Limit on Coding and Modulation Gains in Fiber-Optic Communication - PowerPoint PPT Presentation

Limit on Coding and Modulation Gains in Fiber-Optic Communication Systems Yi Cai Tyco Telecommunications Laboratories, 250 Industrial Way West, Eatontown NJ, 07724, USA

Introduction • A fundamental question for fiberoptic communication systems: “How close is the actual performance to the fundamental capacity limit?” • The fiberoptic channels studied here are channels dominated by Amplified Spontaneous Emission Noise (ASEN), hereafter referred to as ASEN channels • We extend the capacity formulae for Additive White Gaussian Noise (AWGN) channels to ASEN channels by taking into account two orthogonal polarizations • Based on the evaluated capacities of ASEN channels, we discuss possible gains from different coding and modulation techniques

Definition of Channel Capacity • Channel capacity is defined as C = lim T → ∞ (log 2 M ) / T bits/s, where M is the number of different signal functions of duration T on the channel that can be reliably distinguished • Claude Shannon derived the AWGN channel capacity as ⎛ ⎞ C C E ⎜ ⎟ = + b log 2 1 bits/s/Hz, where W is the channel bandwidth, ⎜ ⎟ W ⎝ W N ⎠ 0 and E b / N 0 is the signal to noise ratio per information bit (SNR/bit) • For ASEN channel capacity evaluation, we assume an ideal receiver detects a channel’s full optical field rather than just the intensity

ASEN Channel vs. AWGN Channel • AWGN Channel > One white Gaussian noise source > Noise is additive to signal • ASEN Channel > Two orthogonal polarization modes in the same frequency band > Noises in the two polarizations are independent white Gaussian noises > Only noise component parallel in polarization to the signal is additive, and orthogonal noise component can be eliminated by polarizer An ASEN channel comprises two independent AWGN channels in the same frequency band

Capacity of ASEN Channels • ASEN channel capacity can be evaluated by combining the capacities of two independent AWGN channels in the same frequency band > Double the AWGN channel capacity > Shift the doubled capacity curve towards lower Eb/N0 (SNR/bit) by 3dB • An ASEN channel can achieve two times as much as an AWGN channel capacity with a 3-dB lower SNR/bit • Note that combining two independent AWGN channels occupying different frequency bands does not increase the channel capacity

Capacity Bound: ASEN Channels vs AWGN Channels 4 ASEN channel AWGN channel capacity bound capacity bound C / W (bits/s/Hz) 3 Shannon limit can be 2 “broken” Shannon limit by ASEN channels 1 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 SNR / bit (dB) Shannon limit on AWGN channels is at − 1.6 dB, below which no error-free information can be possibly transmitted The limit on ASEN channels is at − 4.6dB

Capacities of BPSK and QPSK ASEN Channels QPSK system has twice the capacity • 2 capacity bound of BPSK system C/W (bits/s/Hz) The larger channel capacity can be • utilized to save signal power 1 At 0.8bit/s/Hz, QPSK should give • 2.3dB 2.3dB OSNR benefit over BPSK QPSK Q: How to get the OSNR gain? BPSK A: Use large overhead FEC 0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 0.1nm OSNR (dB) for C = 10 Gbits/s Capacity without Polarization Division Multiplexing

Understanding the OSNR Benefit of QPSK over BPSK QPSK 100%OH QPSK QPSK BPSK BPSK 10G symbols/s 10G bits/s BPSK 0%OH 1/2 1/2 (2Es) (2 E s ) 10G symbols/s 10G bits/s To achieve the same error probability (4 E s ) 1/2 1/2 (4Es) If discard the 100% overhead • SNR_QPSK = SNR_BPSK + 3dB If use the 100% overhead for signal averaging • SNR_QPSK = SNR_BPSK Constellation of QPSK and BPSK Constellation of QPSK and BPSK If use the 100% overhead for FEC • SNR_QPSK = SNR_BPSK – Net Coding Gain

Get the OSNR Benefit of QPSK over BPSK 16 At 0.8bit/s/Hz, BPSK and QPSK have • 25% and 150% overhead, respectively Max Net Coding Gain (dB) 2.3dB 14 From 25% to 150% FEC overhead, the • 12 max net coding gain increases by 2.3 dB Soft-decision FEC Hard-decision FEC QPSK requires large overhead FEC to 10 • get the full OSNR benefit over BPSK 25% overhead 150% overhead 8 6 0% 25% 50% 75% 100% 125% 150% FEC Overhead Maximum FEC net coding gain at 10 –15 BER

Capacity of ASEN Channels Employing Different Techniques Without Polarization Division Multiplexing With Polarization Division Multiplexing 4 4 capacity bound capacity bound Soft Dec. QPSK Soft Dec. QPSK 3 3 C / W (bits/s/Hz) C / W (bits/s/Hz) Soft Dec. BPSK Soft Dec. BPSK Hard Dec. BPSK Hard Dec. BPSK 2 2 1 1 state of the art state of the art 0 0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 0.1nm OSNR (dB) for C = 10 Gbits/s 0.1nm OSNR (dB) for C = 10 Gbits/s The state of the art in research corresponds to a linear RZ-DBPSK system with • a 25% overhead TPC having 10.7dB net coding gain at 10 –15 BER The possible gains from different techniques can be evaluated against the • current art in the field

Possible Gain From Different Techniques OSNR Gain (dB) For 0.8bit/s/Hz w/o PDM For 0.8bit/s/Hz w/ PDM 8 8 6 6 9.0 9.0 8.97 4 4 8.3 8.3 6.6 5.9 2 4.7 2 2.2 2.2 0.9 0.9 0 0 t t C C C C C C C C C C i i m m E E E E E E E E E E i i F F F F F F F L F F F L d d t n t n d t t d t t f f f f f f r o r o r o o i r o o i a a a a a a S S S S S S G G H H H H + + + + + + K K K K K K S S S S S S P P P P P P B Q B Q B B Significant gain can be obtained by using QPSK + large overhead FEC • Employing QPSK + soft-decision FEC + PDM, fiberoptic channels can be as • close as 0.03dB to the capacity bound at 0.8bit/s/Hz

Conclusions • At 3dB lower SNR/bit, 2-polarization fiberoptic channels have twice the capacity of AWGN channels. • Significant OSNR gain can be potentially obtained by employing advanced modulation, PDM, and large overhead FEC techniques