SOME REMARKS ABOUT A POSSIBLE NEW STANDARD FOR TELEMETRY CHANNEL CODING WITH HIGH SPECTRAL EFFICIENC

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SOME REMARKS ABOUT A POSSIBLE NEW STANDARDFOR
TELEMETRY CHANNEL CODINGWITH HIGH SPECTRAL
EFFICIENCY

• Gian Paolo Calzolari, Marco Chiani, Franco
  Chiaraluce, Roberto Garello
• Remark The work here presented is one of the
  current contributions to the activities of CCSDS
  Sub Panel 1B where other Member Agencies are also
  very active!

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CCSDS channel coding standard 1 Reed-Solomon,
Convolutional, Concatenated Turbo Codes
1 CCSDS 101.0-B-5, Telemetry Channel Coding,
Blue Book, Issue 5, June 2001

• CRS a (255,223) or CRS (255,239) Reed-Solomon
  code with 8-bit symbols and Error Correction
  Capability ECC 16 or 8 symbols Code-rate R
  0.875 or 0.937.
• CCC a 64-state, rate-1/2 binary convolutional
  code Code-rate R 0.5 puncturable to CCC
  Code-rates 0.667 / 0.750 / 0.833 / 0.875.
• CSC their serial concatenation RS outer code
  through an interleaver of length (255?I) bytes,
  with I 1,2,3,4, or 5 Code-rates 0.437 /
  0.583 / 0.656 / 0.729 / 0.765 / 0.469 / 0.625 /
  0.703 / 0.781 / 0.820.
• CTC a family of turbo codes with nominal rates
  1/2, 1/3, 1/4, or 1/6 Code-rate R 0.500 /
  0.333 / 0.250 / 0.167.

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Requirements for future high data-rate missions

• DATA-RATES Very high, ranging from a few Mbps to
  hundreds of Mbps.
• BANDWIDTH-EFFICIENCY Large (due to high
  data-rates and spectral
• crowding from many satellites). Target spectral
  efficiency at least 1.5
• bit/s/Hz over 4-PSK (binary codes with code-rate
  R ? 3/4).
• POWER-EFFICIENCY Very large coding gains needed
  (due to limited
• transmitted power from satellites of small
  dimensions).
• ERROR RATES Some applications may require
  extremely low error
• probabilities (poor error resilience of video and
  image compression
• techniques). Example Frame Error Rates 10?7.
• COMPLEXITY Limited for both encoders (realized
  on board) and
• decoders (due to very high data rates involved).

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The codes studied by ESOC, University of Ancona
and University of Bologna (2,3)

• Turbo codes (16-state, 8-state, DVB-like,
  partially systematic)
• Product codes
• Low density parity check codes (LDPCC)
• Methods of analysis
• Simulation at high/medium error rates (BER ? 10?7
  or FER ? 10?4),
• Analytical expressions at low/very low error
  rates (BER ? 10?8 or FER ? 10?5) 4 R.
  Garello, P. Pierleoni, and S. Benedetto
  Computing the Free Distance of Turbo Codes and
  Serially Concatenated Codes with Interleavers
  Algorithms and Applications IEEE J. on Select.
  Areas in Commun., vol. 19, pp. 800-812, May
  2001.

2 University of Ancona, Bandwidth-efficient
coding schemes Final Report, ESA/ESOC Contract
No. 14128/00/D/SW, Dec. 2000. 3 University of
Ancona, Highly efficient channel codes for high
data rate missions Final Report, ESA/ESOC
Contract No. 15048/01/D/HK (SC), Dec. 2001.
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ESA proposal Punctured CCSDS Turbo Codes

• PCTC (Punctured CCSDS Turbo Codes) obtained by
  puncturing CCSDS turbo code CTC represent a
  pragmatic and versatile solution.
• Code designed for code-rates 3/4, 7/8, 8/9,
  11/12, and 15/16 with external puncturing.

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Results for PCTC - Punctured CCSDS Turbo Codes

Simulation and Error floor Rate-3/4 N 8920
(dmin 10, Amin 29, wmin 169)
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Results for PCTC - Punctured CCSDS Turbo Codes

Simulations and Error floor Rate-7/8 N 8920
(dmin 5, Amin 79, wmin 316)
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Results for PCTC - Punctured CCSDS Turbo Codes

• Very useful for versatile and re-configurable
  implementations
• a single chip could realize a code-rate ranging
  from 1/6 to 15/16.
• Extremely powerful at high/medium error rates
  (FER ? 10?3).
• Still powerful at low error rates (FER ? 10?4 ,
  10?5).
• Error floor phenomenon (due to small minimum
  distances) not very powerful at very low error
  rates (FER ? 10?8).
• (Exception rate-3/4 codes, which are still
  good, especially for large data frame lengths.)
• Digital implementation at very high data rates
  seems problematic over some tens of Mbit/s.
• Useful as a short term solution (especially for
  rate-3/4 codes).
• Ideal for applications requiring not too low
  error rates.
• Can be adopted as a benchmark for comparison of
  other schemes.

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Improving PCTC (Punctured CCSDS Turbo Codes)
non-systematic (partially systematic)
puncturing patterns
Information bits can be punctured, too

• For every block of 24 information bits
• information bits only 18 transmitted
• parity check bits only 14 transmitted (7 for
  each encoder)
• Nominal rate 24/(1814)3/4

Ex rate-3/4 PCTC
u p1 p2
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Ad-hoc design for CCSDS data-frame lengths and
code-rates

• Data frame lengths (compatible with data frame
  lengths of CCSDS turbo codes, Reed-Solomon codes
  and concatenated codes)
• F 1784 and 8920 bits
• Code-rates R 3/4, 7/8,
  15/16
• Decoding algorithm BCJR algorithm (15
  iterations)
• Performance analysis
• simulation
• error floor evaluation
• comparison with systematic punctured CCSDS turbo
  code

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PCTC (Punctured CCSDS turbo codes) systematic
vs. non-systematic
F 1784 bits and R 3/4
Systematic (dmin/Amin/wmin) (6/4/8)
Better Water-Fall region
Partially systematic (dmin/Amin/wmin)
(10/3/6)
Larger minimum distances Better error floor curves
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Partially Systematic Punctured CCSDS Turbo Codes
comments

• Ad hoc design of partially systematic puncturing
  patterns allows to obtain PCTCs with larger
  minimum distances and better error floors.
• ?
• Improved performance at very low error rates.
• Worse performance at high/medium error rates.
• Penalty paid by iterative decoding looks slightly
  larger than for systematic PCTC
• (? 0.5 dB).
• Minimum distances computed by limiting the input
  weight (true minimum distances could be lower,
  even if the probability of this event should be
  low).
• The design of effective partially systematic
  puncturing patterns is generally difficult.
• Only simple rules of thumb are currently
  available.

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Product Codes

CP C1?C2
C1(n1, k1, d1)
C2(n2, k2, d2)
kP k1k2
CP(nP, kP, dP)
nP n1n2
dP dmin d1d2
?
Special case C1 C2
kP k2,
nP n2,
dmin d2,
RP k2/n2.
Extended Hamming Codes CP (EHl)2 are generally
preferred since they permit to increase the
product code minimum distance from dmin 9 to
dmin 16.
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Product codes

• Very powerful at low/very low error rates (due to
  large minimum distances by construction,
  partially attenuated by very large multiplicity
  which raise up their asymptotic bounds).
• Commercial chips implementing their co-decoders
  already exist, working up to 200 Mbit/s (seem
  useful for re-configurable applications, too).
• Less powerful than punctured CCSDS turbo codes
  for high/medium error rates (usually down to FER
  ? 10?4).
• The design of product codes for typical CCSDS
  data frame lengths and code-rates may require the
  use of
• puncturing
• parity code as constituent codes
• which reduce their minimum distances and raise
  their asymptotic bounds.

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Product codes Design for CCSDS data frame
lengths and data-rates

• Data frame lengths (compatible with data frame
  lengths of CCSDS turbo codes, Reed-Solomon codes
  and Concatenated codes)
• F 1784 and 8920 bits
• Code-rate
• R 3/4, 7/8, 15/16
• Constituent codes
• Shortened extended Hamming codes
• Parity codes when necessary
• (no puncturing)
• Decoding algorithm
• with optimal feedback coefficients
  (15 iterations)
• Performance analysis
• simulation
• error floor evaluation
• comparison with punctured CCSDS turbo code

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Product codes Design for CCSDS data frame
lengths and data-rates
Turbo Product Code with F 1784 bits and
code-rate R 3/4 TPC (2430,1786)
(45,38)x(54,47) (dmin/Amin/wmin)
(16/12664512/148820688)
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Product codes Design for CCSDS data frame
lengths and data-rates
Turbo Product Code with F 1784 bits and
code-rate R 7/8 TPC (2032,1785)
(127,119)x(16,15) (dmin/Amin/wmin)
(8/9921240/69722100)
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Product codes Design for CCSDS data frame
lengths and data-rates
Turbo Product Code with F 8920 bits and
code-rate R 3/4 TPC(11500,8917)(46,37)x(250,2
41) (dmin/Amin/wmin)(16/388728905/4789821944)
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Results for product codes

• Design for CCSDS data frame lengths and
  code-rates confirms that product codes are very
  powerful at low/very low error rates.
• Typically, for code-rate R ? 7/8 they outperform
  systematic PCTC at FER ? 10?4 ? 10?5.
• For code-rate 3/4 and F 8920 bits, PCTC perform
  better than product codes even at very low error
  rates.

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Low Density Parity Check Codes (LDPCC)

• Block Codes with very sparse matrixes, invented
  in 5
• Re-discovered and re-interpreted in 6
• Advantages
• Decoder highly parallelizable
• Implicit Error Detection
• Drawbacks
• Encoder complexity
• Error floor?

5 R.G.Gallager. Low-Density Parity-Check
Codes. IRE Transactions on Information Theory,
vol. IT-8, pp. 21-28, Jan. 1962. 6 D.J.C.
McKay. Good Error-Correcting Codes based on Very
Sparse Matrices. IEEE Transactions on
Information Theory, vol. 45, pp. 399-431, March
1999.
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• Regular LDPCC
• Regular LDPCC have good performance but a little
  worse than turbo code
• Irregular LDPCC 7
• The degree of each node (variable or check) is
  allowed to vary
• according to some distribution
• Problem To find good distributions
• Through optimization Irregular LDPCC can be
  found that compare favorably with the best turbo
  codes

7 T. Richardson, A. Shokrollahi, R. Urbanke.
Design of Capacity-Approaching
Irregular Low-Density Parity Check Codes. IEEE
Transactions on Information Theory, vol. 47, pp.
619-637, Feb. 2001.
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Results for (irregular, non-cyclic) LDPCC

• Very powerful at both high and low error rates,
  especially for high code-rates

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Low Density Parity Check Codes based on Finite
Geometries (LDPCC-FG)

• Recent proposal 8 to design (strictly)
  regular LDPCC
• Exploits some useful properties of Euclidean and
  projective
• geometries over finite fields
• Regular LDPCC can be constructed maintaining a
  large
• minimum distance, and a simple encoder
  structure based on the
• cyclic or quasi-cyclic underlying structure
  of the code

8 Y. Kou, S. Lin and M. P.C. Fossorier. Low
Density Parity Check Codes Based on
Finite Geometries A Rediscovery and New
Results. IEEE Trans. on Inform. Theory, vol.
47, pp. 2711-2736, Nov. 2001.
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• Practical implementations
• Introduction of turbo-like codes in important
  international standards (UMTS, DVB (Return to
  satellite), CCSDS, many others under discussion).
• Large interest for practical implementations.
• Until now ad hoc DSP/FPGA/ASIC implementations
• (e.g., ESA DSP turbo decoder).
• First dedicated commercial chips just available.

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• Commercial chips
• Turbo codes some companies (Broadcom, IMEC,
  STMicroelectronics) have recently announced chips
  able to work with data rates up to 155 Mbps.
• Product codes commercial chips working with data
  rates up to 155 Mbit/s already available (AHA).
• Low Density Parity Check Codes IP cores
  announced, able to support extremely high data
  rates, up to some Gbps (Flarion).

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The lessons learned

• Generally speaking
• Parallel concatenated turbo codes (e.g. CCSDS
  turbo codes) and irregular LDPCC confirm their
  excellent performance at high/medium error rates
  (FER gt 10?4). Some LDPCC may become interesting
  at very low error rates.
• Product codes confirm their excellent performance
  at very low error rates (FER lt 10?8).
• In the intermediate region (10?8 lt FER lt 10?4),
  depending on the frame length and rate, solutions
  can be found (based on partially systematic turbo
  codes, DVB-like turbo codes, double-turbo codes,
  low density parity check codes) which behave
  better.
• An all-powerful code does not exist.
• The choice may depend on the target (possibly
  realistic) for the quality requirements Which
  error rates are really of interest?