As part of our effort in support of the DARPA Internet Program,
software modules to encode and decode facsimile data for the Dacom 450
and 500 models Computerfax facsimile machines have been constructed.
The purpose of these modules is to map the data representations used by
these machines to and from bit-map and run-length representations in
programs for editing, transmission and archiving facsimile images. The
modules are written in the PDP-11 MACRO-11 assembly language and can be
incorporated into programs for, among others, the RT-11 operating system
and the DCNET BOS or VOS operating systems.
The first part of this report describes in detail the Dacom 450
data compression algorithm and is an update and correction to an earlier
memorandum [2]. Following this, the encoding and decoding algorithms
are described along with the supporting programs and file formats.
Reference [3] describes another implementation of the decoding
algorithm. Grateful acknowledgment is made to E. A. Poe of Rapicom
for his assistance in this effort.
The second part of this report describes briefly the Dacom 500 data
compression algorithm as used by the INTELPOST electronic-mail network
under development by the US Postal Service and several foreign
administrations. These machines conform to the CCITT T.4 Draft
Recommendation, described in [5]. Supporting programs and file formats
are described.
The encoding algorithm for the Dacom 450 processes lines scanned by
the machine to produce a two-dimensional run-length code described by
Weber [1]; however, this article contains a number of errors and
omissions, many of which were discovered only after considerable
analysis and experimentation [2,3]. The machine operates over a
coordinate space of l726 by approximately 2200 pels when in
high-resolution (detail) mode. In normal (quality) mode the vertical
resolution is halved, so that about 1100 lines are transmitted, while in
express mode about 733 lines are transmitted (missed lines are filled in
on playback by replicating previous lines).
Data are encoded two rows at a time using a two-dimensional
run-length code. Each row-pair is scanned left-to-right and the
line-pairs themselves processed top-to-bottom of the document. Figure 1
shows how the pels are represented.
Dacom 450/500 Facsimile Data Transcoding PAGE 2
| | |
----+----------+----------+----
... | x(1,j) | x(1,j+1) | ...
----+----------+----------+----
... | x(2,j) | x(2,j+1) | ...
----+----------+----------+----
| | |
Direction of scan ->
Figure 1. Data Representation
For each j the vector (x(1,j),x(2,j)) represents the contents of
the jth column, where x(i,j) can take on values of zero (white) or one
(black). Each of the four possible vectors ranging over these values
will be called a state (Dacom calls these "modes") with the succession
of transitions between these states determined by the picture content of
the particular line-pair. Scanning of the line-pairs follows one after
the other with no special end-of-line code in the data itself. For the
purpose of later discussion and comparison with the published data, the
following conventions will be used (note: the pels read top-bottom):
Pels Vector State
---------------------
W-W (0,0) 0
B-W (1,0) 1
W-B (0,1) 2
B-B (1,1) 3
The algorithm used by Dacom to generate the transmitted data as the
columns are scanned can be described as the non-deterministic
finite-state automaton (nfsa) shown in Figure 2. Conceptually, the nfsa
starts at the beginning of a page in a designated state and at a point
just after scanning the jth column in the jth state. It then scans the
(j + 1)th column and enters that state while emitting the string of bits
shown in the figure.
In the states corresponding to W-W (0) and B-B (3) a special
run-length encoding techniques is used. There are two state variables
associated with each of these two states, one variable used as a
run-length counter and the other the field length (in bits) of this
counter. Upon each entry to either of these two states the counter is
initialized at zero and counts up for every additional column of the
same state. At the end of the run the value of this counter is
transmitted extending with high-order zeros, if necessary, to fill the
field length specified. If, however, the counter equals 2**n - 1, where
n is the field length, then a sequence of n one-bits is emitted and the
counter re-initialized at zero with a field length of n + 1. Thus, if
n = 3, a run length of three is transmitted as {010} and a run length of
seven as {110}, while a run length of eight as two words, {111} followed
by {0000}. The field-length variables are maintained separately for
both the W-W and B-B states, and at each re-entry to either of these
states the previous values are used.
Dacom 450/500 Facsimile Data Transcoding PAGE 3
0100
.--------------------->----------------------------------.
| |
| .-----------------<------------------------------. |
| | 1 | |
| V | |
.--------------. .---------------. | |
| | | | | |
| | 010 | | | |
.->| 1 |-------------------->| 2 |->. | |
| | | | | | | |
0| | B-W | 101 | W-B | |1 | |
\<-| |<--------------------| |<-' | |
| | | | | |
| | .---->| | | |
\--------------' | \---------------' | |
| A | | | A | |
| | .--------->------' | | | | |
| | | 1 | | | | |
| | | | | | A V
| | | | | | | |
0111| |1 | | 1000| |1 | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | 1011 | | | | |
| | | .-------<----------' | | | |
V | | | V | | |
.--------------. | .---------------. | |
| |<--' | | | |
| | 0 | | | |
| 3 |<--------------------| 0 |-----' |
| | | | |
| B-B | | W-W | |
| |-------------------->| |<--------'
| | 0 | |
| | | |
\--------------' \---------------'
| A | A
| | | |
\----' \----'
run run
Figure 2. NFSA Model of Encoding
Dacom 450/500 Facsimile Data Transcoding PAGE 4
Field-length values are constrained not to exceed seven, so that
runs exceeding l27 with n = 7 will be encoded as a separate 7-bit word
of one-bits for each run of l27 except the last, which must always
contain at least one zero-bit. The field length n is decreased by one
under the following circumstances: the current run has been encoded as a
single n-bit field, and for n in the range four through seven the two
high-order bits are zero or for n equal to three the single high-order
bit is zero. The field length is not allowed to be reduced below two
bits.
The encoding algorithm starts in state 0 with both field lengths
set to 7.
For reasons of speed and simplicity it is desirable that the Dacom
450 decoding algorithm be modeled on the basis of a deterministic
finite-state automaton (dfsa). Using straightforward formal procedures,
the dfsa of Figure 3 can be constructed. This machine makes one state
transition for every bit, except for the W-W (0) and B-B (3) states,
which must be treated specially in any case. The states are labeled in
such a way as to correspond to those of Figure 2 for states numbered
from zero to three.
The decoded output symbols, in this case the columns corresponding
to each of the states, are represented by the states themselves. Upon
entry to state B-W (1) or W-B (2) a run-length counter is initialized to
one. Each traversal of a loop back to the same state increments this
counter and, upon exit to any other state, the value of this counter
represents the number of columns to be produced. Upon entry to state
W-W (0) or B-B (3) the run-length counter is initialized to zero and the
associated field-length state variable n established. For each
successive n bits of all-ones, the counter is increased by 2**n - 1 and
then n itself increased by one, but not above seven. If the next n bits
are not all ones, then the counter is increased by the value represented
by the n-bit field plus one. Finally, if upon entry to either state the
next n bits are not all ones, n is decreased by one according to the
rule mentioned in the preceding section.
Dacom 450/500 Facsimile Data Transcoding PAGE 5
.-----------. .-----------.
.-----| | | |-----.
| | 9 | | 6 | |
| .-| |<--. .-->| |-. |
| | \-----------' \ / \-----------' | |
1| 0| \ / |1 |0
| | .->Error \ / Error<-. | |
| | 0| \ / |1 | |
| | .-----------. \ / .-----------. | |
| 1 | | | \ / | | | 0 |
| .---| 7 | \ | 10 |---. |
| | | | | / \ | | | | |
| | | \-----------' / \ \-----------' | | |
| | | A / \ A | | |
| | | | / \ | | | |
| | | 1| / \ |0 | | |
| | | .-----------. 0 / \ 1 .-----------. | | |
| | | | |---' \---| | | | |
| | | | 5 | | 8 | | | |
| | | | | | | | | |
| | | \-----------' \-----------' | | |
| | | A A | | |
| | | | | | | |
| | | 1| |0 | | |
| | | .-----------. .-----------. | | |
| | ->| | | |<- | |
| | | 1 | | 2 | | |
| | | B-W |<-----. .----->| W-B | | |
| | \-----------' | | \-----------' | |
| | | A | | A | | |
| | | | |0 1| | | | |
| | \-----' | | \-----' | |
| | 0 .-----------. 0 | |
| | | | | |
| | | 4 | | |
| | RUN | | RUN | |
| | .-----. \-----------' .-----. | |
| | | | A A | | | |
| | | V | | V | | |
| | .-----------. 1 | | 1 .-----------. | |
| \-->| |------' 0 \------| |<--' |
| | 3 |<--------------------| 0 | |
\---->| B-B |-------------------->| W-W |<----'
\-----------' 0 \-----------'
Figure 3. DFSA Model of Encoding
Dacom 450/500 Facsimile Data Transcoding PAGE 6
Data are encoded for transmission by the Dacom 450 in 585-bit
frames, consisting of a 24-bit synchronization code, 37-bit leader,
512-bit information area and l2-bit checksum. There are two kinds of
frames distinguished by leader format, one for setup or initialization
and the other for the data itself. Serial binary image data are placed
in the data area of succeeding data frames.
The header of each frame is shown in Figure 4. The various fields
are defined in Table 1 following the Figure.
+-----------+--------+-------------------+----------+
| Sync Code | Leader | Data | CRC Code |
+-----------+--------+-------------------+----------+
24 / 37 \ 512 12
.-------' \----------------------.
/ \
+-------+-------+-------+-------+-------+-------+
| Flags | Count | X Pos | Black | White | State |
+-------+-------+-------+-------+-------+-------+
| 7 \ 10 12 3 3 2
| \--------------------------.
| \
+-----+-----+------+-----+-------+-----+
| Seq | RUN | COFB | RPT | Spare | SUB |
+-----+-----+------+-----+-------+-----+
2 1 1 1 1 1
Figure 4. Frame Format
Dacom 450/500 Facsimile Data Transcoding PAGE 7
Table 1. Header Field Definitions
Field Width Function Setup Data
(bits) Block Block
-----------------------------------------------------
Sync Code 24 Synchronization 30474730 (octal)
Seq 2 Sequence number 00 00,01,10,11
RUN 1 Initialize-start 0 1
COFB 1 Unknown 0 0
RPT 1 Unknown 1 0
Spare 1 Unknown 0 0
SUB 1 Indicates setup frame 1 0
Count 10 Number of bits in data All 1's
field (0 - 512)
X Pos 12 Current position on All 1's
scan line (0 - 1725)
Black 3 Current black field All 1's
length (2 - 7)
White 3 Current white field All 1's
length (2 - 7)
State 2 Current state (0 - 3) All 1's
Data 512 Data (0 - 512 bits)
CRC Code 12 CRC checksum. Uses polynomial
x**12 + x**8 + x**7 + x**5 + x**3 + 1
Dacom 450/500 Facsimile Data Transcoding PAGE 8
Setup frames have additional information in the data field; the
various fields and their functions are described in Table 2.
Table 2. Field Definitions for Setup Frame.
Field Width Function
--------------------------------
Start bit 1 Always zero
Speed bit 1 Set if express mode
Detail bit 1 Set if detail mode (speed and detail
bits both zero for quality mode)
14 inch 1 Set if 14-inch paper
5 inch 1 Set if 5-inch inch paper (14-inch
and 5-inch inch paper bits both zero
for 11-inch paper)
Paper present 1 Set if paper present in scanner
Spare 5 Can have any value
Multi-page 1 Set if multi-page mode
20 All 0's
480 Alternate 1's and 0's
The tailing setup frames differ from the leading setup frames only
in bits which indicate whether the system is operating in single or
multiple page mode and whether paper is present in the scanner.
All n-bit numeric fields (except Seq) are transmitted by the Dacom
450 machine least-significant-bit (LSB) first (i.e. Count, X Pos,
Black, White, State, CRC, and run length words in the data field).
All other fields are transmitted left-most bit first.
There are a few important points to be considered in regard to the
header of a data frame. The header contains enough information about
the state of the decoding algorithm to be able to re-establish correct
decoding in the event of loss or mutilation of a data frame. The
decoding algorithm resets its state variables to those in the header
each time it begins decoding a new data frame. One of the most
difficult problems encountered while constructing the decoding algorithm
was the correct synchronization of the algorithm as it proceeds across
the frame boundary with respect to the header information. In order for
synchronization to be maintained, the operation of the algorithm must
Dacom 450/500 Facsimile Data Transcoding PAGE 9
follow exactly that described in the previous section.
This requirement for every data frame to be self-synchronizing,
leads to a few subtleties in the encoding algorithm which seem quite
natural, but were not very obvious in the beginning.
treated (for purpose of decreasing its field length) as if it were
the beginning of a new run, since there is no information in the
header to indicate otherwise.
The decoding algorithm is initialized at the first data frame
received after the sequence of setup frames at the beginning of
transmission. The first data frame has a count of zero, indicating no
data bits are in the frame. The second data frame begins the actual
document; however, its X position appears to be irrelevant. Instead, we
assume the initial X position at this time is one pel to the left of the
right margin (-l mod l726). With these assumptions succeeding X
positions of the algorithm and the frame headers agree.
The decoding algorithm described above has been implemented in the
PDP-11 MACRO-11 assembly language for the RT-11 operating system. This
program contains extensive features for selectively dumping frames and
tracing the operation of the algorithm. It is designed to operate on a
file containing the raw data generated by the machine and does not
depend upon any prior reformatting of the data. However, it will
operate also on files in the so-called UCL format [4], which has been
adopted as the standard for use in the Internet Program. The existing
DCNET supporting software for the Dacom 450 uses the UCL format and
operates normally to copy data directly between the machine and the
file, with decoding operations done at a later time. However, there is
no intrinsic factor, except processing-rate limitations, why input data
could not be decoded directly from the machine.
In operation, the program scans the input data one bit at a time
and searches for the synchronization pattern. Note that all data
processed are inverted from the natural interface conventions. When a
Dacom 450/500 Facsimile Data Transcoding PAGE 10
synchronization pattern is found, the header and data portions are
extracted and the various state variable checked and reset, if
necessary. Checksum verification is performed according to the
polynomial 1 + x**3 + x**5 + x**7 + x**8 + x**12. In the case of setup
frames the format (detail, quality, express), page length (14, 8-l/2,
5-l/4) and multiple-page indicators are extracted from the data area.
Finally, under control of specified options, the header and data
portions of the frame are printed with appropriate headings.
The decoding algorithm itself is called for each data frame. It
produces an output consisting of a sequence of run-length pairs which
can be used to form bit maps and other representations of the data.
Optionally, a printed trace of the operations performed by the algorithm
can be produced.
The encoding algorithm has been implemented in the PDP-11 MACRO-11
assembly language for the RT-11 operating system. The program accepts
facsimile data in 16-bit run-length format or bit-map format. The input
data would normally be in a file, possibly obtained by translating some
other representation (e.g., T.4 format) to run-length or bit-map format.
The program produces an output consisting of data compressed in Dacom
450 format and packed in 585-bit frames along with the corresponding
header and checksum information.
The encoding program needs to be careful about how to break data
across frames and how many bits of data to insert in each frame. The
rules mentioned in section 2.2. help to solve the first problem. The
second problem is a little less understood. The problem arises because
data bits are required by the printing mechanism at a constant rate, but
successive frames transmitted at the line rate can contain different
amounts of decoded information, leading to buffer overrun in extreme
cases.
In order to compensate for the rate mismatch, it has been found
sufficient to control the size of the data portion of the frame
according to a simple set of empirical rules which produce results quite
similar to the scanner iteslf. According to these rules, a frame is
"full" when it contains more than 500 bits of data or when the data
represents more than 4800*X pels (or columns) of information,
where X = 2 for transmission rate 2.4 kbs,
X = 1 for transmission rate 4.8 kbs,
X = 1/2 for transmission rate 9.6 kbs.
Dacom 450 facsimile data is ordinarily stored as an RT-11 file in
the so-called UCL format [4]. In this format, each 585-bit frame is
stored in a 76-byte record. The first byte specifies the length of the
record, the second specifies a command and the remaining 72 bytes
contain the 585 bits of the original Dacom 450 frame zero-filled at the
Dacom 450/500 Facsimile Data Transcoding PAGE 11
end. The command byte is coded as follows:
a. 56 (70 octal): The data field contains a setup frame (the first
record of the file). The length byte is 76 (114 octal).
b. 57 (71 octal): The data field contains a data frame (the remaining
records in the file except the last one). The length byte is 76
(114 octal).
c. 58 (72 octal): End of file (the last frame of the file). There is
no data field and the length byte is 2.
The decode program produces 16-bit run length words as its output.
Each run is encoded in a 16-bit word, with white in positive and black
in negative two's complement values. A zero word terminates each line,
with the trailing white run suppressed if present. An all-white line is
encoded as a single run of length one followed by a zero word. The file
is terminated by a line of length zero, that is, a single zero word.
Bit-map files consist of a four-byte header followed by the data.
The header consists of two 2-byte quantities, the first of which
represents the number of pels in a line and the second the number of
lines in the page. Each scanning line of data is represented in an
integral number of bytes, the last byte of a line zero-filled if
necessary.
The Dacom 500 machines are high-speed versions of the Dacom 450
machines and operate in the 50-Kbps range using the T.4 compression
algorithm. This algorithm, described in the [5], is a one-dimensional
one, rather than the two-dimensional one used in the Dacom 450 and
described in previous sections. Since this algorithm is well known and
the subject of an international standard, it will not be further
discussed here.
The decoding program has been implemented in the PDP-11 MACRO-11
assembly language for the DCNET and RT-11 operating systems. It
operates on a file containing facsimile data encoded using the T.4
algorithm and produces a file in bit-map format.
The decoding program scans the input data bit-by-bit and recognizes
sequences of bits which form valid run-length codes (see the tables in
[5]). The table of Huffman codes can be represented as a binary tree
with the values of the run lengths (e.g. 1, 2, 64, 1728, etc.) at the
terminal nodes and each branch labeled 0 or 1. The code for any run
length then is the sequence of branch labels on the path from the root
to the terminal node representing this length.
Dacom 450/500 Facsimile Data Transcoding PAGE 12
The tables for black and white run-length codes are stored as
separate binary trees in the decoding program. The decoding algorithm
starts by initializing an accumulator at zero. It then begins at the
root of the corresponding tree and traverses the tree as it consumes
bits one-by-one from the input. When a terminal node is reached, the
value stored at that node is added to the accumulator. If a make-up
node is reached, the value at that node is added to the accumulator and
the search is resumed with the same tree to obtain the terminating
value; otherwise, the accumulator represents the current run length and
the search resumes with the alternate tree.
The encoding program is also implemented in the PDP-11 MACRO-11
assembly language for the DCNET and RT-11 operating systems. It scans
the bit-map input and encodes each run of black or white pels by a
simple table lookup of the Huffman codes. It operates on a file
containing facsimile data in bit-map format and produces a file in T.4
format. The T.4 specifications [5] require a minimum transmission time
per scan line of 4.3 milliseconds, which at 50-Kbps corresponds to 242
bits (DATA bits plus any required FILL bits plus the EOL bits equal 242
bits minimum).
The file consists of a number of 512-byte blocks, the first of
which is the header. The header contains a list of two-byte entries,
the first of which contains the number of pages and the remaining the
lengths (in blocks) of each page in turn. The remaining blocks of the
file contain the data for each page in T.4 format. The data for each
page is preceded by a page-setup command and succeeded by a
page-end-of-record command, as transmitted by the Dacom 500. The format
of both commands consists of the 12-bit T.4 EOL code (000000000001)
repeated six times and followed by a special 4-bit code word also
repeated six times. The special code word consists of bits B1 through
B4 as defined below.
B1: VERTICAL RESOLUTION
0 = 7.7 lines per millimeter
1 = future option, not implemented
B2: OUTPUT PAPER LENGTH
0 = short length (Letter size)
1 = long length (Legal size)
B3: DOCUMENT IN SCANNER
0 = no document present (end of page)
1 = document present (beginning of page)
B4: ODD PARITY OVER B1-B4
Dacom 450/500 Facsimile Data Transcoding PAGE 13
Four different file formats are presently used in our system for
facsimile data storage: Dacom 450, Dacom 500 (T.4), 16-bit run-length
and bit-map. The sizes of typical files (in megabits) in these formats
are shown below for comparison.
File Dacom Dacom 16-bit
450 500 run-length
----------------------------------
PNGUIN 0.22 0.5 0.27
INTELP 0.62 0.77 3.3
PANDA 1.02 2.03 6.41
The file called PNGUIN is a block drawing of dancing penguins and
represents a "small" file. The file called INTELP is a composite
INTELPOST test image with text and graphics and represents a "medium"
file. Finally, the file called PANDA is a half-tone newspaper
photograph of a giant panda and represents a "monster" file (this file
was recorded on the Dacom 450 in quality mode and is therefore about
half the size it would be in detail mode). The size of the bit-map file
for all these images is 3.8 megabits.
Figure 5 shows the file sizes (in 512-byte blocks) and transcoding
times (in seconds) for the INTELPOST test page. The file sizes are
indicated on the boxes, while the transcoding times are indicated on the
arrows. All times were obtained on the LSI-11/23 processor.
193 925
+-----------+ 95 +-----------+
| |----------->| |
| T.4 | | Bit-map |
| |<-----------| |
+-----------+ 165 +-----------+
A |
60 | |
.----------------------' |110
| |
| V
+-----------+ 89 +-----------+
| |----------->| |
|Run-length | | Dacom 450 |
| |<-----------| |
+-----------+ 153 +-----------+
413 155
Figure 5. File Sizes and Transcoding Times
Dacom 450/500 Facsimile Data Transcoding PAGE 14