Is there a specification that describe specifically the AAC-LC standard, and is it a realist goal to achieve a codec, not a general one, but for a specific AAC-LC format, with predefined number of channels and sample rate?
Are there some existing projects for AAC-LC specifically?
[EDIT]
I found a first project, coded with MatLab, that is looking promising: http://www.mathworks.com/matlabcentral/fileexchange/28028-mpeg-4-aac-lc-decoder
It directly demux mp4, and decode AAC-LC with no blah-blah. Thousand of hardcoded values and box definitions. Maybe this is exactly built to test common iPhone/Windows Phone MP4s.
AAC (Advanced Audio Coding), including the LC (Low Complexity) profile, was originally specified in ISO/IEC 13818-7 (MPEG-2 Part 7). It was later updated by ISO/IEC 14496-3 (MPEG-4 Part 3); subpart 4 covers AAC specifically, and subpart 1 (Main) is likely to also be helpful.
General information can be found on the Wikipedia page.
There are a few existing open source implementations. Currently one of the better quality ones is the Fraunhofer FDK AAC Codec Library for Android; it was released as open source as part of Android but is not Android-specific. Its primary disadvantage is that its license is considered to be incompatible with the GPL. Some other open source implementations are listed in FFmpeg's AAC Encoding Guide, including FFmpeg's native AAC encoder, which is in development.