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 James Vuckovic 10045194 March 31, 2016 1 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 2 / 22
Section 1 Motivation and Background 1 Motivation and Background Motivation Background 2 Coding Principles 3 Third Generation Technology Connor Hendricks 10086654 Jack Heysel 10062814 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 3 / 22
Mathematical Model of Signal Transmission We will use the additive white Gaussian noise (AWGN) channel: N t ∼ N (0 , σ 2 ) y x f ( x ) g ( y ) + Alice Encoder Decoder Bob 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 � � P C ( P ) = B log 2 1 + N 0 B where B is the channel bandwidth, P is the signal power, and N 0 is the noise spectral power density. Connor Hendricks 10086654 Jack Heysel 10062814 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 4 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 5 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 6 / 22
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 or 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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 7 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 8 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 9 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 10 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 11 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 12 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 13 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 14 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 15 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 16 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 17 / 22
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 cH T = 0 where c = codeword and x = sourceword LDPC: Example: Irregular LDPC(3367,2821) Connor Hendricks 10086654 Jack Heysel 10062814 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 18 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 19 / 22
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 ELEC 486 Final Presentation James Vuckovic 10045194 March 31, 2016 20 / 22
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