Patent Publication Number: US-10763970-B2

Title: Encoding for optical transmission

Description:
PRIORITY 
     
         
         
           
             This nonprovisional application is a U.S. National Stage Filing under 35 U.S.C. § 371 of International Patent Application Serial No. PCT/EP2016/069085 filed Aug. 10, 2016 and entitled “Encoding For Optical Transmission” which is hereby incorporated by reference in its entirety. 
           
         
       
    
     TECHNICAL FIELD 
     The present disclosure relates generally to methods of encoding an input signal for optical transmission, to corresponding apparatus for encoding, to corresponding transmission systems, and to corresponding computer programs for carrying out such methods. 
     BACKGROUND 
     It is known to provide various types of encoding for optical transmission systems. A particular field of application of such optical transmission systems is related to the introduction of 5G mobile systems which need higher capacity (100+Gbit/s) in the fiber transport network, starting from its first aggregation stages. Using dedicated fibers for backhauling radio base stations or for fronthaul connections between remote radio unit (RRU) and baseband processing unit (BBU) in a split architecture, is not always a solution, due to cable leasing or installation costs. Moreover, operators may use the same fiber infrastructure for multiple purposes, not only for mobile front-, mid-, and back-haul (i.e. X-haul) but also for fixed access and aggregation, further increasing the capacity requirement per installed fiber. 
     The trend towards network centralization and cloudification requires the capability to convey traffic from several non co-located RRU sites to one hub node, which hosts centralized network and baseband processing functions. This adds to the capacity requirement a distance requirement. Typical distances to be supported are up to 20 km, according to the maximum fiber propagation delay that the most common fronthaul protocols can tolerate (e.g. 100 μs, corresponding to 5 μs/km). 
     The capability to comply with any kind of network topology (bus, ring, tree, mesh) is also important to ensure the maximum deployment flexibility of future X-haul networks, enabling them to meet scenarios that can vary over a wide range, depending on operator and country. 
     DWDM networks can satisfy all the previous requirements. Coherent optical transceivers for transmission in Dense Wavelength Division Multiplexed (DWDM) optical transmission systems are known and can meet the distance requirement. However, the cost of coherent optical transceivers makes them less suitable for cost-sensitive network segments such as access and aggregation. New access technologies are increasing the traffic levels in access and aggregation networks segments, requiring higher optical channel capacities from 25 to 100 Gbit/s. There is a need for more cost-effective high speed optical transceivers. 
     A lower cost alternative to a coherent optical interface is a direct detection optical interface. Direct detection is widely used to provide 10 Gbit/s On Off Keying (OOK) optical channels. This technology is cheaper but suffers from two main drawbacks: (i) reduced sensitivity and noise tolerance; (ii) poor tolerance to chromatic dispersion. The first issue can be solved by using optical amplification, or by splitting the optical channels into two sub-channels at two different wavelengths, or by splitting the optical channels into two orthogonal linear polarization states. The second issue requires either the use of devices to compensate for the chromatic dispersion (e.g. Dispersion Compensating Fiber (DCF) or Fiber Bragg Grating (FBG)), or the use of a spectrally efficient modulation technique. For whatever modulation format, the narrower the spectrum, the lower the chromatic dispersion penalty. A narrow spectrum can be achieved by use of a multi-level modulation format or line coding. However, when using multi-level modulation formats, the achievable transmission distance is not always improved as the increased number of levels counterbalances the improved spectral efficiency, due to the lower tolerance of multi-level formats to the noise. 
     One typical solution provided by optical modules suppliers is the upgrade to DWDM of PAM-4 or DMT grey interfaces, (i.e. interfaces with no stabilized laser working in the 850 nm or 1310 nm wavelength regions) now used for interconnection purposes, which requires the minimal effort of replacing an uncooled laser with a stabilized one in the 1550 nm wavelength region. However, this solution is largely sub-optimal for system vendors or operators, for the reasons explained below. 
     DWDM uses the C band, centered on 1550 nm, rather than the O band, centered on 1310 nm. This has the big advantages of exploiting the EDFA amplification bandwidth and lower fiber attenuation values (attenuation coefficient is about 0.2 dB/km in C band and 0.3 dB/km in O band). However, moving from 1310 to 1550 nm, the fiber chromatic dispersion (roughly 1 and 17 μs/nm/km in O and C band, respectively), introduces a sensitivity penalty. At 10 Gbit/s the tolerated chromatic dispersion with 2 dB penalty is 800 μs/nm (about 47 km of fiber). Since the penalty scales with the square of the bit-rate, at 100 Gbit/s we obtain 8 μs/m for the same penalty value, which corresponds to about 500 m of fiber. Implementing DWDM systems in O band would not solve the problem because in absence of chromatic dispersion the four wave mixing (FWM, a fiber non-linear effect) would cause unacceptable inter-channel cross talk also at low channel power. 
     To deal with such chromatic dispersion in C band, non-coherent channels (e.g. based on 10 Gbit/s pluggable modules) rely on external dispersion compensators, which are modules that are placed in line to introduce a dispersion value equal and opposite to the fiber one. Coherent interfaces exploit instead electrical equalization at the receiver at the same purpose. In the former case, we have external devices that introduce additional cost and losses. In the latter one, energy consumption (tens of Watts) is the main drawback. Particularly for cost sensitive applications such as X-haul networks it would be desirable to avoid both of these issues. 
     Two known types of modulation formats at the transmitter side suitable for such front-haul interfaces are DQPSK and CAPS-3, which have benefits of good tolerance to chromatic dispersion. However, CAPS-3 has a better sensitivity and chromatic dispersion tolerance and significantly outperforms DQPSK for longer distances over about 15 km. For CAPS-3 the drawbacks are the cost and complexity of 8-state encoding circuitry, and the power consumption of the required high speed DAC. Accordingly, there is a need for a simplified encoding for optical transmission. 
     SUMMARY 
     An aspect of this disclosure provides a method of encoding for optical transmission of an input signal, comprising generating a first signal based on the input signal by providing a first delay, and by low pass filtering of the input signal. A second signal is generated based on the input signal and based on a second delayed version of the input signal having a second delay larger than the first delay, such that in response to a pulse on the input signal, the second signal has a sequence of two pulses, the two pulses coinciding respectively with leading and trailing edges of a corresponding pulse on the first signal. An encoded optical output signal is generated based on the first signal and the second signal. 
     Examples of apparatus having these features can have reduced complexity and cost for a given level of performance. Notably the particular arrangement of delays and filtering can enable important features of CAPS-3 encoded optical signal to be simulated so that the chromatic dispersion tolerance advantage of such known CAPS-3 coding can be achieved without needing the costly hardware such as a DAC and 8-state encoding circuitry of a known CAPS-3 encoder. Compared to other known coders of comparable simplicity and hardware cost, the chromatic dispersion tolerance can be notably higher which can enable longer reach without costly dispersion compensators, while maintaining the benefit of not needing expensive coherent receivers. It is based on an insight that the I and Q waveforms for the known CAPS-3 can be approximated or simulated by suitably delayed and filtered signals, and an insight that this means that simpler and less costly hardware can be used. 
     Any additional features can be added optionally. One such optional feature is the first signal and the second signal comprising first and second electrical signals and the step of generating based on the first signal and the second signal comprising modulating an I input of an IQ modulator according to the first electrical signal and modulating a Q input of the IQ modulator according to the second electrical signal, to provide the encoded optical output signal for transmission. 
     Another option is that the first and second signals have waveforms simulating I and Q waveforms of a CAPS-3 encoder. 
     Optionally the step of generating the second signal comprises adding the input signal to the second delayed version of the input signal. 
     Optionally for the steps of generating the first and second signals, the second delay is twice the duration of the first delay. 
     Optionally, for the steps of generating the first and second signals, the first delay is one symbol time of the input signal. 
     Optionally there is a step of altering a relative amplitude of the first and second signals before the step of generating the encoded optical output signal based on the first signal and the second signal. 
     Optionally the generating of the first and second signals is such that in response to multiple pulses on the input signal, the corresponding pulses of the first signal are alternately positive-going and negative-going, and the corresponding two pulses of the second signal go in the same direction as those of the first signal. 
     Optionally the low pass filtering has a pass band up to ¼T where T is a symbol time of the input signal. 
     Optionally the step of generating the second signal comprises using a low pass filtered version of the input signal. 
     Optionally the low pass filtering has a pass band up to 1/T where T is a symbol time of the input signal. 
     Optionally the first and second signals comprise first and second optical signals, and there is a step of using a modulator to generate an optical input signal from the input signal. In this case the step of generating the first signal comprises using a first optical delay for delaying the optical input signal, and the step of generating the second signal comprises generating the second optical signal based on the optical input signal and based on a second delayed version having a second optical delay longer than the first optical delay. The second optical signal is generated such that in response to a pulse on the input signal, the second optical signal has a sequence of two pulses, the two pulses coinciding respectively with leading and trailing edges of a corresponding pulse on the first optical signal. The step of generating the encoded optical output signal is based on optically combining the first optical signal and the second optical signal. 
     Optionally there is a step of using nested interferometers to generate the first and second optical signals, and to combine the first and second signals. 
     Optionally the step of altering a relative amplitude of the first and second signals comprises optically changing a relative amplitude of the first optical signal and the second optical signal. 
     Optionally the optical transmission is for front-haul between a radio terminal and a baseband processing unit. 
     Optionally there are subsequent steps of transmitting the encoded optical output signal to a receiver and using direct detection at the receiver to receive the optical transmission. 
     Another aspect of this disclosure provides apparatus for encoding an input signal for optical transmission, the apparatus comprising a first component configured to generate a first signal based on the input signal by providing a first delay, and by low pass filtering the input signal, and a second component configured to generate a second signal. The second signal is generated based on the input signal and based on a second delayed version of the input signal having a second delay larger than the first delay, such that in response to a pulse on the input signal, the second signal has a sequence of two pulses, the two pulses coinciding respectively with leading and trailing edges of a corresponding pulse on the first signal. There is an optical output component configured to generate an encoded optical output signal based on the first signal and the second signal. 
     Optionally the first component and the second component comprise first and second electrical circuitry, the first and second signals comprise first and second electrical signals, and the optical output component comprises an IQ modulator configured such that an I input of the IQ modulator is modulated according to the first electrical signal and a Q input of the IQ modulator is modulated according to the second electrical signal, to provide the encoded optical output signal for transmission. 
     Optionally the first and second components are configured to generate first and second signals having waveforms simulating I and Q waveforms respectively of a CAPS-3 encoder. 
     Optionally the second component is also configured to generate the second signal by adding the input signal to the second delayed version of the input signal. 
     Optionally the second component is configured to generate the second delayed version based on the second delay being twice the duration of the first delay. 
     Optionally the first component is configured to generate the first signal based on the first delay being one symbol time of the input signal. 
     Optionally there is a third component configured to alter a relative amplitude of the first and second signals before they are used to generate the encoded optical output signal. 
     Optionally the first and second components are configured to generate the first and second signals such that in response to multiple pulses on the input signal, the corresponding pulses of the first signal are alternately positive-going and negative-going, and the corresponding two pulses of the second signal go in the same direction as those of the first signal. 
     Optionally the low pass filtering has a pass band up to ¼T where T is a symbol time of the input signal. 
     Optionally the second component is configured to use a low pass filtered version of the input signal for generating the second signal. 
     Optionally the low pass filtered version of the input signal for generating the second signal having a pass band up to 1/T where T is a symbol time of the input signal. 
     Optionally the first and second components comprise first and second optical components and the first and second signals comprise first and second optical signals, the apparatus also comprising a modulator for generating an optical input signal based on the input signal, and the first optical component being configured to generate the first optical signal having a first optical delay based on the optical input signal. In this case the second optical component is configured to generate the second optical signal based on the optical input signal and based on a second delayed version having a second optical delay, longer than the first optical delay, such that in response to a pulse on the optical input signal, the second optical signal has a sequence of two pulses, the two pulses coinciding respectively with leading and trailing edges of a corresponding pulse on the first optical signal. The optical output component is configured to generate the encoded optical output signal by optically combining the first optical signal and the second optical signal. 
     Optionally the first and second optical components comprise interferometers configured as nested interferometers to generate the first and second optical signals, and the optical output component comprises a part of the nested interferometers configured to combine the first and second signals. 
     Optionally the third component comprises a third optical component configured to change a relative amplitude of the first optical signal and the second optical signal before they are optically combined. 
     Another aspect of this disclosure provides an optical transmission system comprising a transmitter and a receiver, the transmitter having the apparatus of described above. 
     Optionally the optical transmission system is configured for front-haul between a radio terminal and a baseband processing unit. 
     Optionally the receiver is configured to use direct detection to receive the optical transmission. 
     Another aspect of this disclosure provides a computer program for encoding a signal for optical transmission, the computer program comprising computer code which, when run on processing circuitry of an encoding apparatus, causes the encoding apparatus to generate a first signal based on the input signal by providing a first delay, and by low pass filtering of the input signal. It also causes the encoding apparatus to generate a second signal based on the input signal and based on a second delayed version of the input signal having a second delay larger than the first delay, such that in response to a pulse on the input signal, the second signal has a sequence of two pulses, the two pulses coinciding respectively with leading and trailing edges of a corresponding pulse on the first signal, and to cause the encoding apparatus to generate an encoded optical output signal based on the first signal and the second signal. 
     Another aspect of this disclosure provides a computer program product comprising a computer program as set out above, and a computer readable storage medium on which the computer program is stored. 
     Another aspect of this disclosure provides an apparatus for encoding an input signal for optical transmission, the apparatus comprising processing circuitry; the processing circuitry being configured to cause the apparatus to generate a first signal based on the input signal by providing a first delay, and by low pass filtering of the input signal. The processing circuitry being further configured to generate a second signal based on the input signal and based on a second delayed version of the input signal having a second delay larger than the first delay, such that in response to a pulse on the input signal, the second signal has a sequence of two pulses, the two pulses coinciding respectively with leading and trailing edges of a corresponding pulse on the first signal, and generate an encoded optical output signal based on the first signal and the second signal. 
     Any of the additional features can be combined together and combined with any of the aspects. Other effects and consequences will be apparent to those skilled in the art, especially over compared to other prior art. Numerous variations and modifications can be made without departing from the claims of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the invention will now be described, by way of example, with reference to the appended drawings, in which: 
         FIG. 1  shows a schematic view of an example of a conventional optical transmission system, 
         FIG. 2  shows a schematic view of apparatus according to an embodiment, 
         FIG. 3  shows steps according to a method according to an embodiment, 
         FIG. 4  shows steps according to another method according to an embodiment, 
         FIG. 5  shows a timechart of waveforms of first and second signals, 
         FIG. 6  shows a method according to an embodiment having electrical domain signals, 
         FIG. 7  shows a schematic view of apparatus according to an embodiment having electrical domain signals, 
         FIG. 8  shows a time chart of a waveform of a first signal, 
         FIG. 9  shows a time chart of a waveform of a second signal, 
         FIG. 10  shows I and Q waveforms for a conventional CAPS-3 encoder overlaid with the I and Q waveforms for an embodiment 
         FIG. 11  shows a schematic view of apparatus according to an embodiment having electrical domain signals and a precoder, 
         FIG. 12  shows a method according to an embodiment having optical domain signals, 
         FIG. 13  shows a schematic view of apparatus according to an embodiment having optical domain signals, 
         FIG. 14  shows a schematic view of an example of an optical transmission system for front-haul between a radio terminal and a baseband processing unit, and 
         FIG. 15  shows an example of apparatus for encoding implemented with a processing circuit, a memory circuit and a stored program. 
     
    
    
     DETAILED DESCRIPTION 
     The present invention will be described with respect to particular embodiments and with reference to certain drawings but the scope of the invention is not limited thereto and modifications and other embodiments are intended to be included within the scope of the disclosure. The drawings described are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn to scale for illustrative purposes. 
     Definitions 
     Where the term “comprising” is used in the present description and claims, it does not exclude other elements or steps and should not be interpreted as being restricted to the means listed thereafter. Where an indefinite or definite article is used when referring to a singular noun e.g. “a” or “an”, “the”, this includes a plural of that noun unless something else is specifically stated. 
     The steps of the methods described herein may be carried out in any suitable order, or simultaneously where appropriate. 
     References to computer programs or software can encompass any type of programs in any language executable directly or indirectly on processing hardware. 
     References to processors, hardware, processing hardware or circuitry can encompass any kind of logic or analog circuitry, integrated to any degree, and not limited to general purpose processors, digital signal processors, ASICs, FPGAs, discrete components or logic and so on. References to a processor are intended to encompass implementations using multiple processors which may be integrated together, or co-located in the same node or distributed at different locations for example. 
     
       
         
           
               
             
               
                   
               
               
                 Abbreviations: 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 ADC  
                 Analog to Digital Converter  
               
               
                   
                 ASIC  
                 Application Specific Integrated Circuit  
               
               
                   
                 BBU  
                 Base Band Unit  
               
               
                   
                 CAPS  
                 Combined Amplitude Phase Shift  
               
               
                   
                 CW  
                 Continuous Wave  
               
               
                   
                 DAC  
                 Digital to Analog Converter  
               
               
                   
                 DCF  
                 Dispersion Compensating Fiber  
               
               
                   
                 DMT  
                 Discrete Multi Tone  
               
               
                   
                 DQPSK  
                 Differential Quadrature Phase Shift Keying  
               
               
                   
                 DWDM  
                 Dense Wavelength Division Multiplexing  
               
               
                   
                 EDFA  
                 Erbium Doped Fiber Amplifier  
               
               
                   
                 FBG  
                 Fiber Bragg Grating  
               
               
                   
                 FEC  
                 Forward Error Correction  
               
               
                   
                 FWM  
                 Four Wave Mixing  
               
               
                   
                 IQ  
                 In phase in Quadrature  
               
               
                   
                 MZM  
                 Mach Zehnder Modulator  
               
               
                   
                 OADM  
                 Optical Add Drop Multiplexer  
               
               
                   
                 OOK  
                 On Off Keying  
               
               
                   
                 OSNR  
                 Optical Signal to Noise Ratio  
               
               
                   
                 PAM  
                 Pulse Amplitude Modulation  
               
               
                   
                 RRU  
                 Remote Radio Unit  
               
               
                   
                 SFP  
                 Small Form Pluggable 
               
               
                   
                   
               
            
           
         
       
     
     By way of introduction to the embodiments, some issues with conventional designs will be explained. 
       FIG. 1 . Conventional Optical Transmission System 
       FIG. 1  shows an example of a conventional optical transmission system having an optical transmitter  10  and an optical receiver  20 . The optical transmitter  10  has an input to receive digital data. The optical transmitter  10  comprises an encoder  12  (also referred to as a line encoding apparatus) which maps binary digital data to line symbols. The encoder  12  can comprise, or be considered to operate as, a state machine  40 . The encoder  12  may directly output analog signals at amplitudes corresponding to the set of line symbols. The encoder  12  is for encoding a signal for transmission, e.g. optical transmission. Alternatively, the encoder  12  may indicate, for each operation of the state machine, a line symbol required. For example, each of the line symbols can correspond to a digital code which is used internally by the transmitter. A digital-to-analog converter (DAC)  13  outputs an analog value, corresponding to the digital code of the required line symbol. The output of the encoder, or DAC  13  (if used), is a multi-level analog signal  14 . Optionally, a low pass filter may be included in the transmitter  10  to low pass filter the signal. Alternatively, a low-pass filtering effect is provided by the limited bandwidth of the modulator. The analog signal is used to modulate an optical carrier in an optical modulation stage  15  (e.g. Mach Zehnder Modulator) and output a modulated optical signal  16 . 
     The receiver  20  has an input to receive the modulated optical signal  16 . The receiver  20  comprises a photodetection stage  21  which is configured to receive the optical signal and to output an electrical signal  22 . As described above, the photodetection stage  21  outputs an electrical signal which is proportional to power of the received optical signal. The photodetection stage may include an electrical amplifier (e.g. a transimpedance amplifier). The electrical signal can represent a set of possible received symbols. A digital data recovery stage  23  is configured to recover digital data from the received symbols. The digital data recovery stage  23  comprises a threshold decision unit  25  which is configured to compare the electrical signal with one or several amplitude thresholds. The digital data recovery stage  23  can also comprise a clock extraction and sampling unit  24  which is configured to extract a clock signal from the detected electrical signal and to sample the detected electrical signal at points in time determined by the extracted clock. The threshold decision unit  25  is configured to determine that the digital data is a first binary value when the electrical signal  22  is less than an amplitude threshold TH or a second binary value when above the amplitude threshold TH for example. The determined symbol value is output as digital data  26 , corresponding to the transmitted digital data  11 . If CAPS-3 type encoding for example, is used at the transmitter, this means the state machine  40  is relatively complex and expensive to implement in sufficiently fast logic circuitry. The DAC  13  used has unavoidably high power consumption because of the high frequency of operation, and therefore is costly. 
       FIG. 2 . Apparatus According to an Embodiment 
       FIG. 2  shows a schematic view of an embodiment showing apparatus  240  for encoding an input signal for optical transmission. The apparatus can replace parts  12 ,  13  and  14  in the transmitter of  FIG. 1  and enable considerable simplification and thus cost reduction while maintaining the performance needed for the applications described above. A first component  27  is shown for generating a first signal, and can be implemented in various ways as will be described in more detail with reference to other figures. A second component  28  is shown for generating a second signal, and again can be implemented in various ways as will be described in more detail with reference to other figures. An optical output component  29  is shown as being coupled to receive the first and second signals and is for generating an encoded optical output signal for optical transmission, based on the first and second signals. 
     Examples of how these components can operate will now be described with reference to  FIGS. 3 to 13  at least. 
       FIGS. 3 and 4 . Operational Steps According to an Embodiment 
       FIG. 3  shows a step  30  of generating the first signal based on the input signal by providing a first delay and by low pass filtering of the input signal. This may be carried out by the first component shown in  FIG. 2 . Step  40  shows a step of generating the second signal based on the input signal and on a second delayed version of the input signal such that in response to a pulse on the input signal, the second signal has a sequence of two pulses (e.g. a first pulse and a second pulse) coinciding respectively with the leading and trailing edges of a corresponding pulse on the first signal. Step  45  shows generating the encoded optical output signal based on the first and second signal. 
     This simplified scheme is based on the observation that CAPS-3 coding can be effectively simulated by generating two low pass filtered signals, having specified bandwidths and amplitudes, for driving the I and Q branches of an IQ modulator. Notably the two signals can be generated by delays and filters, as set out above, without needing the complex and power consuming circuitry of the state machine and DAC of the conventional arrangement. Hence a significant simplification and thus cost reduction can be achieved. 
     This is a particularly simple and thus less costly way of implementing encoding for transmission. Notably the particular arrangement of delays and filtering can enable important features of a CAPS-3 encoded optical signal to be simulated so that the chromatic dispersion tolerance advantage can be achieved, without needing the complexity and high power consumption of hardware such as the DAC and 8-state encoding circuitry. Compared to other known coders of comparable simplicity and hardware cost, the chromatic dispersion tolerance can be notably higher which can enable longer reach without costly optical amplification and dispersion compensators, while maintaining the benefit of not needing expensive coherent receivers since it can be used with direct detection, avoiding the cost of an additional laser used as the local oscillator at the receiver. In some examples it avoids the costs of external dispersion compensation for distances of up to about 18 to 20 km. In some examples the resulting receiver sensitivity and OSNR tolerance can be 4 dB better than a conventional PAM-4 encoding scheme. And the energy efficiency is good, by avoiding the need for a DAC at the transmitter. 
       FIG. 4  shows similar steps to those of  FIG. 3 , but limited explicitly to an example in which the first signal is generated at step  36  to have a waveform simulating an I (in-phase) waveform of a CAPS-3 encoder and the second signal is generated at step  46  to have a waveform simulating a Q (quadrature) waveform of a CAPS-3 encoder. As in  FIG. 3  there is a step  45  of generating the encoded optical output signal based on the first and second signal. 
       FIG. 5 . Timechart Showing Waveforms of First and Second Signals 
       FIG. 5  shows a chart having time along the x-axis and amplitude on the y-axis, and shows an idealized example of the I and Q waveforms superimposed, for a CAPS-3 type encoding, which is to be simulated by the first and second signals respectively. It is idealized in that it shows square shaped pulses whereas a more practical example would be more rounded as a result of the low pass filtering, and circuit characteristics. Other examples are possible. The chart shows a response to a pulse of duration T on the input signal. The first signal is shown as g I (t), and the second signal as g Q (t). The output signal based on these first and second signals would be:
 
 g ( t )= g   I ( t )+ jg   Q ( t )
 
     As shown, the first signal has a waveform having main upward pulse of duration 2T, with optional small downward negative pulses before and after, of duration T, which are present in the theory of the CAPS-3 encoding scheme but which can be largely neglected in practice. This shape can be achieved approximately by low pass filtering. The first signal is delayed slightly to enable the leading upward transition to coincide with the first of the two pulses forming the second signal. The second of the two pulses in the second signal can be formed by the second delayed version of the input signal, which should be delayed longer than the first delay, to enable it to coincide with the trailing downward edge of the first signal. The resulting waveforms shown, effectively pre-compensate for chromatic dispersion in the transmission path, so that the received pulse after suffering chromatic dispersion is as close as possible to the shape of the input pulse. 
     The relative amplitudes (shown as 1 and β) of the first and second signal, and the amount of undershoot (shown as α) which will depend on the characteristics of the low pass filtering, can be tuned to optimize the transmission according to the actual chromatic dispersion and other characteristics of the transmission path. 
     CAPS-3 Coding Theory 
     CAPS-N is a family of modulation formats [Enrico Forestieri and Giancarlo Prati: Novel Optical Line Codes Tolerant to Fiber Chromatic Dispersion, IEEE JLT VOL. 19, NO. 11, NOVEMBER 2001] where the source bits are encoded to narrow the transmitted spectrum so that the signal is more robust to the chromatic dispersion introduced by the fiber. 
     The order-N code has 2 N  states Σ i , i=1, 2, . . . , N. 
     At time kT (state Σm), the information bit u k  forces a transition to state Σ q  and the transmission of the waveform s i (t), where q and i are given by: 
     
       
         
           
             
               
                 
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                             ) 
                           
                           ⁢ 
                           
                             g 
                             ⁡ 
                             
                               ( 
                               
                                 t 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       
                                         
                                           n 
                                           + 
                                           1 
                                         
                                         2 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   T 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       , 
                     
                   
                   
                     
                       0 
                       ≤ 
                       t 
                       ≤ 
                       T 
                     
                   
                 
                 
                   
                     0 
                   
                   
                     otherwise 
                   
                 
               
             
           
         
       
     
     where g(t) is a complex pulse (i.e. a pulse requiring an IQ modulator) of length D=(n+1)T. 
     For CAPS-3, which is the relevant case here, 
     
       
         
           
             
               
                 s 
                 i 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 3 
                               
                               ⁢ 
                               
                                 
                                   ( 
                                   
                                     
                                       b 
                                       
                                         i 
                                         , 
                                         k 
                                       
                                     
                                     - 
                                     
                                       0 
                                       . 
                                       5 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   g 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       + 
                                       
                                         
                                           ( 
                                           
                                             k 
                                             - 
                                             2 
                                           
                                           ) 
                                         
                                         ⁢ 
                                         T 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             , 
                           
                         
                         
                           
                             0 
                             ≤ 
                             t 
                             ≤ 
                             T 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       ι 
                       ´ 
                     
                   
                   = 
                   1 
                 
                 , 
                 2 
                 , 
                 … 
                 ⁢ 
                 
                     
                 
                 , 
                 8 
               
             
           
         
       
     
     Where 
     
       
         
           
             
               b 
               
                 i 
                 , 
                 k 
               
             
             = 
             
               
                 ⌊ 
                 
                   
                     i 
                     - 
                     1 
                   
                   
                     2 
                     k 
                   
                 
                 ⌋ 
               
               ⁢ 
               
                   
               
               ⁢ 
               mod 
               ⁢ 
               
                   
               
               ⁢ 
               2 
             
           
         
       
     
     This gives the waveforms shown in  FIG. 5 . 
       FIGS. 6-11 , Electrical Signal Embodiments 
       FIG. 6  shows a shows similar steps to those of  FIG. 3 , but limited explicitly to an example in which the first and second signals are electrical signals, and these two signals are used to modulate the I and Q inputs of an IQ modulator to generate the encoded optical output. Hence there is shown a step  32  for generating the first signal as an electrical signal based on the input signal by providing a first delay and by low pass filtering in the electrical domain. A step  42  is provided for generating the second signal as an electrical signal based on the input signal and on a second delayed version of the input signal in the electrical domain. As before, the second signal is generated such that in response to a pulse on the input signal, the second signal has a sequence of two pulses (first and second pulses) coinciding with the leading and trailing edges of the corresponding pulse on the first signal. 
     The step of generating the encoded output signal has step  50  of modulating the I input of an IQ modulator according to the first signal, and a step  60  of modulating the Q input of the IQ modulator according to the second signal. 
       FIG. 7  shows a schematic view of apparatus according to an embodiment having components for generating the first and second signals in the electrical domain as described above for  FIG. 6 . The first component  27  receives input signal b k  and has a delay element  70  for providing a first delay of time T. This feeds a low pass filter  74  with a cut off frequency of approximately ¼T. (In principle the order of these parts can be changed, and in one example a common low pass filter may be applied to the input signal before it is divided for generating the first and second signals.) An amplifier  78  or attenuator is provided to alter a relative amplitude of the first and second signals. The resulting first signal is coupled to drive the I input  86  of the IQ modulator which forms the optical output component  29 . 
       FIG. 7  also shows how the second component in this example has delays of 2T formed by sharing the first delay element  70  and providing in series, a further delay element  72  to give a total delay of 2T. This gives a second delayed version having a longer delay than that of the first signal. An adder  73  is provided for adding the original input signal to the second delayed version output by the delay  72 . This provides a second signal having a sequence of two pulses in response to a pulse on the input signal. An optional low pass filter  76  having for example a cut off at frequency 1/T is provided here or at some other point in the processing chain. An amplifier  80  (or attenuator) is provided for altering the relative amplitude, at this point or elsewhere, and then the second signal is fed to drive the Q input  84  of the IQ modulator. The IQ modulator has an optical source, shown here as a CW laser  82 , and has separate MZMs for generating I and Q optical outputs in this case. The optical I and Q outputs of the modulator would be combined optically (not shown) in a conventional manner, before transmission along the optical path to the receiver. The figure also shows an example of waveforms showing how the light output of each MZM varies with each of the I and Q drive signals. The light output is at a minimum when the driving signal is in the middle of its range. 
     This figure shows an example where for the steps of generating the first and second signals, the second delay is twice the duration of the first delay. This can help to optimise the delay for recreating a CAPS-3 type of encoding for a transmission path without differences between I and Q delays, but other delay values can be used if useful to compensate for distortions such as differences between I and Q path delays for example. It also shows an example in which the first delay is one symbol time of the input signal. This can help to optimise synchronisation of the I and Q inputs for simulating a CAPS-3 type of encoding of symbols, but again other delay values can be used for example for the purpose of compensating for differences in propagation delays between I and Q paths at the transmitter or for compensation of other distortions. 
     This is also an example of an embodiment in which there is a third component in the form of an amplifier  78 ,  80  for altering a relative amplitude of the first and second signals before the step of generating the encoded optical output signal based on the first signal and the second signal. This relative amplitude can be set or made adjustable according to a fiber distance and/or a fiber dispersion characteristic to enable optimisation of the dispersion tolerance of the encoding for example. 
     The figure also shows an example of the low pass filtering comprising filtering corresponding to duobinary encoding of the input signal in the sense that alternate pulses are made positive and negative-going. A digital or analog low pass filtering step is one way to generate such a duobinary encoded signal, and this can be combined with the low pass filtering to help to optimise narrowing of the bandwidth, to further approximate to the CAPS-3 type waveform to improve the tolerance of chromatic dispersion. 
     The example here shows low pass filtering having a pass band up to ¼T where T is a symbol time of the input signal. This can help optimise a narrowing of the bandwidth and help approximate to a waveform of a CAPS-3 encoder, but a range of pass bands can be used, such as up to ½T or 1/T for example. 
     In the example here, LPF  76  shows generating the second signal using a low pass filtered version of the input signal and this can help to optimise narrowing of the bandwidth, to improve the tolerance of chromatic dispersion. In principle this LPF can be located earlier in the signal path or even be applied to the input signal before it is split for generating the first and second signals. As shown this low pass filtering can have a pass band up to 1/T where T is a symbol time of the input signal. This can further help optimise an approximation to a waveform of a CAPS-3 encoder. Again a range of pass bands can be used. 
       FIGS. 8 and 9  show other examples of first and second signals for driving the I and Q inputs. In this case there is no relative amplitude difference. The first signal in  FIG. 8  is a pulse of duration 2T in response to an input pulse of length T. The second signal in  FIG. 9  shows a sequence of two pulses of length T in response to a pulse of length T on the input signal. They are shown on separate time scales, so no attempt has been made to illustrate their relative timing so that the leading and trailing edges of the pulse on the first signal coincide with the two pulses respectively on the second signal. 
       FIG. 10  shows a time chart showing the I and Q waveforms for a conventional CAPS-3 encoder overlaid with the I and Q waveforms for an embodiment of this disclosure, labelled IQ-DUO in the figure. At the top of the chart is a binary digital representation of an input signal. The signals are duobinary in that alternate pulses on the first signal (I) are positive and negative-going, and the second (Q) signals show both positive and negative going pulses. The pulses of the second (Q) signal are shown going in the same direction as corresponding pulses of the first signal. The CAPS-3 I waveform has a detail in that it has multiple levels at its positive peaks wherever the pulse has a duration of more than 2T, and this detail is not reproduced in the IQ-DUO waveform, simulating the CAPS-3 waveform. Also, the IQ-DUO I waveform shows some oscillation about the zero amplitude not shown by the CAPS-3 I waveform. Otherwise, in most important features, the IQ-DUO waveforms generally show a good simulation of CAPS-3 waveforms. 
       FIG. 11  shows another schematic view of an embodiment using first and second signals in the electrical domain, similar to the view of  FIG. 7 . In this case a precoder  100  is shown for preprocessing a binary input signal to provide a differential binary data stream. This is a conventional precoder circuit, other designs are known, and the purpose is to avoid a single transmission bit error propagating endlessly. In principle the advantages of the simpler encoding apply with or without the precoder. The precoder has a XOR gate  104  and a feedback path around the XOR gate via a delay element  102  providing a delay of duration T. Otherwise the circuitry is similar to that of  FIG. 7  and similar reference numerals have been used as appropriate. In  FIG. 11  the apparatus is shown as having three separate modules. One is a digital binary circuit  92  including the precoder, delays and adder. A second module  94  has the filters and amplifiers, and a third module  96  has the IQ modulator. 
       FIGS. 12 and 13 . Optical Domain Embodiment 
       FIG. 12  shows similar steps to those of  FIG. 3 , but limited explicitly to an example in which the first and second signals are optical signals, and these two optical signals are not used to modulate I and Q inputs of an IQ modulator, but can simply be combined optically to generate the encoded optical output. Hence there is shown a step  34  for generating the first signal as an optical signal based on the input signal by providing a first optical delay and by low pass filtering in the optical domain. Such optical low pass filtering can be implemented either by the inherent narrow band frequency response of an interferometer, or by a separate optical filter element at some point in the optical path, or both. 
     A step  44  is provided for generating the second signal as an optical signal based on the input signal and on a second delayed version of the input signal in the optical domain. As before, the second signal is generated such that in response to a pulse on the input signal, the second signal has a sequence of two pulses coinciding with the leading and trailing edges of the corresponding pulse on the first signal. The step of generating the encoded output signal has a step  70  of optically combining the first and second optical signals. This can be implemented by a recombining part of an interferometer for example. 
       FIG. 13  shows an apparatus for encoding according to another embodiment which can be used to implement the optical domain operations described above with respect to  FIG. 12 . The input signal is converted to an optical input signal by a modulator such as an MZM  112 , coupled to an optical source such as a CW laser  110 . The figure shows a waveform of the modulator output, showing it has lowest optical amplitude at the midpoint of the input range. The apparatus for encoding has nested interferometers with different delays. The first component  27  has a first interferometer having a first splitter  122  for dividing an optical path into two branches. An optical delay  114  of delay T is provided in one branch, and the branches are recombined by coupler  120 . Contained in its other branch is a second interferometer itself having a second optical delay  116  of duration 2T in one sub-branch and an uninterrupted path in its other sub-branch. The optical input signal is fed into one end of these nested interferometers, is divided by splitter  122 , so that half of the signal is fed to optical delay  114  and the first optical signal will appear at the output of optical delay  114 . 
     The other half of the optical input signal is fed to the second interferometer. This divides the other half of the optical input signal so that a quarter part goes to the optical delay  116  and serves to generate the second delayed version. This is combined with the quarter part which reaches the other branch of the second interferometer. These two quarter parts are recombined at the output of the second interferometer to provide the second optical signal. An optical attenuator  118  (or amplifier) is provided on either the path of the first optical signal or the second optical signal to alter a relative amplitude of the two signals. Then the first and second optical signals are combined by the recombiner  120  of the first interferometer to form the encoded optical output. 
     In summary, the optical front-end splits the optical signal in two branches. A bit time delay line is present on the first branch. On the second branch, the signal is further split in two sub-branches and delayed twice the bit time on one of the sub-branches. The sub-branches are then recombined in one only branch, where a variable optical attenuator is placed. Finally, the second branch is recombined with the first one. The optical front-end is fed by the input optical signal in the form of a pre-coded duobinary optical signal. The first component  27  is formed by parts of the first interferometer (that also realise the low pass filtering) and the first optical delay  114 . The second component is formed by the second interferometer, and optionally parts of the first interferometer if this applies some low pass filtering to the second optical signal. The optical output component for combining the first and second optical signals is formed by the recombiner  120  of the first interferometer. 
     Hence this optical domain embodiment has features which correspond and has operational steps which correspond closely to the electrical domain version. The waveforms of the first and second optical signals combined by recombiner  120 , can correspond to those shown in  FIG. 10 . In practice the optical front-end could be realized in silicon photonics, further simplifying the encoder and modulator. Notably the modulator is now a common optical modulator, based on a MZM, instead of an IQ modulator. This can be easier and cheaper to realise as there are fewer optical ports requiring to be controlled. A drawback of this optical domain implementation is the use of the optical delay lines (currently they would typically be implemented by relatively long waveguides that introduce insertion loss). 
       FIG. 14 . Front Haul Transmission System 
       FIG. 14  shows a schematic view of an example of an optical transmission system. In this case the optical the optical transmission is for front-haul between a radio terminal (e.g. RRU)  200  and a baseband processing unit  210 . This is a particularly cost sensitive application where the currently available coding schemes are either too complex and thus expensive, or too short range (up to 20 km is needed, without repeaters and without external dispersion compensation). The radio terminal has a transmitter  220  which has apparatus  240  for encoding according to any of the examples described above. The apparatus for encoding feeds an optical output signal onto an optical transmission path. This is received by a direct detection receiver  230  at the baseband processing unit. The receiver has apparatus  250  for decoding. This is a two way transmission so there is a (optionally separate) optical transmission path in the other direction from the baseband processing unit to the radio terminal. Hence the baseband processing unit has a transmitter  220  with apparatus  240  for encoding. Equally the radio terminal has a direct detection receiver  230  coupled to the apparatus  250  for decoding. Hence this figure shows an example of transmitting the encoded optical output signal to a receiver and using direct detection at the receiver to receive the optical transmission. The cost saving of not needing coherent receivers is particularly useful. 
     FIG.  15 . Program Example 
     Any electrical domain circuitry can in principle be implemented by a processing circuit running a program.  FIG. 15  shows an example of apparatus for encoding including a processing circuit  320 , coupled to a storage medium in the form of a memory circuit  330  having a stored program  325 . Hence this is an example of computer program for encoding a signal for optical transmission, the computer program comprising computer code which, when run on processing circuitry of an encoding apparatus, causes the encoding apparatus to carry out any of the method steps described above for generating the first or second signals in the electrical domain, for encoding the input signal for optical transmission. It is also an example of a computer program product comprising a computer program and a computer readable storage medium on which the computer program is stored. The storage may also comprise persistent storage, which, for example, can be any single one or combination of magnetic memory, optical memory, solid state memory or even remotely mounted memory. Other variations can be envisaged within the claims. Aspects of the disclosure provide an apparatus for encoding an input signal for optical transmission. The apparatus comprising the processing circuitry. The processing circuitry being configured to cause the apparatus to carry out the method or functions of any example. For example, the processing circuitry is configured to: generate a first signal based on the input signal by providing a first delay, and by low pass filtering of the input signal, generate a second signal based on the input signal and based on a second delayed version of the input signal having a second delay larger than the first delay, such that in response to a pulse on the input signal, the second signal has a sequence of two pulses, the two pulses coinciding respectively with leading and trailing edges of a corresponding pulse on the first signal, and generate an encoded optical output signal based on the first signal and the second signal.