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

• rthogonal 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 = limT→∞ (log2M) / 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
• For ASEN channel capacity evaluation, we assume an ideal receiver

detects a channel’s full optical field rather than just the intensity

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + =

2 1

log N E W C W C

b

bits/s/Hz, where W is the channel bandwidth, and Eb/N0 is the signal to noise ratio per information bit (SNR/bit)

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

• rthogonal 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

Shannon limit can be “broken” by ASEN channels 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

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1 2 3 4 5 SNR / bit (dB) C / W (bits/s/Hz) ASEN channel capacity bound AWGN channel capacity bound Shannon limit

Capacities of BPSK and QPSK ASEN Channels

Capacity without Polarization Division Multiplexing

• QPSK system has twice the capacity
• f BPSK system
• The larger channel capacity can be

utilized to save signal power

• At 0.8bit/s/Hz, QPSK should give

2.3dB OSNR benefit over BPSK Q: How to get the OSNR gain?

A: Use large overhead FEC

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• 6 -5 -4 -3 -2 -1 0

1 2 3 4 5 6 0.1nm OSNR (dB) for C = 10 Gbits/s C/W (bits/s/Hz) QPSK BPSK 2.3dB capacity bound

Understanding the OSNR Benefit of QPSK over BPSK

QPSK 100%OH 10G symbols/s 10G bits/s BPSK 0%OH 10G symbols/s 10G bits/s

To achieve the same error probability

• If discard the 100% overhead

SNR_QPSK = SNR_BPSK + 3dB

• If use the 100% overhead for signal averaging

SNR_QPSK = SNR_BPSK

• If use the 100% overhead for FEC

SNR_QPSK = SNR_BPSK – Net Coding Gain

(4Es)

1/2

(2Es)

1/2

QPSK BPSK Constellation of QPSK and BPSK (4Es)1/2 (2Es)

1/2

QPSK BPSK Constellation of QPSK and BPSK

Get the OSNR Benefit of QPSK over BPSK

• At 0.8bit/s/Hz, BPSK and QPSK have

25% and 150% overhead, respectively

• From 25% to 150% FEC overhead, the

max net coding gain increases by 2.3 dB

• QPSK requires large overhead FEC to

get the full OSNR benefit over BPSK

6 8 10 12 14 16 0% 25% 50% 75% 100% 125% 150% FEC Overhead

Max Net Coding Gain (dB)

Soft-decision FEC Hard-decision FEC 2.3dB 25% overhead 150% overhead

Maximum FEC net coding gain at 10–15 BER

Capacity of ASEN Channels Employing Different Techniques

• 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

Without Polarization Division Multiplexing With Polarization Division Multiplexing

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1 2 3 4 5 6 0.1nm OSNR (dB) for C = 10 Gbits/s C/ W (bits/s/Hz) Soft Dec. QPSK Soft Dec. BPSK Hard Dec. BPSK capacity bound state of the art 1 2 3 4

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1 2 3 4 5 6 0.1nm OSNR (dB) for C = 10 Gbits/s C/ W (bits/s/Hz) Soft Dec. QPSK Soft Dec. BPSK Hard Dec. BPSK capacity bound state of the art

Possible Gain From Different Techniques

• 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

For 0.8bit/s/Hz w/o PDM

9.0 8.3 0.9 2.2 4.7 5.9

2 4 6 8 H a r d F E C S

• f

t F E C B P S K + H a r d F E C B P S K + S

• f

t F E C Q P S K + S

• f

t F E C G a i n L i m i t OSNR Gain (dB) For 0.8bit/s/Hz w/ PDM

8.3 6.6 2.2 0.9 8.97 9.0

2 4 6 8 H a r d F E C S

• f

t F E C B P S K + H a r d F E C B P S K + S

• f

t F E C Q P S K + S

• f

t F E C G a i n L i m i t

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