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

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)

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, 0347 76C7 2728 95B0 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

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

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

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 ...0101... 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

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

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

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

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.

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)

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?

Backup

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.

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.

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

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 7.8125 bits/sec. Example: F=64, n=128, c=100×7.8125=781. Overhead: 1.056=0.24 dB

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: 1.0003=0.0014 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+64)/16384 = 1.004 = 0.017 dB

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.