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ELEC 486 Final PresentationForward Error Correction in Coherent Optical Systems.

Connor Hendricks 10086654Jack Heysel 10062814

James Vuckovic 10045194

March 31, 2016

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

Outline

1 Motivation and BackgroundMotivationBackground

2 Coding PrinciplesSoft and Hard FEC

3 Third Generation TechnologyTurbo CodesLDPC


Section 1

Motivation and Background

1 Motivation and BackgroundMotivationBackground

2 Coding Principles

3 Third Generation Technology


Mathematical Model of Signal Transmission

We will use the additive white Gaussian noise (AWGN) channel:

Alicex

Encoder +

Nt ∼ N(0, σ2)

f(x) yDecoder Bob

g(y)

Can Alice hope to communicate reliably to Bob? Yes, if the data rateis less than or equal to the channel capacity (in Bits/sec), given by

C(P ) = B log2

(1 +

P

N0B

)where B is the channel bandwidth, P is the signal power, and N0 is thenoise spectral power density.


Relation to Optical Communication

The channel capacity is a best case scenario. In reality, we are lowerthan that. How can we transmit reliably?

Increase SNRIncrease complexity of the transmission schemeAdd (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 needsFigure 2: Effect of FEC on BER.

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


Definition

1 A coding scheme is a pair of functions f, g that map sourcesymbols to code symbols, and code symbols to source symbolsrespectively.

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 ofsource symbols. This is commonly called redundancy.

3 A error detecting code is a coding scheme that can detect oneor more symbol errors in a recieved message y. A errorcorrecting 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 10-40Gbsystems


Section 2

Coding Principles

1 Motivation and Background

2 Coding PrinciplesSoft and Hard FEC

3 Third Generation Technology


Hard decision FEC

Definition (Hard FEC)

A hard FEC coding scheme is a coding scheme whereby the decoderdetermines whether the bit is a “1” or “0” based on a single decisionthreshold.


Soft decision FEC

Definition (Soft FEC)

A soft FEC coding scheme is a coding scheme the decoder determineswhether 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 samplingand saves that data to aid in the error coreection process, hard decisionFEC does not


16 QAM Constellation

Hard FEC makes an immediate decision on the identity of each bit SoftFEC 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 powernecessary to maintain the same BER as an uncoded system due toFEC.

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 theperformance 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 bereduced 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 spreadconcentrated errors across multiple code wordsThis is used to turn a large unsolvable error into many smallersolvable errors.


Section 3

Third Generation Technology

1 Motivation and Background

2 Coding Principles

3 Third Generation TechnologyTurbo CodesLDPC


Turbo Codes

Each encoder creates p/2 parity bits generally using RecursiveSystematic Convolutional Codes (RSC Codes)

Two Decoders provide soft analysis on the p/2 parity and theyshare results with each other

The process works iteratively until ideally both decoders reach thesame conclusion


Low Density Parity Check codes (LDPC)

Definition (LDPC)

LDPC is a linear code obtained from the sparse parity check matrixinvented by Gallager in the 1960s.

Linear Code:

Can be described by a generator matrix G or a partiy checkmatrix 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 apost-FEC BER of 10−9

Generalized LDPC(3639, 3213) 23.6% redundancy with which arecord NCG of 10.9dB at a post-FEC BER of 10−13 demonstratedin a Monte-Carlo simulation.


Comparing Turbo Codes and LDPC Codes

Similarities

Both codes provide similar BER curves and both allow systems toget 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 codesevaluate 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.


References I

[1] F. R. Kschischang and B. P. Smith, “Forward error correction (fec) in optical communication,” inLasers 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 compensationby using coded-ofdm and girth-10 ldpc codes,” Opt. Express, vol. 16, no. 14, pp. 10 269–10 278, Jul2008. [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 CommunicationTechnologies, 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 digitalcoherent 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 developmentof 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 checkcodes 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 turboproduct 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


http://www.opticsexpress.org/abstract.cfm?URI=oe-16-14-10269

https://books.google.ca/books?id=3by7rSVR0MUC

http://www.opticsexpress.org/abstract.cfm?URI=oe-18-26-26978

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


http://www.kitz.co.uk/adsl/interleaving.htm

http://cnx.org/contents/d01eb103-9ac8-4698-8930-35fd157ad32f@3

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