IEEE Geoscience and Remote Sensing Magazine - December 2021 - 110

◗ Otherwise, (( ))tkz0 d
by the binary representation of ()tz
consists of Umax
d
zeros, followed
using D bits.
Here, Umax is a user-specified parameter utilized to limit the
maximum codeword length, and D is the image's bit depth.
Two variables are used to keep track of the input data
statistics and to choose the GPO2 family's index () toktz
and a counter ().tC The
code ():tz
d
an accumulator ()tz
R
ratio of these two variables determines ():ktz
◗ If () ()
◗ Otherwise, () is the largest positive integer such that
kt
2492ztt ()/,t
ktz
CR2
()
t
#
CR#
2 tt
2
z ()
kt
z()
D- ,
z() +6@ (18)
49 27
ktz
C()/.
Mapped quantizer indices typically follow a nonstationary
geometric distribution, for which ()
estimator. Note that the counter and accumulator variables
are initialized based on user-specified parameters.
The values of the counter and the accumulator varid
-
ables are updated after coding each input sample ().
z t 1
More specifically, C is increased by one, and R is increased
by ().
d -
z t 1
In addition, both C and R are periodically
divided by two (rounding down) to enable calculation using
finite-precision arithmetic. This division is hereafter referred
to as renormalization.
HYBRID CODER
The hybrid coder uses the statistics of previously encoded
data to classify each input-mapped quantizer index as either
a high- or low-entropy sample. The high-entropy samples
are compressed using a variation of the length-limited
GPO2 code family described in the " Sample-Adaptive Coder "
section. The low-entropy samples are coded using another
family of 16 variable-to-variable-length codes, i.e., several
input samples can be encoded with a single codeword.
A detailed description of these variable-to-variable-length
Start
Input
Sample
δz(t)
Update
Counter and
Accumulator
High
Entropy
Sample
Type?
Low
Entropy
Calculate
Low-Entropy
Code Index
Code
Index i
δz(t) ≤
Code i Symbol
Limit Li?
No
(Unlikely
Sample)
Emit
R′0(δz(t) - Li - 1)
Complete Code i's
Codeword With
Scape Symbol
FIGURE 5. A flow diagram of CCSDS 123.0-B-2's hybrid coder. The logical decisions are highlighted in orange, the processes that update the
codes' internal state are shown in green, and the processes that emit codewords are presented in purple background.
110
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
Yes
(Likely
Sample)
Calculate GPO2
Code Index
kz(t)
Emit Reversed,
Limited-Length
GPO2 Codeword
R′kz(t)(δz(t))
Update
Code i
Prefix
Is Code i's
Prefix
Complete?
Yes
Emit Code i's
Codeword Given
Its Current Prefix
No
End
is a good parameter
z
+ C6@ then () .kt 0
7
=
codes can be found in [68]. The ability to adaptively switch
between GPO2 and variable-to-variable-length codes gives
this code the name hybrid.
Variable-to-variable-length codes enable very efficient
compression of highly predictable (low-entropy) samples,
which become more prevalent when near-lossless error
limits are used in the predictor stage. Meanwhile, variableto-variable-length
codes introduce variability in the latency
between the arrival of a low-entropy mapped quantizer
index and the output of the codeword that encodes it. To
accommodate this, codewords emitted by the hybrid coder
are designed so that they can be decoded in reverse order.
This is possible thanks to two main properties of the coder.
First, output codewords are suffix-free rather than prefixfree.
Second, the compressed image ends with a specification
of the final state of the coder. A set of flush tables is
provided in the standard to signal the code states in an unambiguous
and compact manner. Reverse decoding allows
for simpler and more memory-efficient implementations
than does FLEX's original hybrid entropy coder [62]. The
remainder of this section describes Issue 2's hybrid coder. A
flow diagram of this coder's logic is provided in Figure 5 to
support this description.
The classification of samples as high or low entropy is
performed using a similar statistical approach to that of
the sample-adaptive coder. Two variables are used to keep
track of these statistics: a counter ()tC
tion accumulator ().tzRu
and a high-resoluThese
variables are updated the
same way as in the sample-adaptive coder, with two main
differences. First, variables are updated before coding the
input sample; this is done so that decoding can proceed
in reverse order. To this effect, the least-significant bit of
the accumulator variable is output before renormalization
so that the decoder can invert this process. Second, ()tz
is increased by 4d ()tz
Ru
instead of ()tz
d
to enable a more
Clear
Code i
Prefix
IEEE Geoscience and Remote Sensing Magazine - December 2021

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