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ELEC 486 Final Presentation Forward Error Correction in Coherent Optical Systems. Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 March 31, 2016 Connor Hendricks 10086654 Jack Heysel 10062814 ELEC 486 Final Presentation

SLIDE 1

ELEC 486 Final Presentation

Forward Error Correction in Coherent Optical Systems. Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 March 31, 2016

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 1 / 22

SLIDE 2

Outline

1 Motivation and Background

Motivation Background

2 Coding Principles

Soft and Hard FEC

3 Third Generation Technology

Turbo Codes LDPC

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 2 / 22

SLIDE 3

Section 1 Motivation and Background

1 Motivation and Background

Motivation Background

2 Coding Principles 3 Third Generation Technology

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 3 / 22

SLIDE 4

Mathematical Model of Signal Transmission

We will use the additive white Gaussian noise (AWGN) channel: Alice x Encoder + Nt ∼ N(0, σ2) f(x) y Decoder Bob g(y) Can Alice hope to communicate reliably to Bob? Yes, if the data rate is less than or equal to the channel capacity (in Bits/sec), given by C(P) = B log2

P N0B

where B is the channel bandwidth, P is the signal power, and N0 is the

noise spectral power density.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 4 / 22

SLIDE 5

Relation to Optical Communication

The channel capacity is a best case scenario. In reality, we are lower than that. How can we transmit reliably? Increase SNR Increase complexity of the transmission scheme Add (clever) redundancy

(a) (b) Figure 1: (a) Filled circles represent achieved channel capacity at 7% redundancy, hollow circles represent the twice the constellation points. (b) Several estimates of channel capacity.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 5 / 22

SLIDE 6

Role of FEC

The basic question is why should we bother with FEC? We want: Low optical power High data rate Low system complexity Low BER The system constrains us by: Limited power budget Noise Demanding transmission needs

Figure 2: Effect of FEC on BER.

Conclusion: We need FEC to bridge the gap between the optimal communication rate and engineering tradeoffs.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 6 / 22

SLIDE 7

Definition

1 A coding scheme is a pair of functions f, g that map source

symbols to code symbols, and code symbols to source symbols respectively.

2 The code rate of an (n, k) coding scheme is the fraction

R = n k where n is the number of code symbols and k is the number of source symbols. This is commonly called redundancy.

3 A error detecting code is a coding scheme that can detect one

r more symbol errors in a recieved message y. A error

correcting code is a coding scheme that can correct said error. The benchmark code is the Reed-Solomon(255,239) code, with 7%

redundancy. This is “2nd generation” technology, used for 10-40Gb

systems

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 7 / 22

SLIDE 8

Section 2 Coding Principles

1 Motivation and Background 2 Coding Principles

Soft and Hard FEC

3 Third Generation Technology

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 8 / 22

SLIDE 9

Hard decision FEC

Definition (Hard FEC)

A hard FEC coding scheme is a coding scheme whereby the decoder determines whether the bit is a “1” or “0” based on a single decision threshold.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 9 / 22

SLIDE 10

Soft decision FEC

Definition (Soft FEC)

A soft FEC coding scheme is a coding scheme the decoder determines whether the bit is a “1” or “0” based on a multiple decision thresholds.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 10 / 22

SLIDE 11

Soft FEC vs Hard FEC

Soft decision FEC makes use of multiple level quantization sampling and saves that data to aid in the error coreection process, hard decision FEC does not

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 11 / 22

SLIDE 12

16 QAM Constellation

Hard FEC makes an immediate decision on the identity of each bit Soft FEC begins processing the bits that the system is very certain about.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 12 / 22

SLIDE 13

Performance Comparison: Hard FEC vs Soft FEC

Transfer coding gain is the decrease in operating power necessary to maintain the same BER as an uncoded system due to FEC. Coding loss is the power increase (due to added redundancy) necessary to maintain the same operating BER. Net Coding Gain = Transfer Coding Gain − Coding loss

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 13 / 22

SLIDE 14

Error Floors

Definition (Error Floor)

The error floor is the term given to areas on BER curves where the performance of the system degrades. Error floors are common to both Turbo Codes and LDPC codes Through effective algorithms, the error floors of these codes can be reduced considerably

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 14 / 22

SLIDE 15

Interleaving

Definition (Interleaver)

Interleavers re-arrange the values of many code words among each other Errors tend to occur in bursts so interleavers are used to spread concentrated errors across multiple code words This is used to turn a large unsolvable error into many smaller solvable errors.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 15 / 22

SLIDE 16

Section 3 Third Generation Technology

1 Motivation and Background 2 Coding Principles 3 Third Generation Technology

Turbo Codes LDPC

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 16 / 22

SLIDE 17

Turbo Codes

Each encoder creates p/2 parity bits generally using Recursive Systematic Convolutional Codes (RSC Codes) Two Decoders provide soft analysis on the p/2 parity and they share results with each other The process works iteratively until ideally both decoders reach the same conclusion

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 17 / 22

SLIDE 18

Low Density Parity Check codes (LDPC)

Definition (LDPC)

LDPC is a linear code obtained from the sparse parity check matrix invented by Gallager in the 1960s. Linear Code: Can be described by a generator matrix G or a partiy check matrix H c = xG and cHT = 0 where c = codeword and x = sourceword LDPC: Example: Irregular LDPC(3367,2821)

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 18 / 22

SLIDE 19

LDPC State of the art

Irregular LDPC(3367,2821) 19% redundancy, NCG of 8.1 dB at a post-FEC BER of 10−9 Generalized LDPC(3639, 3213) 23.6% redundancy with which a record NCG of 10.9dB at a post-FEC BER of 10−13 demonstrated in a Monte-Carlo simulation.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 19 / 22

SLIDE 20

Comparing Turbo Codes and LDPC Codes

Similarities Both codes provide similar BER curves and both allow systems to get much closer to the Shannon Limit Both codes use iterative processes to evaluate errors in codes Differences Turbo codes evaluate data at a fixed rate, while LDPC codes evaluate data at a variable rate. LDPC codes can be evaluated in parallel. Turbo Codes Cannot LDPC generally have a lower level of complexity Overall LDPC codes are the faster alternative.

Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 20 / 22

SLIDE 21

References I

[1]

F. R. Kschischang and B. P. Smith, “Forward error correction (fec) in optical communication,” in

Lasers and Electro-Optics (CLEO) and Quantum Electronics and Laser Science Conference (QELS), 2010 Conference on, May 2010, pp. 1–2. [2]

I. B. Djordjevic, L. Xu, and T. Wang, “Simultaneous chromatic dispersion and pmd compensation

by using coded-ofdm and girth-10 ldpc codes,” Opt. Express, vol. 16, no. 14, pp. 10 269–10 278, Jul

2008. [Online]. Available: http://www.opticsexpress.org/abstract.cfm?URI=oe-16-14-10269

[3] Hauwei, “Soft-decision fec: Key to high-performance 100g transmission,” Hauwei Inc, Tech. Rep., 2016. [4]

M. Nakazawa, K. Kikuchi, and T. Miyazaki, High Spectral Density Optical Communication

Technologies, ser. Optical and Fiber Communications Reports. Springer Berlin Heidelberg, 2010. [Online]. Available: https://books.google.ca/books?id=3by7rSVR0MUC [5]

S. J. Johnson, “Introducing low-density parity-check codes,” University of Newcastle, Australia, 2006.

[6]

T. Sugihara, T. Yoshida, and T. Mizuochi, “Collaborative signal processing with fec in digital

coherent systems,” in Optical Fiber Communication Conference. Optical Society of America, 2013,

pp. OM2B–3.

[7]

K. S. Andrews, D. Divsalar, S. Dolinar, J. Hamkins, C. R. Jones, and F. Pollara, “The development
f turbo and ldpc codes for deep-space applications,” Proceedings of the IEEE, vol. 95, no. 11, pp.

2142–2156, Nov 2007. [8]

K. Fagervik and A. S. Larssen, “Performance and complexity comparison of low density parity check

codes and turbo codes,” in Proc. Norwegian Signal Processing Symposium,(NORSIG’03), 2003, pp. 2–4. [9]

Y. Han, A. Dang, Y. Ren, J. Tang, and H. Guo, “Theoretical and experimental studies of turbo

product code with time diversity in free space optical communication,” Opt. Express, vol. 18, no. 26,

pp. 26 978–26 988, Dec 2010. [Online]. Available:

http://www.opticsexpress.org/abstract.cfm?URI=oe-18-26-26978 Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 21 / 22

SLIDE 22

References II

[10]

M. Y. Leong, “Coherent optical transmission systems: Performance and coding aspects,” 2015.

[11] KITZ.co.uk, “Interleaving explained,” 2006. [Online]. Available: http://www.kitz.co.uk/adsl/interleaving.htm [12]

P. Grant, “Turbo coding,” May 2009. [Online]. Available:

http://cnx.org/contents/d01eb103-9ac8-4698-8930-35fd157ad32f@3 Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 ELEC 486 Final Presentation March 31, 2016 22 / 22

SLIDE 23

ELEC 486 Final Presentation

Forward Error Correction in Coherent Optical Systems. Connor Hendricks 10086654 Jack Heysel 10062814 James Vuckovic 10045194 March 31, 2016

Outline

1 Motivation and Background

Motivation Background

2 Coding Principles

Soft and Hard FEC

3 Third Generation Technology

Turbo Codes LDPC

Section 1 Motivation and Background

1 Motivation and Background

Motivation Background

2 Coding Principles 3 Third Generation Technology

Mathematical Model of Signal Transmission

We will use the additive white Gaussian noise (AWGN) channel: Alice x Encoder + Nt ∼ N(0, σ2) f(x) y Decoder Bob g(y) Can Alice hope to communicate reliably to Bob? Yes, if the data rate is less than or equal to the channel capacity (in Bits/sec), given by C(P) = B log2

P N0B

noise spectral power density.

Relation to Optical Communication

The channel capacity is a best case scenario. In reality, we are lower than that. How can we transmit reliably? Increase SNR Increase complexity of the transmission scheme Add (clever) redundancy

(a) (b) Figure 1: (a) Filled circles represent achieved channel capacity at 7% redundancy, hollow circles represent the twice the constellation points. (b) Several estimates of channel capacity.

Role of FEC

The basic question is why should we bother with FEC? We want: Low optical power High data rate Low system complexity Low BER The system constrains us by: Limited power budget Noise Demanding transmission needs

Figure 2: Effect of FEC on BER.

Conclusion: We need FEC to bridge the gap between the optimal communication rate and engineering tradeoffs.

Definition

1 A coding scheme is a pair of functions f, g that map source

symbols to code symbols, and code symbols to source symbols respectively.

2 The code rate of an (n, k) coding scheme is the fraction

R = n k where n is the number of code symbols and k is the number of source symbols. This is commonly called redundancy.

3 A error detecting code is a coding scheme that can detect one

correcting code is a coding scheme that can correct said error. The benchmark code is the Reed-Solomon(255,239) code, with 7%

systems

Section 2 Coding Principles

1 Motivation and Background 2 Coding Principles

Soft and Hard FEC

3 Third Generation Technology

Hard decision FEC

Definition (Hard FEC)

A hard FEC coding scheme is a coding scheme whereby the decoder determines whether the bit is a “1” or “0” based on a single decision threshold.

Soft decision FEC

Definition (Soft FEC)

A soft FEC coding scheme is a coding scheme the decoder determines whether the bit is a “1” or “0” based on a multiple decision thresholds.

Soft FEC vs Hard FEC

Soft decision FEC makes use of multiple level quantization sampling and saves that data to aid in the error coreection process, hard decision FEC does not

16 QAM Constellation

Hard FEC makes an immediate decision on the identity of each bit Soft FEC begins processing the bits that the system is very certain about.

Performance Comparison: Hard FEC vs Soft FEC

Transfer coding gain is the decrease in operating power necessary to maintain the same BER as an uncoded system due to FEC. Coding loss is the power increase (due to added redundancy) necessary to maintain the same operating BER. Net Coding Gain = Transfer Coding Gain − Coding loss

Error Floors

Definition (Error Floor)

The error floor is the term given to areas on BER curves where the performance of the system degrades. Error floors are common to both Turbo Codes and LDPC codes Through effective algorithms, the error floors of these codes can be reduced considerably

Interleaving

Definition (Interleaver)

Interleavers re-arrange the values of many code words among each other Errors tend to occur in bursts so interleavers are used to spread concentrated errors across multiple code words This is used to turn a large unsolvable error into many smaller solvable errors.

Section 3 Third Generation Technology

1 Motivation and Background 2 Coding Principles 3 Third Generation Technology

Turbo Codes LDPC

Turbo Codes

Each encoder creates p/2 parity bits generally using Recursive Systematic Convolutional Codes (RSC Codes) Two Decoders provide soft analysis on the p/2 parity and they share results with each other The process works iteratively until ideally both decoders reach the same conclusion

Low Density Parity Check codes (LDPC)

Definition (LDPC)

LDPC is a linear code obtained from the sparse parity check matrix invented by Gallager in the 1960s. Linear Code: Can be described by a generator matrix G or a partiy check matrix H c = xG and cHT = 0 where c = codeword and x = sourceword LDPC: Example: Irregular LDPC(3367,2821)

LDPC State of the art

Irregular LDPC(3367,2821) 19% redundancy, NCG of 8.1 dB at a post-FEC BER of 10−9 Generalized LDPC(3639, 3213) 23.6% redundancy with which a record NCG of 10.9dB at a post-FEC BER of 10−13 demonstrated in a Monte-Carlo simulation.

Comparing Turbo Codes and LDPC Codes

References I

References II

Questions?