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I gave a quick answer to part of this question which had not been covered by previous answers, trying to clarify the reason you would say time of decoding but not decoding’s time. I said it was ’s usually indicates possession, but of course there were several counterexamples that would have occurred to me after a moment’s consideration, and these where helpfully supplied:

• Britain’s climate


• two days’ time


• a day’s work


• the sun’s rays

I am still of a mind to say that possession of some sort is what allows the ’s. Even though the sun does not have title to its rays, they do belong to the sun. Now, at the risk of duplicating the original question and/or being pigheaded, I am curious as to why time of decoding but not decoding’s time is correct, if not for the reason I gave.

In The New Fowler's Modern English Usage, the late Burchfield offered a guide to the use of possessive s and of with inanimate nouns. It is the most comprehensive and well founded stylistic advice I could find on the subject. He had worked on the Oxford English Dictionary and knew a lot about language and style. A summary:

A noun that is possessive or preceded by of modifies another noun: in my mother's bed / the bed of my mother, bed is the head noun, modified by my mother's / of my mother. Usually, inanimate modifier nouns should be preceded by "of"; but there are many possible exceptions, some of which are given here.

1. 
   

   An important exception is the so called thematic genitive: if a noun has gained strong topical value, because it is central in a discussion or description, it may get the possessive s.

   
   
   

   
   

   
   
   • That is a beautiful teapot. And those teacups must be Meissen. Notice the teapot's ornate lid and slender figure.
   
   

   
   

   
   


2. 
   

   Nouns defining a specific quantity of time or space, as used in many semi-fixed expressions, may get the possessive s.

   
   
   

   
   

   
   

   • A day's work

   
   

   • A hair's breadth

   
   

   
   

   
   


3. 
   

   Words modifying the word sake.

   
   
   

   
   

   
   
   • For heaven's sake
   
   

   
   

   
   


4. 
   

   Words modifying the word edge.

   
   
   

   
   

   
   
   • The cliff's edge
   
   

   
   

   
   


5. 
   

   Words for a ship or boat (and probably other vehicles; these could be classified as thematic genitives, or as cases of personification: see 1 and 7, and compare the use of she for vessels).

   
   
   

   
   

   
   

   • The ship's crew

   
   

   • The plane's left wing

   
   

   • The train's front car

   
   

   
   

   
   


6. 
   

   Other fixed expressions, usually monosyllabic nouns.

   
   
   

   
   

   
   

   • Out of harm's way

   
   

   • The sun's rays

   
   

   
   

   
   


7. 
   

   A personified inanimate noun; i.e. whenever a thing is invested with a will or the ability to act (this exception is an addition of my own). This is related to the use of she for certain countries and vehicles.

   
   
   

   
   

   
   

   • Britain's might

   
   

   • Fear's claws

   
   

   
   

   
   

The pronoun its is by definition reserved for inanimate objects and hence universally possible. The use of whose with inanimate objects appears to be much less restricted than the possessive s, perhaps because relative clauses always express elaboration on a central theme (thematic genitive). This is not surprising, since the essence of a pronoun is that it refers to existing information, i.e. it is highly topical.

The relevant passages from Burchfield:

For inanimate nouns, and particularly for such nouns consisting of more than one syllable, the of-construction is customary (e.g. the roof of the church, not the church's roof: the resolution of the problem, not the problem's resolution).

...

There is general agreement that the non-personal genitive is frequently used with nouns of time (e.g. the day's routine, an hour's drive) and space (e.g. the journey's end, a stone's throw, at arm's length). It is also often used before sake (e.g. for pity's sake, for old times' sake), and in a number of fixed expressions (e.g. at death's door, out of harm's way, in his mind's eye). Jespersen noted the prevalence of 's genitives before the word edge (the cliff's edge, the water's edge, the pavement's edge, etc.). He also noted that ship, boat, and vessel tend to turn up with an 's genitive when we might expect of (the ship's provisions, the boat's gangway, etc.).

In 1988 Noel Osselton demonstrated that the somewhat unexpected types the soil's productivity and the painting's disappearance (as well as others) represent a legitimate class of what he called thematic genitives. When a noun that cannot 'possess' is of central interest in a particular context, it tends to acquire the power to 'possess', and is therefore expressed as an 's genitive.

One major genitival area remains virtually untransformable into 's genitives. Only the of-construction is appropriate for partitive genitives: e.g. a glass of water cannot be re-expressed as a water's glass, and try converting a dose of salts.

I tested these rules against my files and found them largely in accord with my own evidence. The great majority of 's genitives still occur with
animate nouns. ... It does seem from the evidence available to me that the 's genitive for inanimate nouns is commoner now than it was a century ago[.]

There are actually three possible constructions to express what you want to (using decoding + time): decoding time, time of decoding, and decoding's time.

Yes, that's right: I'm going out on a limb here and saying there are cases where you might use "decoding's time" — as odd as that may sound. Let's look at the different meanings (N.B. I am taking the most likely meaning of each, but all could be used in any of the senses):

1. decoding time — meaning the time it takes to decode something or
   


2. time of decoding — meaning the time at which something was or will be decoded


3. decoding's time — taking the decoding itself as an entity which can have a right time or a wrong time, or some other qualitative measure of timeliness, and judging whether it was appropriate in that respect.

Example:

Yes, the decoding could have been done upon receipt of the message, but it wasn't the decoding's time. That would come later.

This could be said in other ways, but this way keeps "the decoding" as the subject, without transferring that property to time itself; it also keeps the noun time at the end of the sentence, where it is in an appositive relationship to the sentence that follows. I'm not sure if there is any real benefit to this, but it is a possibility and might serve as a stylistic variant in some cases.

It's true that the Saxon Genitive indicates possession but there is a rule that I think hasn't been mentioned yet (in this question at least), that says that the it is usually adopted with animated objects or better with nouns that refer to living things:

• 
  Kate's website;


• 
  Robert's car.

This rule is not absolute and strict, and many people use the possessive also with non-animated objects. But well, this document goes a bit in depth in this matter, although not all of it. This part is related to your question:

Although the analytic and synthetic genitives of English may be interchangeable in a grammatical sense, they are often not so from the viewpoint of stylistics. The genitive formed with apostrophe + s is usually preferred with nouns, both proper and common, that refer to persons and other living things; the analytic genitive formed with of is more usual, at least in formal speech and writing, with inanimate objects.

But this distinction is far from absolute. The synthetic genitive seems perfectly proper in such phrases as the ship’s cargo, our country’s future,
and yesterday’s newspaper, and the resistance to expressions such as the liver’s oxygen consumption and Paraguay’s climate is gradually lessening. However, the synthetic genitive is quite impossible in certain circumstances. A single example must suffice. One can say at the back of the room (al fondo del cuarto) but never at the room’s back, which, to a speaker of English, would seem to mean something like “a espaldas del cuarto.

I have been debating this question myself. Both apostrophe+s and of denote possession of some type. The difference seems to be in the type of thing that possesses. For example:

• 
  Person: 's; Bob's age; Bob's temperature


• 
  Object: of; the temperature of the water; the age of the fossil


• 
  Process (something that alters the state of an object or person): of; the time of reaction; the force of impact


• 
  Quantity: 's; One day's time; One cup's volume

Just a thought.

I am still of a mind to say that possession of some sort is what allows the 's.

As reported from the NOAD, genitive in grammar means "relating to or denoting a case of nouns and pronouns (and words in grammatical agreement with them) indicating possession or close association."

The genitive could also be used for

• reporting the participation in an action, as agent: he benefited from her mother's love.


• a reference: the empire's capital.