This article is from the MPEG FAQ, by Frank Gadegast phade@cs.tu-berlin.de with numerous contributions by others.
All Layers use the same basic structure. The coding scheme can be
described as "perceptual noise shaping" or "perceptual subband / transform
coding".
The encoder analyzes the spectral components of the audio signal by
calculating a filterbank or transform and applies a psychoacoustic model
to estimate the just noticeable noise-level. In its quantization and coding
stage, the encoder tries to allocate the available number of data bits in a
way to meet both the bitrate and masking requirements.
The decoder is much less complex. Its only task is to synthesize an audio
signal out of the coded spectral components.
All Layers use the same analysis filterbank (polyphase with 32 subbands).
Layer-3 adds a MDCT transform to increase the frequency resolution.
All Layers use the same "header information" in their bitstream, to support
the hierarchical structure of the standard.
All Layers have a similar sensitivity to biterrors. They use a bitstream
structure that contains parts that are more sensitive to biterrors ("header",
"bit allocation", "scalefactors", "side information") and parts that
are less sensitive ("data of spectral components").
All Layers support the insertion of programm-associated information
("ancillary data") into their audio data bitstream.
All Layers may use 32, 44.1 or 48 kHz sampling frequency.
All Layers are allowed to work with similar bitrates:
Layer-1: from 32 kbps to 448 kbps
Layer-2: from 32 kbps to 384 kbps
Layer-3: from 32 kbps to 320 kbps
The last two statements refer to MPEG-1; with MPEG-2, there is an
extension for the sampling frequencies and bitrates (see below).
 
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