1. Short Uplink LDPC Codes: Proposed Methods
for CLTU Acquisition and Termination
Kenneth Andrews *
and Massimo Bertinelli †
* Jet Propulsion Laboratory, California Institute of Technology
† European Space Agency
© 2015 California Institute of Technology
Government sponsorship acknowledged.
CCSDS Fall Meetings Darmstadt November 9-12, 2015

2. Start and Tail Sequences for TC LDPC Codes
Objective
Our goal is to offer LDPC codes as an alternative to the existing BCH code in the telecommand Blue Book
We have agreed to add two binary rate-1/2 LDPC codes: (n=128,k=64) and (n=512,k=256)
A pseudo-randomizer will be used, as in the TM standard
Communication is still via CLTUs (Communications Link Transmission Units): independent transmissions consisting of one or more codewords
Optimal applications remain similar: low data volume, low complexity receivers, including emergency communications. High data-volume links, likely at high data rates, would be better served by using the TM standard.
Remaining issues
Method to detect the start of a CLTU
Method to detect the end of a CLTU
Four teleconferences (mostly) resolved these issues
The following slides are a summary of those discussions
If we reach consensus, we can proceed with Pink Sheets to add a chapter to the TC Synchronization and Channel Coding Blue Book (231.0-B-2)

3. Start and Tail Sequences for TC LDPC Codes
Methods to detect the start of a CLTU
Markerless acquisiton, using LDPC code structure
16- or 32-symbol start sequences
Preferred option: 64-symbol start sequence, C B0
Methods to detect the end of a CLTU
In-band signaling: one bit per codeword
In-band signaling: one-byte count field in first codeword
Undecodable codeword
Preferred option: 64-symbol tail sequence, value TBD
Preferred option: No tail sequence; end of CLTU detected by decoder failure

4. 1. Start sequences of various lengths
Markerless acquisition, using LDPC code structure
Advantage: No overhead
Disadvantage: High computational complexity
Disadvantage: Insufficient detection performance with the (128,64) code

5. 2. and 3. Start sequence of 16, 32, or 64 symbols
Start sequences of various lengths
Advantage: A shorter start sequence has less overhead
Disadvantage: A shorter start sequence has poorer detection performance
A 64-symbol marker is necessary and sufficient
Implementation options
A hard correlator is sufficient if the threshold is well chosen
The “approximate Massey” algorithm provides plenty of margin, with modestly increased implementation complexity

6. 3. 64-symbol start sequence
Start sequence selection:
The 64-symbol sequence from the TM standard is familiar, and has reasonable auto-correlation and cross-correlation properties.
Randomized
all-ones
TM-standard
64-sym ASM
Cross-correlation with idle seq.
Auto-correlation ±6 ±4 64
Zero-one balance
35/29
(surplus of
3 zeros)
30/34
2 ones)
Max values: ±6
9,10,13

7. 1. In-band signaling: one bit per codeword
“Distributed” signaling, using first bit of each codeword
Advantage: Low overhead, if CLTU consists of only a few codewords (as it should)
Disadvantage: Message length is an inconvenient 63 or 255 bits

8. 2. In-band signaling: one-byte count field
“One-shot” signaling, with count of codewords in CLTU
Advantage: Modestly lower error rate
Disadvantage: First message is 8 bits shorter than the others
Disadvantage?: This treads into protocol territory

9. 3. Terminate with undecodable codeword
Undecodable codeword, as with BCH codes
Advantage: Greatest similarity to existing standard
Disadvantage: An undecodable LDPC codeword would be 128 or 512 symbols long.
Disadvantage: This is not compatible with an incomplete decoder

10. 4. Terminate with a tail sequence
Termination with a 64-symbol tail sequence
Advantage: Similar to start sequence detection in performance, implementation, and complexity
Advantage: Compatible with a complete LDPC decoder
Disadvantage: More overhead than most of the alternatives, but this may not be very important.

11. 5. No tail sequence Use no tail sequence
Tail of CLTU is declared when decoder over-runs and fails to decode
Advantage: No overhead
Disadvantage: Incompatible with complete decoders
Disadvantage?: The end of a CLTU cannot be distinguished from a communications error. This is a disadvantage if the receiver should behave differently in the two cases.
Back up to beginning of failed codeword
Table 4-2: CLTU Reception Events (Receiving End)

12. Open question: Should we allow both options 4 and 5?
Preferred option: 64-symbol tail sequence, value TBD
Preferred option: No tail sequence; end of CLTU detected by decoder failure
Open question: Should we allow both options 4 and 5?
How does a complete decoder recover if it misses the tail sequence?
Open question: If a tail sequence is used, what should its value be?
I think it cannot be the start sequence, without creating confusion.
The undecodable BCH tail sequence is C5C5 C5C5 C5C5 C579
Any better suggestions?

13. Backup

14. Error analysis with no tail sequence
Probabilities and consequences of incorrect state transitions
Missed S2->S3; P(miss). Lost CLTU.
Accidental S2->S3; P(FA). If so, next outcome is one of ...
Decoding failure; probability near unity. No consequence.
Improper decoding; probability similar to code’s undetected error rate? Codeword passed to protocol parser, and next outcome is one of ...
If this appears as a multiple-codeword TF, one of them will probably fail. If this appears as a one-codeword TF, it is probably rejected; probability near 1 if CRC is used, or if SCID and other fields verified.
Unintended command received. Probability ~ P(FA) × P(UER) × P(proto) per symbol, where P(proto)~2-16 if a CRC is used, or 2-10 if SCID is validated.
Accidental S3->S2. Lost remainder of CLTU; P(CWER) per CW.
Missed S3->S2; probability similar to code’s undetected error rate? If so, next outcome is one of ...
Improper decoding, as above.
Probability of unintended command ~ P(UER) × P(proto) per CLTU.

15. Error analysis with 64-symbol tail sequence
Decoder performance
Correlator performance
With the (512,256) LDPC code, Eb/No~3.5 dB, the hard correlator is sufficient. The Massey algorithm provides plenty of margin with modestly increased complexity.

16. Complexity analysis with 64-symbol tail sequence
Complexity comparison
(128,64) LDPC (512,256) LDPC
Method Complexity Complexity
64-symbol, hard correlator 63 XORs/sym 63 XORs/sym
64-symbol, Massey 32 ops/sym 32 ops/sym
LDPC decoding 114 ops/sym 177 ops/sym
Units
operation: add, subtract, table-lookup, clipping
XOR: exclusive-OR; results are counted

17. Overhead analysis with 64-symbol tail sequence
A complete one-codeword transmission
A complete transmission includes a carrier sweep, and acquisition time for subcarrier and symbol lock.
carrier only
176 symbol acquisition
F symbol start seq
n symbol codeword
64 symbol term. seq?
(carrier only)
Acquisition time: a common value is 176 symbols
Carrier sweep: typical values are ±5 KHz (twice) at 200 Hz/sec, for a total time of >100 sec. Carrier-only time at end could be zero.
time f0
f0+5 kHz
200 Hz/sec
Overhead: F symbols out of c+176+F+n+64 symbols, where c=(carrier-only time)/(symbol period). Minimum data rate is typically bits/sec.
Example: F=64, n=128, c=100×7.8125=781. Overhead: 1.056=0.24 dB

18. Overhead analysis with 64-symbol tail sequence
Overhead (continued)
A secure one-codeword transmission
A spacecraft within range of a back-yard transmitter should use a cryptographically secure uplink.
Example: one (512,256) codeword, with 56 bits of USLP header, 48 bits of security header, 24 bits of data, and 128 bits of message authentication code.
Overhead: F symbols out of c+176+F+n+64 symbols, where c=(carrier-only time)/(symbol period). Maximum data rate is typically 2Kbps.
Example: F=64, n=512, c=100×2000=2e5. Overhead: = dB
carrier only
176 symbol acquisition
64 sym start seq
512 symbol codeword
64 symbol term. seq?
(carrier only)
File upload
JPL generally performs the carrier sweep and sends the acquisition sequence once. Then many transfer frames are sent, one transfer frame per CLTU. The minimum length of a transfer frame is one codeword; the maximum length is 1024 bytes.
Example: Suppose a file is transmitted as a series of 1024-byte CLTUs, encoded with a rate-1/2 LDPC code.
Overhead: ( )/16384 = = dB

19. Overhead analysis with 64-symbol tail sequence
Overhead conclusions
For short transmissions, the carrier sweep dominates the transmit time. Overhead from the start sequence is not important. The power efficiency of coding also is not important. The primary value of coding is to lower the undetected error rate.
For long transmissions, the start sequence is repeated with each CLTU. For long CLTUs, overhead from the start sequence is not important. However, a large number of short CLTUs (i.e. short transfer frames) is inefficient and should be avoided. Coding is important for power efficiency, and long codewords should be encouraged.