References: Phonetics

Phonetics is a branch of linguistics for the study of sounds of human speech: physical properties, production, acoustics, articulation, etc.

Phoneme

In any given language, a phoneme is the smallest sound segment that can be used to distinguish one word from another. For example "bat" and "chat" have only one sound different but this changes the word. The phonemes in question are "B" and "CH". What exactly these are and how many exist varies a bit and may be influenced by accents included. Generally, US English consists of 39 to 44 phonemes. See ARPAbet below for more phoneme examples.

Grapheme

The definition of a grapheme is somewhat inconsistent in the literature. In our context, a grapheme is the smallest symbol that distinguishes one written word from another. For example, "bat" and "chat" have a difference of two graphemes, even though "CH" is considered to be a single phoneme. In US English, 26 letters and a space combine for 27 possible graphemes.

Lexicon

A lexicon for speech recognition is a lookup file for converting speech parts to words. An example of this is cmudict, the Carnegie Mellon tool for speech recognition compatible with the open source Sphinx project. Here's a short excerpt:

AARDVARK    AA R D V AA R K
AARON    EH R AH N
AARON'S    EH R AH N Z
AARONS    EH R AH N Z
AARONSON    EH R AH N S AH N
AARONSON'S    EH R AH N S AH N Z
AARONSON'S(2)    AA R AH N S AH N Z
AARONSON(2)    AA R AH N S AH N
...

ARPAbet

A set of phonemes developed by the Advanced Research Projects Agency(ARPA) for the Speech Understanding Project (1970's).

ARPAnet on Wikipedia
ARPAnet dictionary at CMU: