AN2121 Freescale Semiconductor / Motorola, AN2121 Datasheet - Page 17

• Manufacturer Part Number: AN2121
• Description: JPEG2000 Arithmetic Encoding on StarCore SC140
• Manufacturer: Freescale Semiconductor / Motorola

2.4.2.2
If an MPS (‘0’ for context CX) is received, the CODEMPS procedure (see Figure C-7 on page 42) is
called. When symbol ‘0’ (MPS for CX) occurs, normally the length of the interval A is updated to (A – Q
and C is updated to (C + Q
value of A is always checked after it has been updated to determine if it has fallen below 0.75, thus
requiring a renormalization. If it does, it could also mean that stage (A – Q
Q
associated with symbol ‘1’ (LPS for CX). However, it should be noted that this does not indicate that
symbol ‘1’ is necessarily more likely to happen than symbol ‘0’ on receipt of context CX, because the
encoder is still receiving ‘0’s with CX. It just means that the MPS must be assigned to the larger
subinterval of A. When the subinterval representing MPS falls below that of the LPS, A is set to Q
larger of the two subintervals, and C remains unchanged (it is already pointing to the lower bound of the
LPS subinterval). A renormalization then occurs to ensure that A remains greater than 0.75. This
arrangement allows the decoder to detect the change and decode the symbol correctly. Setting A to the
larger subinterval generally reduces the number of renormalization operations required. This slows the
growth of the encoded bit stream (i.e., improves data compression) because its growth varies with the
frequency of renormalization.
2.4.3
Again, a primary advantage of the JPEG2000 BAC is that the probabilities associated with the LPS and
MPS can be adapted. In order for a coder to be adaptive, a statistical model of the input data symbols is
required to update the probabilities associated with the MPS and LPS. The model must also determine
whether each incoming event is an MPS or an LPS.
In JPEG2000, the coefficient bit modeler performs the statistical modelling by providing the BAC with
context/data pairs. The context is calculated from the properties of up to 8 of the wavelet coefficient’s
nearest neighbors. This context is used to index into Table C-2 (page 50), which contains the LPS
probability values (Q
i.e., for each context the MPS has previously been declared as either a 1 or a 0. Thus, for example, if the
data input from the coefficient bit modeler is a '1', and the MPS 'sense' is also a '1', then this input is treated
as an MPS; otherwise, it is treated as an LPS.
The JPEG2000 arithmetic coder has adopted the practice of updating the probabilities associated with the
MPS and LPS only when renormalization has occurred. This practice was first introduced in the Q-coder
[5]. A probability model is needed for both the encoder and decoder. This probability model can be viewed
as a finite-state machine. In practice, the various states are stored in the indexed table of Q
presented in Table C-2. These probabilities have been derived through an extensive optimization
procedure which includes both theoretical modelling and coding of actual data.
Table C-2 also includes associated next states (i.e., new table positions) for each type of renormalization.
For convenience, a portion of this table is reproduced in Table 2. In this table, the index represents the
current state, the NLPS (Next LPS) represents the next state to go to if an LPS occurs, the NMPS (Next
MPS) represents the next state to go to if an MPS occurs, and the SWITCH value indicates if the sense of
the MPS must be inverted.
e
, meaning that the subinterval associated with symbol ‘0’ (MPS for CX) is smaller than the subinterval
MPS Case
An Adaptive BAC: Probability Estimation Process
e
). In addition, for each possible context, there is a ‘sense’ associated with the MPS,
e
). The interval A becomes progressively smaller as the encoding proceeds. The
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Background Theory
e
JPEG2000 Arithmetic Coding
) has fallen below the value of
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probabilities
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, the
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