awakening it appears that the progression towards awakening of the unawakened subjective individuality was insignificant, almost irrelevant. Almost. Except for the subjective individual for whom it is all important. There is no awakening without the intent to awaken. So although awakening may be sudden, when the idea is seen in it's totality, awakening is gradual.
Here I have finally seen a convincing argument for translating 'saññā-vedayita-nirodha' as 'ending-sense-perception-sense-experience' meaning ending of sense-perception and sense-experience.
This is how it is explained in this sutta.
I have sometimes used this translation and sometimes used 'the ending of perception of sense experience' which I will change hereafter throughout the site as I come across it.
The complication here for me has always been that there is perception (saññā) beyond the attaining of the sphere of neither-perception-nor-non-perception (which, as an aside, should be being translated 'the sphere of neither-sense-perception-nor-non-sense-perception') which I have taken to be the 'saññā-vedayita-nirodha' which is described by Sāriputta as:
"One perception arose in me:
to end becoming is nibbana;
another perception faded out in me:
to end becoming is nibbana."
And again, in AN 10.6 The Buddha describes the highest state, the conclusion as having percption.
Hense my understanding was that this jhāna ended sense-perception, but not all perception. Since that must still be the case however this term is translated, (it is just another own-made mental state like all the other jhānas) and though it may involve the ending of perception, that state too is not to be confused with Nibbāna. Hense the necessity (as with 'consciousness' and 'experience') of distinguishing between experience through the senses versus the experience of one detached from the senses:
Vedana: experience vs. sense-experience
Saññā: perception vs. sense-perception
Viññāṇā: consciousness vs. sense-consciousness.
See also SN 4.36.14: Where the Buddha likens the various sense experiences to the various sorts of guests that inhabit a guest house.
This sutta is one of the few places where the vedanas are described in the two modes found in the Satipatthana Sutta. It is very important to understand how this works. The sense experience produced by contact with an identical object or situation can be experienced in different, opposite ways depending on one's mental state, perspective or orientation. From the point of view of one letting go of the world, what would have produced a pleasant sense experience for one downbound to the world will be experienced as unpleasant (both in it's nature as temptation, and as transient and leading inevitably to pain); what would have produced an unplesant sense experience will be experienced as plesant (because experienced as no longer pertaining to the self) and what would have been experienced as a neutral sense experience inclining the downbound to seek pleasant sense experience will be experienced by the renunciate as a taste of Nibbāna. For the one the experience is impersonal and mental and does not equate to our idea of 'sensation' but is more like 'idea'; for the other it is a subjective experience that is a mixture of bodily and mental sensations. Because of the need for the one word to satisfy both uses I suggest that vedana be translated not as 'sensation' but as 'sense experience' or just 'experience' depending on whether the case is of the one downbound to the world or is beyond sense-experience. 'Feeling' which is the most frequent translation, but which does not relate to the literal meaning of 'vedana' ('the given experience'), does not well serve both needs.
See also: [SN 3.22.29]
Especially: In Pain, Olds translation.
The Buddha declares that whoever takes delight in the Stockpiles of Existence (khandhā) takes delight in Pain, but whoever takes no delight in them is free from pain. See especially for this, SN 2.14.35.
In putting the translation of this sutta together I came upon the problem of rendering the term 'vedana' (for which issue see the Discussion of MN 12). I decided the best option in this case would be to render the term 'sense-experience' as when this term is used in the khandhas it implies the experience of the senses of the individual. Then, seeing there also the terms for perception, and consciousness it occurred to me that the same issue applies to these terms as well, that is that they are used for both the Arahant and the Individual but are to be understood differently for each, and that the solution applied to 'vedana' would also be helpful if applied to 'sañña' and 'viññāṇa': that is, to distinguish the term 'consciousness' where it is being used of the consciousness of the ordinary person we should translate it 'sense-consciousness', and similarly for 'perception', 'sense-perception'. Where the terms apply to the Arahant (see discussion of viññāṇa anidassana and AN 11.8 and others there like it) we can just leave them un-augmented. Previously I have tried to point out this distinction with regard to 'consciousness' by translating 'individualized consciousness' which is what it is. It is difficult to understand why there were in these cases no new terms invented to distinguish the ordinary person and the Arahant, but it may have been that in the creation of a new set of terms there would have been seen to be the implication that where they were the states of the Arahant they were 'states of existence' which would be exactly wrong. Or may be it just did not seem important as the ordinary person would not be concerned and the student of this Dhamma would be taught. Or maybe it was thought wise to leave it as a challenge to figure out as bearing down would be needed to comprehend the issue anyway. The best I can do to offer a distinction for the reader is something like: The Arahant has the consciousness of the not-consciousness of sense-consciousness. His consciousness depends on freedom from sense-consciousness as it's basis and by that cannot be said to 'be in existence'. It has not crossed over into personal identification with rūpa, 'matter.' One can experience the idea of 'extra-sensory' sight simply by recollecting an image from a dream or noting the fact of 'seeing' objects in daydreams or jhāna. This is 'seeing' an object other than by way of the eye.
See also The Discussion of MN 12 One of the few direct statements that the experience of Nibbāna has Vedana associated with it.