VOYAGER IMAGE DATA COMPRESSION AND BLOCK ENCODING

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1 VOYAGER IMAGE DATA COMPRESSION AND BLOCK ENCODING Michael G. Urban Jet Propulsion Laboratory California Institute of Technology 4800 Oak Grove Drive Pasadena, California ABSTRACT Telemetry enhancement techniques implemented through flight software modifications and utilization of special flight hardware enable the Voyager 2 spacecraft to reduce telemetry transmission rates used at Saturn by over 50% for the extended mission to Uranus and Neptune with negligible loss in information return. Techniques employed include: C Parallel operation of the redundant Flight Data Subsystem (FDS) processors C Image Data Compressor (IDC) using noiseless (fully reconstructable) coding techniques C Reed-Solomon (RS) encoding of downlink telemetry INTRODUCTION Although Voyager 2 is travelling along a trajectory which permits encounters with Uranus and Neptune, the Voyager spacecraft design was optimized for telemetry return from Jupiter and Saturn only. Throughout the remainder of this paper, the nominal mission refers to the Voyager 1 and 2 encounters with Jupiter and Saturn, and the extended mission refers to the the Voyager 2 encounters with Uranus and Neptune. Uranus and Neptune, with their greater distances from Earth, require that the spacecraft transmit data at approximately 1/4 and 1/9 the signal levels, respectively, achievable at Saturn. In order to return the same volume of data at the lower transmission rates necessary during the extended mission, more efficient telemetry techniques are required.

2 BACKGROUND Due to the differences in the amount and required quality of the data, a distinction is made between image data and General Science and Engineering (GS&E) data. GS&E data are generated by Voyager in a fixed format at a rate of 3.6 kb/s. Good data quality (bit error rate P # 5 E-5) is required for GS&E. e Real-time image data represent the majority of the data volume returned from the Voyager spacecraft. Voyager image data are output to the Flight Data Subsystem (FDS) as a digital data stream consisting of 800 image lines, each containing 800 picture elements, or pixels. Line 1 is the top line of the image and pixel 1 is the leftmost pixel of the line. Each pixel is digitized as an 8-bit word, so its brightness is discretized as one of 256 levels. Due to constraints imposed by development cost and spacecraft power, volume, and weight requirements, the telemetry system was designed to return the image data uncompressed for the nominal mission. Return of one complete uncompressed image requires transmission of 5.12 million bits. Since a noise-induced bit error is confined to a single pixel, acceptable bit error rates are higher (up to P = 5 E-3) than for GS&E. e Figure 1 illustrates the Voyager telemetry system design for the nominal mission. The GS&E data were Golay encoded prior to combining in the FDS with the image data to form a single telemetry stream. The Golay encoder has an overhead of 100%, but since only the GS&E data were encoded, the encoder parity represented a small fraction of the total telemetry stream. The bit error correction capability of the Golay decoding process allows the combined telemetry stream to be recovered at the higher bit error rates acceptable for image data and still satisfy the GS&E bit error rate requirements. After output from the FDS, the telemetry stream is convolutionally encoded in the Modulation/ Demodulation Subsystem (MDS). This concatenated encoding scheme permitted data rates 5.5 times higher than would have been possible with an uncoded telemetry stream satisfying GS&E data quality requirements (1). Since the output rate of the GS&E is fixed, the total downlink data rate is controlled by the output rate of image data. Note that as the downlink data rate is reduced, the parity data generated by the Golay encoder becomes a larger fraction of the total telemetry stream, reducing the efficiency of the nominal telemetry configuration. At Jupiter, kb/s were recoverable from both Voyager spacecraft, permitting return of one image per 0.8 min when combined with the Golay encoded GS&E. At Saturn, 29.9 kb/s were recoverable from Voyager 2, permitting return of one image per 4 min when combined with the Golay encoded GS&E.

3 REQUIREMENTS FOR THE EXTENDED MISSION At the lower signal levels available from Voyager 2 during the extended mission, lower tranmission rates are necessary. Golay code becomes a significant fraction of the total data rate (25% at 14.4 kb/s). Utilizing the nominal mission telemetering techniques at the lower transmission rates necessary in the extended mission would have required significant further reductions in the output rate of image data. This has two adverse effects. Obviously, the total number of images returned during a time-constrained observation is less. Also, increasing the readout time of the image from the camera to the FDS reduces the quality of the image. Image readout times in the range of 8 to 12 min would have been necessary at the transmission rates available for the extended mission. A more efficient means of telemetry transmission is needed. A simple Image Data Compressor (IDC) is employed to reduce the number of bits required to return an image (2) in the extended mission. In order to accommodate the storage and execution of the IDC algorithm, the primary and secondary FDS, which were previously redundant, are operated in parallel. The primary FDS executes the normal tasks of instrument control, GS&E processing, and telemetry format construction, and the secondary FDS compresses the image data. Compressing the image data has the effect that a single bit error in the image line now propagates through the remainder of the line. This effect results in the compressed image data requiring a data quality comparable to that of the GS&E. Achieving this at useable data rates requires block encoding the entire telemetry stream for error correction. Employing the Golay encoder on the entire telemetry stream would double the downlink data rate, offsetting any performance gained through error correction. A Reed-Solomon (RS) encoder had been installed on the spacecraft to allow more efficient data transmission at Saturn with the S-band transmitter in the event the X-band transmitter normally used for science had failed. This RS encoder is used instead to block encode the combined telemetry stream for the extended mission. The RS encoder is non-redundant on Voyager. Figure 2 illustrates the telemetry system used for the extended mission. As with the system used for the nominal mission, an inner convolutional code is applied in the MDS. The FDS configurations for the nominal and extended missions are compared in Figure 3. The convolutional encoder is external to the FDS and is not shown. As non-redundant configurations and hardware are employed, a backup FDS operating program utilizing the nominal mission telemetry configuration is kept available to uplink to the spacecraft in the event of a non-recoverable failure to the FDS.

4 REED-SOLOMON ENCODER The Voyager RS encoder is a systematic block encoder implemented in hardware on the spacecraft. Symbol length is 8 bits. One codeword consists of 223 input symbols and 32 parity symbols. If input data is less than 223 symbols, lead zeroes are added for parity symbol generation but are not transmitted. This results in a overhead for parity symbol output which can vary from format to format. At peak efficiency (all 223 input symbols are data), parity overhead is about 15%. Error correction threshold is 16 symbols (input or parity) per codeword. If threshold is exceeded, no errors can be corrected in the affected codeword. Output of the RS encoder hardware consists of the parity symbols only. The original data are delivered to the downlink directly along a separate path from the FDS and combined with the parity bits from the RS encoder, as illustrated in Figure 4. With this configuration, the input data can be extracted from the telemetry stream and processed uncorrected if the RS encoder fails or if the error correction capability is exceeded. To improve the RS encoder tolerance to burst errors inherent in the decoding of the convolutional data stream, input and parity symbols are interleaved to a depth of four. That is, successive input data symbols are assigned to successive codewords for parity symbol generation in a cycle that repeats every four symbols until the 223-symbol input data fields for the four codewords have been constructed. Note that since the input data symbols (the original data) are delivered to the telemetry stream along a separate data path, the original data are not interleaved in the actual downlink. Codeword data symbol interleaving is shown in Figure 4. Codeword parity symbols are similarly interleaved prior to output, as illustrated in Figure 5. This interleaving process allows burst error correction for up to 4 x 16 = 64 consecutive symbols (data or parity) in the telemetry stream without exceeding the threshold of the RS decoding process. The four interleaved codewords comprise a code block of 8 x 223 x 4 = 7136 data bits followed by 8 x 32 x 4 = 1024 parity bits. IDC ALGORITHM The IDC algorithm is a universal noiseless coding compressor which permits exact reconstruction of the original data (2). The algorithm is implemented in software in the secondary FDS processor. Sophistication of the algorithm is constrained by the the following spacecraft characteristics: C FDS memory size ( bit words) C FDS processing speed (1008 machine cycles per 2.5 ms)

5 C Fixed-length telemetry formats C RS encoder data block size (7136 bits) Principle The primary constraint on IDC design is processing speed. The IDC algorithm employs a simplified split-pixel compressor which has been dubbed the FAST compresssor (2). For a given pixel in a line, the difference between adjacent pixels is assumed (1) to have the probability distribution: Pr(d=0) $ Pr(d=+l) $ Pr(d=-l) $ Pr(d=+2)... (1) where Pr is the probability and d is the difference between adjacent pixel words. In other words, the difference between adjacent pixels is usually small and therefore can be telemetered with a smaller word. This strategy is accommodated by running a line of image data through a reversible pre-processor which determines the difference, ), j between 8-bit pixels p and P for all 800 pixels in the line. The pre-processor then maps j j-1 these differences into the set of non-negative integers, *, as shown in Table I. Figure 6 is j a block diagram of the reversible pre-processor. Split-pixel compression schemes are employed when the distribution of differences is expected to be broad, rather than concentrated at d = 0. Let P N be the original sequence of N 8-bit pixel words, p 1,... p i,... p N, and * N be the N-pixel block of 8-bit pixel integers, * 1,... * j,... * N. In split pixel compression, * N is split into 2 separate sequences: L k, containing the sequence of samples of the k Least Significant Bits (LSBs) of * j, and M 8,k, containing the sequence of samples of the 8-k Most Significant Bits (MSBs) of * j. Separate operators, R L,k and R M,8-k are then applied to encode each of the two sequences. The operator chosen for each is the most efficient encoder for that particular sequence. L k samples tend to be random; M 8-k samples have the distribution given in (1). The two encoded sequences are then combined and output into the telemetry stream. A block diagram of the general splitpixel compressor is shown in Figure 7. The Voyager FAST compressor is an adaptive split-pixel compressor. That is, the value of k is selected adaptively on a block-by-block basis to minimize the total bits required to output the combined encoded sequences. An identifier (ID) which specifies the value of k used in a given block must then be combined with the compressor output for the N-pixel block. the k chosen for the N-pixel block is the minimum value for which all bits in the sequence M 8,k are zero. This way the sequence M 8,k is known a priori and need not be transmitted. The operator R L,k is defined as:

6 R L,k [L k ] = L k (2). where L k is the k LSBs of the N-pixel block of pixel integers, and R L,k is the operator for compression of L k. This means that the operator R L,k does not modify the N x k -bit sequence L. k The FAST compressor operator R N,k (where N, the empty set, is used to signify that M 8,k is not transmitted) used to encode the original sequence P is: R [P ] = L ; k # 6 N,k N k R [P ] = P ; k $ 7 N,k N k where R N,k the FAST compressor operator, P N is the original sequence of N 8-bit pixel words, and L is the k LSBs of each of the N samples of the pixel differences *. k For a block of N pixels, the FAST compressor transmits the k LSBs of the N pixel difference integers when k # 6, and transmits the original N 8-bit pixel words when k $ 7. While implementing R to permit a value of k = 7 would have resulted in increased L,7 compression efficiency, the occurence of sequences L is rare and the savings would be 7 negligible. Note that k is determined by the largest * j of the block and is used for all * j of the block, regardless of their size. The block length N must be fixed in the algorithm design. Here a trade must be made between the overhead in telemetry for transmission of the 3-bit ID k and the cost of transmitting k-bit pixel differences when k is large due to one large pixel difference in N. The two values of N most readily implemented in FDS processing were 5 and 10 pixels/ block. Better performance is provided by 5 pixels/block. This is what the FAST compressor uses. A block diagram of the Voyager FAST compressor is shown in Figure 8. Implementation One line of image data (800 pixels) is buffered in secondary FDS memory. In order to avoid the bit cost of encoding noise which exists on the left edge of the image, pixels 1 through 3 are set equal to pixel 4. The differences between adjacent pixels are determined. Each difference is then mapped into the field of non-negative integers. N (3) N

7 The resulting 800 integers are grouped into 160 blocks of 5 integers each. For each block i, k i is determined and used to select the word length and 3-bit block ID as indicated in Table II. For any word length greater than 6 bits, the uncompressed 8-bit pixels are transmitted instead for that block. For k # 6, the pixel difference integers for block i are i packed by deleting the 8 - k most significant bits (all zeroes). Each line of compressed i image data is preceded by an 8-bit reference pixel, the initial pixel of the 1-line image field. The literature (1,2) defines Pixel Entropy over a line of image as the theoretical minimum number of bits required to transmit the image line divided by the number of pixels in the line, giving an average bits/pixel for that line. Due to the simple scheme required by spacecraft constraints, the FAST compressor is not an optimum design. A more useful parameter is the average bits/pixel, E, over an image line required by the IDC algorithm to telemeter the line: E = M/800 (4) where E is the observed pixel entropy (in bits/pixel), and M is the total number of bits required by the Voyager IDC algorithm to telemeter one line of imaging. As defined, M does not include the 8-bit reference pixel. In general, the FAST compressor operates about 0.6 bits/pixel below optimum over the range of interest in Voyager image data (2). Note that the overhead for the 3-bit Block IDs k,... k contributes 0.6 bits/pixel to E Voyager FDS processing requires a fixed length for a given telemetry format. A fixed field, B, of the format minor frame must be budgeted for the compressed image data. A trade must be made between image field length and transmission efficiency. If B > M, then B - M bits in the minor frame are wasted. If B < M, the image data has exceeded its budget and some of the image data are lost. The trade is complicated by the inability to determine E a priori for a given scene. This discussion suggests a definition which could serve as a performance parameter for compressed image formats; namely, the pixel entropy tolerance, b, for the image format: b = B/800 (5) where b is the pixel entropy tolerance and B is the number of bits in the image format budgeted for one line of compressed imaging. The pixel entropy tolerance b for a given compressed image format is the maximum permissible observed pixel entropy for full information return in that format. If E > b, the image line is truncated. Figure 9 illustrates the format of compressed image data generated by the Voyager IDC algorithm.

8 In test cases run using Saturn images, 85% of the test images experienced less than 3% image data loss when b = 3 bits/pixel due to line truncation. This is significant, as it will be shown later that RS encoder block length limits b to a maximim of 3.09 bits/pixel. To reduce the effect of data loss due to line truncation when it occurs, two enhancements are included in the Voyager IDC algorithm. First, adjacent lines are compressed from opposite sides of the image. This way the image data lost due to line truncation can be approximately reconstructed by averaging the data from the adjacent lines. Odd numbered lines are compressed and telemetered left-to-right (forward compressed), and the reference pixel is pixel number 1. Even numbered lines are compressed and telemetered right-to-left (reverse compressed), and the reference pixel is pixel number 800. Figure 10 shows the effect of line truncation on a Saturn test image. The left image is the original, returned uncompressed from the spacecraft. The right image is compressed with a low pixel entropy tolerance of b = 2.23, chosen to exaggerate the effect. Line truncation is observed. The effect is most pronounced in lines which cross the camera reseau marks, where a large difference between adjacent pixels is to be expected. The second technique for minimizing the effect of line truncation reduces E by less than or equal to 1 bit/pixel by right-shifting the pixel data prior to differencing in the pre-processor. The leftmost bit is the MSB in the FDS. The inequality derives from the fact that no improvement is observed on blocks which would have a word length of 1 without the right-shifting operation. When reconstructing the image, the effect of the right-shift operation is that the least significant bit of the original pixel word is lost, and its discretization is reduced by half, to 128 shades of gray. Figure 11 shows the reduced line truncation effect from right-shifting on a Saturn test image. The adverse discretization can t be perceived by the human eye but does affect quantitative analysis of the image data. The right-shifting function can be enabled and disabled on a picture-by-picture basis on the spacecraft and is useful when the observed pixel entropy E for an image is expected a priori to exceed the pixel entropy tolerance b. While faster image readout rates are both desired and recoverable at the downlink signal levels available in the extended mission, FDS processing speed constrains the compressed image readout rate to no faster that 1 image per 4 min, the same as was used at Saturn. At this rate the FAST compressor in FDS software is compressing /3 pixels per second. VOYAGER COMPRESSED IMAGE DATA FORMAT Voyager employs five compressed image data formats (one recorded, four real-time) for the extended mission. One uncompressed image data format with embedded, Golay encoded GS&E is retained to record data at kb/s. Most of the compressed image

9 data formats trade image readout rate, image editing, and/or pixel entropy tolerance, b, in order to achieve lower transmission rates on the telemetry stream. Discussed here is the telemetry format most commonly used for return of compressed real time image data during the extended mission. This format is illustrated in Figure 12. It utilizes both the fastest image data readout rate (1 image in 4 min) and the highest pixel entropy tolerance available within spacecraft constraints. Minor frame duration is 0.6 s. Start of the minor frame is defined by the 48 bit header, which contains the JPL-standard 32 bit frame sync code, 8 zeroes, and an 8 bit ID which defines the format for telemetry processing. The header is not RS encoded. The standard 3.6 kb/s GS&E data contribute 2160 bits to the minor frame; these are RS encoded. A fill field of 16 bits follows the GS&E data. This is inserted as an expedient to FDS processing. Recall that the RS encoder can encode a maximum of 7136 bits per code block. Subtracting the 2176 bits of GS&E and fill, 4960 bits remain for encoding and telemetering of reference pixels and compressed image data. At the readout rate of 1 image (800 lines) in 4 min, two image lines must be included in the format minor frame. Each image line is therefore budgeted 2472 bits for its compressed data field. This results in a pixel entropy tolerance, b, of 3.09 bits/pixel. The RS code block parity bits contribute 1024 bits to the minor frame. This completes the data content of the minor frame and would provide a downlink data rate of kb/s. However, FDS hardware permits telemetry output only at certain discrete rates. The next data rate available, in the FDS is 14.4 kb/s. Therefore, an indeterminate field of 432 bits is added to fill out the minor frame to a 14.4 kb/s data rate. This final data rate is less than 50% of the 29.9 kb/s data rate used to return the same amount of data (neglecting line truncation) at Saturn. RESULTS AT URANUS Due to the low light levels and feature contrast in the Uranus atmosphere and ring system, the IDC algorithm performed extremely well on Voyager 2. Closeup images of the five major moons of Uranus, which would have had higher values of E, required the spacecraft to perform Image Motion Compensation (IMC) maneuvers to cancel smear induced by the relative motion of the spacecraft and target (3). The Voyager high-gain antenna is rigidly attached to the spacecraft bus, so these maneuvers interrupted the downlink from the spacecraft, requiring storage of the images on an onboard tape recorder for later playback. The telemetry format used to record the IMC images recorded the image data uncompressed. No modifications to the Voyager IDC algorithm will be made for the Neptune encounter.

10 SUMMARY AND CONCLUSIONS The Voyager spacecraft design, and in particular the FDS, employing block redundancy and in-flight reprogrammability, allows in-flight modifications which significantly improve mission science return. Utilization of a simplified IDC algorithm (the FAST compressor) reduced by greater than a factor of 3 the bits required to return an image. The FAST compressor and RS encoding combined to reduce by over half the transmission rates necessary for return of combined image data and GS&E when compared to the nominal telemetry configuration used at Saturn. The improvements result in an increase in mission risk, as non-redundant hardware and spacecraft configurations are necessary, but contingency strategies are provided. The performance improvements justify the increased risk. ACKNOWLEDGEMENT The work described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. ACRONYMS AND ABBREVIATIONS FDS GS&E ID IDC IMC JPL LSB MDS MSB RS Flight Data Subsystem General Science and Engineering data Identifier Image Data Compression Image Motion Compensation Jet Propulsion Laboratory Least Significant Bit Modulation/Demodulation Subsystem Most Significant Bit Reed-Solomon REFERENCES 1. Rice, Robert F., End-to-End Imaging Information Rate Advantages of Various Alternative Communication Systems, JPL Publication Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, September, 1982.

11 2. Rice, Robert F. and Lee, Jun-Ji, Some Practical Universal Noiseless Coding Techniques, Part II, JPL Publication Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, March, Marderness, Howard P., Voyager Engineering Improvements for Uranus Encounter, NO , AIAA Astrodynamics Conference, Williamsburg, Va., August Table 1: Pixel Difference Integer Mapping DIFFERENCE )(j) = P(j) - P(j-1) INTEGER *(j) Table II: Pixel Block ID Mapping BLOCK COMPRESSED WORD DIFFERENCE ID LENGTH k(j), bits RANGE , , , , , , (NOT USED) 000 (SEND UNCOMPRESSED 8-bit PIXELS)

12 Figure 1: Voyager Telemetry System Design, Nominal Mission Figure 2: Voyager Telemetry System Design, Extended Mission Figure 3: Flight Data Subsystem (FDS) Configurations For Real-Time Image Data Return, Nominal vs. Extended Missions

13 Figure 4: Reed-Solomon Input Data Symbol Interleaving Figure 5: Reed-Solomon Parity Symbol Interleaving

14 Figure 6: Reversible Pre-Processor for IDC Figure 7: General Split-Pixel Compressor

15 Figure 8: Voyager FAST Compressor Block Diagram Figure 9: Format of Compressed Image Data

16 UNCOMPREESSED IMAGE COMPRESSED IMAGE (b = 2.23 bits/pixel) Figure 10: Effect of Line Truncation 8-bit PIXEL RESOLUTION 7-bit PIXEL RESOLUTION (RIGHT-SHIFTED) Figure 11: Line Recovery Due to Right-Shifting of Original Data

17 Figure 12: Voyager Real-Time Data Format