Patent Description:
The use of optical fiber has grown tremendously over the last decades. Optical-fibers are used in numerous applications such as in telecommunications. Telecommunication applications include for example applications in global networks and desktop computers. Such telecommunication applications may involve the transmission of voice, data, or video over distances of less than a meter to thousands of kilometers.

Over the last twenty years, the demand for more network capacity has significantly increased as a result of the development of internet and of the growing traffic generated by an increasing number of internet users. Optical fiber transmissions appear as key technologies to meet such continuous demand for higher transmission data rates in global telecommunication infrastructures. Optical fibers are used as a means to transmit light between two ends in fiber-based communication systems. The light carries data and allows transmission over long distances at higher bandwidths than in wire-based or wireless communication systems.

Optical fibers represent optical waveguides that guide electromagnetic waves in the optical spectrum. The propagation of the waves along an optical fiber depends on several parameters related to the fiber such as its geometry, its mode structure, the distribution of the refractive index, and the material it is made of. Optical fibers typically include a transparent core surrounded by a transparent cladding material with a lower index of refraction. Light carrying data propagates in the fiber, which acts as a waveguide, following a succession of internal reflections.

Optical fibers can be classified into two categories depending on the number of propagation modes (also called "transverse modes", "spatial modes" or "spatial propagation modes") which can be supported by the fiber. These modes define the distribution of the waves while propagating in the fiber.

Optical fibers include single-mode fibers (SMF) and multimode fibers (MMF). Single mode fibers are designed to carry light according to a single mode, termed the "fundamental mode". A single-mode optical fiber cable has a core of a small diameter that allows only the fundamental mode to propagate. As a result, the number of light reflections created as the light passes through the core decreases and leads to low attenuations and fast propagation of the signal. Single mode fibers are typically used for long distances applications.

Multi-mode fibers allow the propagation of many modes in a single-core or multi-core fibers where each core can be single-mode or multi-mode. A multi-mode optical fiber cable has a core of a large diameter that allows the propagation of multiple modes of light. As a result, the number of reflections created as the light passes through the core increases, creating the ability to propagate more data at a given time slot. The various propagation modes form a set of orthogonal channels over which independent data symbols can be multiplexed. Space Division Multiplexing (SDM) techniques and in particular mode division multiplexing (MDM) techniques can be used for this purpose and can enable a multiplication of the capacity of a link by the number of propagating modes.

Multi-mode fibers can offer higher transmission rates than single-mode fibers. However, taking advantage of the presence of multiple modes to multiplex and transmit larger amount of data symbols requires managing several modal detrimental impairments. These impairments are mainly due to imperfections of the optical components (e.g. fibers, amplifiers and multiplexers) and to the crosstalk effects between the various propagation modes. Such imperfections induce non-unitary impairments, i.e. impairments that cause a loss of orthogonality and/or a loss of energy between the different channels over which independent data symbols are multiplexed. Such impairments can significantly reduce the capacity of the optical links and deteriorate the performance of the transmission system, particularly in long distances applications.

In particular, propagating modes through multi-mode fibers are affected by a non-unitary crosstalk known as mode dependent loss (MDL). MDL effects require either optical or digital signal processing solutions to be reduced.

Optical solutions using mode scrambling or strong mode coupling were proposed to reduce the impact of MDL on the capacity of optical fiber links. For example, a technique based on placing mode scramblers between the fiber spans is disclosed in "<NPL>". This technique enables the reduction of the MDL effect. However, it fails to completely mitigate MDL and requires a high number of scramblers which induces an additional implementation complexity of the transmission system.

In the presence of N spatial modes, the multi-mode fiber-based transmission system can be modeled as a N × N optical Multiple-Input Multiple-Output (MIMO) system. The optical transmitter sends data symbols over the N modes and the optical receiver receives N different replicas of the original symbols over the N different available modes. Based on this observation, digital signal processing solutions using Space-Time codes were recently investigated in "<NPL>" and in "<NPL>". The use of existing Space-Time codes such as the Silver code, the Golden code, the TAST (for Threaded Algebraic Space-Time) code, and the Alamouti code for MDL mitigation was analyzed in these articles for SDM systems involving <NUM> and <NUM> propagation modes. Such analysis highlighted the promising potential of the use of Space-Time codes for MDL mitigation at low implementation costs. Digital processing techniques including bandwidth efficient Space-Time coding, error correcting coding, and bandwidth efficient Space-Time modulations have been further proposed in the patent application N° <CIT>.

Existing coding solutions use Space-Time codes originally designed for data multiplexing and coding in wireless environments characterized by Rayleigh fading propagation models. Although optical-fiber transmission systems can be represented as MIMO systems, the optical fiber propagation environment differs from the wireless one. Consequently, existing Space-Time codes may not be sufficiently adapted to optical MIMO systems, in particular to SDM systems.

There is accordingly a need for designing digital coding techniques enabling a complete mitigation of MDL effects for SDM systems.

Advantageously, the various embodiments provide low-complexity encoding solutions for mitigating mode-dependent loss effects in optical transmission systems using multi-mode fibers.

Advantageously, some embodiments of the invention provide combinations of Forward Error Correction coding and Space-Time coding solutions adapted to a predefined value of the mode-dependent loss affecting modes propagation in a multi-mode optical-fiber transmission system.

Advantageously, in combination with the selection of a set of propagation modes over which independent data symbols are transmitted and/or received, the various embodiments provide a joint Forward Error Correction coding and Space-Time coding solution adapted to the number of selected modes. Such solution enables a complexity reduction and an optimization of the use of the available transmission power.

Further advantages of the present invention will become clear to the skilled person upon examination of the drawings and the detailed description. It is intended that any additional advantages be incorporated herein.

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate various embodiments of the invention and, together with the general description of the invention given above, and the detailed description of the embodiments given below, illustrate some embodiments of the invention.

Embodiments of the present invention provide an optical transmitter configured to transmit a data sequence over at least two spatial propagation modes through an optical transmission channel in a single-core multi-mode optical fiber transmission system, the transmission system being associated with a predefined value of the mode-dependent loss. The optical transmitter is configured to encode a digital data sequence using a concatenation of at least one forward error correcting (FEC) code and a Space-Time (ST) code. The data sequence comprises a set of symbols to be transmitted through an optical transmission channel in a single-core multi-mode optical fiber transmission system comprising at least two spatial propagation modes. Embodiments of the present invention provide joint FEC coding and Space-Time coding devices and methods enabling a complete mitigation of the mode-dependent loss effects resulting from the crosstalk between the various channels made available by the propagation modes in the multi-mode optical fiber.

Devices, methods and computer program products according to the various embodiments of the invention may be implemented in optical fiber transmission systems applied to a wide variety of applications. Exemplary applications comprise, without limitation, telecommunications, aerospace and avionics, data storage, automotive industry, imaging, and transportation.

Telecommunication applications are widespread and range from desktop computers or terminals to nationwide networks. Such applications may involve transfer of data over distances ranging from less than one meter up to hundreds or thousands of kilometers (e.g. transmission of voice, data, images or video) or connection of networks (e.g. connection for switches or routers in local area networks).

In the aerospace and avionics industries, optical fiber-based products may be used in military and/or commercial applications. Optical fiber technologies and products are designed in such applications to meet rigorous testing and certifications requirements in harsh environments and conditions.

In data storage applications, optical fibers may be used in data storage equipment as a link between multiple devices in a network and/or as part of a storage system. Optical fiber connectivity offers very high bandwidth even over extended distances.

In automotive industry applications, optical fiber technologies may be used for example in lighting, communications, and sensing for safety and control devices and systems.

In imaging applications (e.g. telemedicine), the optical transmission properties of the optical fibers may be used to transmit an image of a target or a subject area to the image view end for analysis and/or interpretation.

In transportation systems, smart highways with intelligent traffic lights, automated tollbooths and changeable message signs use telemetry systems based on optical fibers.

The following description of certain embodiments will be made with reference to telecommunication systems, for illustration purpose only. However, the skilled person will readily understand that the various embodiments of the invention may be applied to other types of systems for different applications.

<FIG> illustrates an exemplary application of the invention in a communication system <NUM> based on optical fiber transmission. The communication system <NUM> comprises at least one optical transmitter device <NUM> (hereinafter referred to as a "transmitter") configured to encode an input data sequence into an optical signal and transmit it to at least one optical receiver device <NUM> (hereinafter referred to as a "receiver") through an optical fiber transmission channel <NUM>.

The optical fiber transmission channel <NUM> comprises an optical fiber <NUM> including one or more fiber slices <NUM>. The optical fiber <NUM> is a cylindrical non-linear waveguide consisting of one core, a cladding and a coating. The optical signal sent by the optical transmitter <NUM> is confined in the core through total internal reflections due to the difference between the refractive indices of the core and the cladding.

The optical fiber transmission channel <NUM> may also comprise one or more amplifiers <NUM> inserted in the fiber. The amplifiers <NUM> may be inserted between each pair of fiber slices <NUM> along the optical fiber link to compensate for the fiber attenuation and carry the signal over long distances without the need to regenerate the optical signal. Exemplary optical amplifiers comprise Erbium doped fiber amplifiers (EDFA). Such amplifiers may be implemented in long-haul optical transmissions. They may be inserted every <NUM> to <NUM> kilometers to enhance the signal power depending on the type of the fiber, the length of the optical link and the application.

In some embodiments using multi-mode fibers, the amplifiers <NUM> may be configured to simultaneously amplify the optical signal corresponding to a plurality of propagation modes. Exemplary amplifiers in such embodiments comprise Few Mode Amplifiers such as Few Mode Erbium Doped Fiber Amplifiers.

In some embodiments, the optical signal amplification may be performed in a distributed manner using the non-linear simulated Raman scattering effect. In such embodiments, the fiber may be used as both a transmission link and an amplification medium.

In other embodiments, signal amplification may be achieved by a joint use of regularly arranged optical amplifiers (such as EDFA amplifiers) and of simulated Raman Scattering effects.

In still other embodiments, the signal amplification may be performed in the electrical domain through an optical/electrical conversion (not shown in <FIG>). In such embodiments, the optical fiber transmission channel <NUM> may comprise, at each amplification stage:.

The propagation of the optical signal along the optical fiber slices <NUM> is defined by the number of propagation modes that may depend on several parameters such as the radius of the fiber core, the wavelength of the optical carrier and the difference between the refraction index of the core and the cladding.

In some embodiments, space division multiplexing techniques may be implemented at the optical fiber transmission channel <NUM>, using for example multi-mode fibers supporting a number N ≥ <NUM> of propagation modes. Large core fibers are examples of multi-mode fibers supporting a large number of propagation modes. Few-mode fibers support a number of propagation modes comprised between two (<NUM>) and ten (<NUM>). Each propagation mode may be characterized by a different velocity.

In some embodiments using space division multiplexing in multi-mode fibers, the different propagation modes may overlap in a form of an energy transfer between the modes. As a result, the various data symbols carried by each mode may couple along the fiber inducing a crosstalk and an inter-symbol interference. In such embodiments, the optical fiber transmission channel <NUM> may further comprise a plurality of scrambling components <NUM> (hereinafter referred to as "scramblers"). The scramblers <NUM> may be regularly inserted in the channel with a given scrambling period for reducing the crosstalk effect and averaging the losses experienced by the different propagation modes.

According to some embodiments, a scrambler <NUM> may be associated with each optical amplifier.

<FIG> shows the components of an optical transmitter <NUM> according to certain embodiments. The optical transmitter <NUM> may be configured to transform an input data sequence into an optical signal to be transmitted through the optical transmission channel <NUM>. The optical transmitter <NUM> may comprise:.

According to some embodiments, the input data sequence may be a binary sequence comprising k bits. The FEC encoder <NUM> may be configured, in such embodiments, to encode the input binary sequence into a binary codeword vector comprising n bits by applying at least one binary FEC code.

In other embodiments, the input data sequence may comprise symbols that take values in a Galois Field GF(q) with q > <NUM> representing the order of the Galois Field. In such embodiments, the FEC encoder <NUM> may be configured to encode the input data sequence into a codeword vector comprising n symbols, each symbol comprised in the codeword vector taking value in the Galois Field GF(q). The encoding process in this case may be performed using a non-binary FEC code constructed over GF(q) with q > <NUM>.

The following description of certain embodiments will be made with reference to a binary input sequence and binary FEC encoding, for illustration purpose only. However, the skilled person will readily understand that the various embodiments of the invention apply to non-binary FEC coding. Binary FEC codes can be seen as codes constructed over the Galois Field GF(q) of order equal to q = <NUM>. A forward error correcting code <IMG> encoding a sequence of k bits into a sequence of n bits has a coding rate equal to <MAT> (hereinafter referred to as "forward error correction coding rate").

The encoded sequence or codeword vector denoted by c belongs to a set of codeword vectors known as "alphabet" or "codebook", and denoted by AFEC. The codebook AFEC comprises the set of all possible values of the codeword vectors. Card(AFEC) designates the number of codeword vectors in the alphabet AFEC.

To each couple of different codeword vectors in the codebook AFEC , a distance denoted by dFEC, known as the 'Hamming distance', may be associated. The Hamming distance between two different codewords ci ≠ cj is defined as: <MAT>.

In equation (<NUM>), ci(l) (respectively cj(l)) designates the lth component of the codeword ci (respectively cj). The Hamming distance indicates the number of bits in which the codewords ci and cj are different.

Using the Hamming distance, the forward error correcting code <IMG> can be represented by a value of the minimum distance denoted by dmin,FEC and defined by: <MAT>.

A Space-Time code <IMG> encoding a sequence of Q modulated symbols into a codeword matrix X of dimensions Nt × T has a Space-Time coding rate equal to rST = <MAT> symbols per channel use (s/c. T denotes the temporal dimension of the Space-Time code <IMG> and Nt designates the 'space' dimension equal to the number of used spatial propagation modes in the multi-mode fiber. A codeword matrix X can be written in the form: <MAT>.

In equation (<NUM>), each value xij of the codeword matrix X corresponds to the ith propagation mode, for i = <NUM>,. , Nt, and the jth time of use, for j = <NUM>,. Each codeword matrix X belongs to a set of codeword matrices termed also codebook or alphabet and denoted by AST. The codebook AST comprises the set of all possible values of the codeword matrices. Card(AST) designates the number of codeword matrices in the alphabet AST.

Each pair of different codeword matrices Xi and Xj for i ≠ j, may be associated with a difference codeword matrix Dij determined by computing the difference between the two codeword matrices Xi and Xj such that Dij = Xi - Xj. Furthermore, each difference codeword matrix may be associated with a distance metric equal to the Euclidean norm of the difference codeword matrix and given by: <MAT>.

Using the Euclidean distance definition, the Space-Time code <IMG> can be represented by a value of the minimum Euclidean distance denoted by dmin,ST and defined by: <MAT>.

The various embodiments of the invention provide FEC and ST encoding devices and methods for a total and efficient MDL mitigation in SDM systems using single-core multi-mode fibers. Accordingly, the error correcting code <IMG> implemented by the FEC encoder <NUM> and the Space-Time code <IMG> implemented by the Space-Time Encoder <NUM> may be determined such that a predefined value of the mode-dependent loss affecting the optical transmission channel <NUM> can be completely mitigated.

The optical transmitter <NUM> may accordingly comprise a processing unit <NUM> configured to determine at least one error correcting code and a Space-Time code such that the joint design or concatenation of the codes enables a complete removal of the mode-dependent loss effects.

In some embodiments, the FEC code <IMG> may be represented by a set of parameters (hereinafter referred to as `error correcting code parameters') comprising at least the set of codeword vectors or codebook AFEC, the error correction coding rate rFEC, and the minimum distance dmin,FEC. The FEC code being accordingly denoted by <IMG>(AFEC, rFEC, dmin,FEC).

Further, the ST code <IMG> may be represented by a set of parameters (hereinafter referred to as `Space-Time code parameters') comprising at least the set of codeword matrices or codebook AST, the Space-Time coding rate rST, and the minimum Euclidean distance dmin,ST. The ST code being accordingly denoted by <IMG>(AST, rST, dmin,ST).

In such embodiments, the processing unit <NUM> may be configured to determine at least one parameter of at least one error correcting code <IMG> and at least one parameter of a Space-Time code <IMG> according to the mitigation of a predefined value of the mode dependent loss, denoted by MDL.

According to some embodiments, the processing unit <NUM> may be configured to determine the values of the components of the codeword vectors representing the FEC code and/or the values of the components of the codeword matrices representing the Space-Time <IMG> according to a criterion related to the predefined value of the mode dependent loss. In other words, the processing unit <NUM> may be configured to determine the values of the components ci(l), l = <NUM>,. ,n of the codewords ci for i = <NUM>,. Card(AFEC) and/or the components xij for i = <NUM>,. , Nt; j = <NUM>,. ,T for each codeword matrix X in the codebook AST depending on a criterion that depends on a predefined value of the MDL.

According to a particular embodiment, the processing unit <NUM> may be configured to determine at least one parameter of at least one error correcting code and at least one parameter of a Space-Time code according to a criterion being satisfied if the product between the error correction coding rate rFEC, the Space-Time coding rate rST, the square of the error correction minimum distance value <MAT>, and the square of the Space-Time code minimum Euclidean distance <MAT> is greater than a function of the mode dependent loss value such that: <MAT>.

In equation (<NUM>), the function f(. ) designates any function of the mode-dependent loss value.

According to some embodiments, the function f(. ) may be a multiplicative function defined by a slope coefficient denoted by a. The slope coefficient is a real number.

In some embodiments, the processing unit <NUM> may be further configured to determine at least one parameter of at least one FEC code and/or at least one parameter of a Space-Time code depending on the signal-to-noise ratio. In such embodiments, the slope coefficient of the function f(. ) may depend on the signal-to-noise ratio.

According to some embodiments, the processing unit <NUM> may be configured to determine at least one parameter of at least one error correcting code depending on a predefined group of error correcting codes.

According to one embodiment, the predefined group of error correcting codes may comprise binary error correcting codes.

According to another embodiment, the predefined group of error correcting codes may comprise non-binary error correcting codes.

In a particular embodiment, the predefined group of error correcting codes may comprise the Hamming codes, the Reed-Solomon codes, the convolutional codes, the BCH codes, the Turbo codes, binary Low-Density Parity Check (LDPC) codes, and non-binary LDPC codes.

According to certain embodiments, the processing unit <NUM> may be configured to determine at least one parameter of a Space-Time code depending on a predefined group of Space-Time codes.

In a particular embodiment, the predefined group of Space-Time codes may comprise orthogonal codes, quasi-orthogonal codes, the Perfect codes, and the TAST code. Exemplary orthogonal codes comprise the Alamouti code.

Further, according to certain embodiments, the processing unit <NUM> may be configured to determine at least one parameter of at least one error correcting code <IMG> and/or at least one parameter of a Space-Time code <IMG> depending on a predefined coding gain denoted by ΔG and/or depending on the number of used spatial propagation modes Nt.

According to some embodiments, the optical transmitter <NUM> may be configured to transmit the optical signal using all available propagation modes. In such embodiments, the number of used propagation modes Nt may be equal to all the propagation modes N.

Generally, the various propagation modes in a space division multiplexing system do not undergo the same losses due for example to imperfections of the waveguide and imperfections of the optical components inserted in the optical transmission link. Such imperfections result in different modal loss disparities. In such cases, a selection of modes may be performed at the transmitter and/or receiver according to a selection criterion such that only a selected set of modes is used to propagate the optical signal along the fiber. Several selection criteria have been disclosed in the patent application N° <CIT>. Exemplary criteria comprise the selection of a set of modes according to the maximization of the capacity of the space division multiplexing system and the optimization of the average received energy.

Accordingly, in embodiments using mode selection at the transmitter, the optical transmitter <NUM> may be configured to transmit the optical signal using a set of propagation modes previously selected among the available propagation modes. The number of used propagation modes Nt may be in this case strictly lower than the number of available modes, i.

In such embodiments, the processing unit <NUM> may be configured to determine at least one parameter of at least one error correcting code <IMG> and/or at least one parameter of a Space-Time code <IMG> depending on the number of selected spatial propagation modes.

The optical transmitter <NUM> may further comprise a plurality of multi-carrier modulators <NUM> configured to generate a multi-carrier symbol by implementing a multi-carrier modulation technique within each optical carrier involving a large number of orthogonal sub-carriers. Moreover, multi-carrier modulations may be implemented in the presence of multi-mode fibers to decouple the different modes and provide a better resistance to the inter-symbol interference resulting from the fiber dispersion and crosstalk between the various modes. Exemplary multi-carrier modulation formats comprise Orthogonal Frequency Division Multiplexing (OFDM) and Filter Bank Multi-Carrier (FBMC).

The frequency-domain signal delivered by the multicarrier modulators <NUM> may be then processed by a digital-optical Front-End <NUM> configured to convert the received frequency-domain signal to the optical domain. The digital-optical Front-End <NUM> may perform the conversion using a number of lasers of given wavelengths and a plurality of optical modulators (not shown in <FIG>) associated with the used polarization states and the different propagation modes. A laser may be configured to generate a laser beam of a same or different wavelength. The different laser beams may be then modulated using the different outputs of the OFDM symbols (or the different values of the codeword matrix in embodiments using single-carrier modulations) by means of the optical modulators and polarized according to the different polarization states of the fiber. Exemplary modulators comprise Mach-Zehnder modulators. A phase and/or amplitude modulation may be used. In addition, the modulation scheme used by the various optical modulators for modulating the different optical signals may be similar or different.

The number of the optical modulators and lasers depends on the number of used polarization states, the number of used propagation modes, and in general on the number of cores in the fiber. The optical signal thus generated may be then injected in the optical fiber to propagate therein according to the different available propagation modes.

The determined at least one forward error correcting code <IMG> is implemented by the FEC encoder <NUM> for adding redundant bits (in general redundant symbols) to the input binary sequence so that the receiver can detect and/or correct common transmission errors. The use of a FEC code provides an additional protection and immunity against transmission errors and allows significant improvement in performance with respect to uncoded transmission (i.e. transmission of modulated data without FEC encoding).

Additional improvements and reduction on the probability of error may be achieved through the concatenation of two or more FEC codes. Concatenation of codes may follow a serial, a parallel, or a multi-level architecture. The FEC encoder <NUM> may be accordingly configured to implement two or more FEC codes.

<FIG> is a block diagram of the FEC encoder <NUM> according to some embodiments in which a serial architecture for concatenating two forward error correcting codes, referred to as an "inner code" and "outer code", is considered. The FEC encoder <NUM> may accordingly comprise:.

<FIG> is a block diagram of the FEC encoder <NUM> according to some embodiments in which a parallel architecture for concatenating two error correcting codes is considered. In such embodiments, the same input binary sequence is encoded by two or more different encoders. However, one of the encoders acts on an interleaved copy of the input sequence. The FEC encoder <NUM> may accordingly comprise:.

In some embodiments (not shown in <FIG>), parallel concatenation can be extended to more than two codes by adding additional interleavers and encoders.

In embodiments involving more than one forward error correcting code, the processing unit <NUM> may be configured to determine at least one code parameter for each concatenated code depending on a predefined value of the mode-dependent loss and/or on a predefined coding gain and/or on a the number of used spatial modes and/or on the signal-to-noise ratio according to any of the preceding features involving a single FEC code.

<FIG> is a block diagram of the Digital-Optical Front-End <NUM> according to some embodiments in which a single-core multi-mode fiber and a single polarization state are used. In such embodiments, the number of used propagation modes is lower than or equal to the number N of available propagation modes Nt ≤ N. The Digital-Optical Front-End <NUM> may accordingly comprise:.

In another embodiment in which wavelength division multiplexing is used, each laser <NUM>-n may use a plurality of wavelengths. The wavelengths may be similar or different. In such embodiment, the plurality Nt of used modes may be combined with a plurality of W wavelengths, each mode being associated with W wavelengths. Accordingly, the Digital Optical Front-End <NUM> may comprise W lasers of different wavelengths, the beam generated by each laser being modulated by Nt optical modulators (not show in <FIG>).

In still other embodiments in which polarization division multiplexing is used, the optical signal may be transmitted over the two polarization states of the optical field. In such embodiments (not shown in the figures), the Digital Optical Front-End <NUM> may comprise Nt lasers, Nt polarization splitters configured to provide two orthogonal polarizations, and <NUM>Nt optical modulators. Each pair of modulators may be associated with a laser and may be configured to modulate the signals which are polarized orthogonally. Exemplary polarization splitters comprise for example Wollaston prisms and polarization splitting fiber couplers. In addition, the optical fiber transmission link <NUM> may further comprise polarization scramblers (not depicted in <FIG>) configured to compensate the polarization dependent losses.

The optical signal generated according to any of the preceding embodiments may propagate along the fiber until it reaches the other end of the optical transmission system <NUM> where it is processed by an optical receiver <NUM>.

<FIG> is a block diagram of an optical receiver <NUM> according to some embodiments. The optical receiver <NUM> is configured to receive the optical signal transmitted by the optical transmitter <NUM> through the transmission channel <NUM> and to generate an estimate of the original input data sequence. The optical receiver <NUM> may comprise:.

The Space-Time decoder <NUM> may implement a Space-Time decoding algorithm chosen in a group consisting of a maximum likelihood decoder, a Zero-Forcing decoder, a Zero-Forcing Decision Feedback Equalizer, and a Minimum Mean Square Error decoder.

Exemplary maximum likelihood decoders comprise the sphere decoder, the Schnorr-Euchner decoder, the stack decoder, the spherical-bound-stack decoder.

In embodiments using single-carrier modulations, the plurality of multi-carrier modulators <NUM> may be replaced by a single modulator. Similarly, the multi-carrier demodulators <NUM> may be replaced by a single demodulator.

In some embodiments, the FEC encoder <NUM> may be configured to implement a concatenation of two or more forward error correcting codes. In such embodiments, a corresponding structure may be implemented by the FEC decoder <NUM>. For example, in embodiments based on a serial concatenation of an inner code and an outer code, the FEC decoder <NUM> may comprise an inner code decoder, a de-interleaver, and an outer code decoder (not shown in <FIG>). In embodiments involving two codes in a parallel architecture, the FEC decoder <NUM> may comprise a de-multiplexer, a de-interleaver, and a joint decoder (not shown in <FIG>).

According to some embodiments in which a mode selection is performed at the transmitter, the optical receiver <NUM> may be configured either to process only the selected propagation modes by the optical transmitter <NUM> using a mode selection at the receiver or to process the totality of the available propagation modes over which the optical signals propagate.

<FIG> is a flowchart depicting the joint FEC coding and ST coding method according to some embodiments in which the transmission system uses space division multiplexing in a single-core multi-mode fiber, single carrier modulation formats, single wavelength, and a single polarization.

The following description of certain embodiments will be made with reference to binary FEC coding using a single FEC code and assuming a hard-decision decoding at the receiver, for illustration purpose only. However, the skilled person will readily understand that the various embodiments of the invention apply to non-binary coding schemes and to any concatenation of two or more binary or non-binary FEC codes and is not restricted to the use of hard-decision decoding, soft-decision decoding can also be considered.

In step <NUM>, an input binary sequence may be received. The binary sequence may comprise k bits and may be written in a vector notation as: <MAT>.

In step <NUM>, a set of input parameters may be received or retrieved (for example from some storage means comprised in the optical transmitter device <NUM>). The set of input parameters may comprise:.

The various embodiments of the invention provide encoding methods combining forward error correction coding and Space-Time coding enabling a complete mitigation of the mode-dependent loss effects impacting the optical transmission system.

A binary forward error correcting code of coding rate <MAT> encodes the binary sequence b = (b<NUM>, b<NUM>,. , bk) composed of k bits into a codeword vector c which comprises n bits and can be written in a vector notation as c = (c<NUM>, c<NUM>,. For the different values taken by the input binary sequence, the corresponding codeword vectors are different and take values in a set of codeword vectors, the codebook, denoted by AFEC. The total number of the different codeword vectors represents the cardinality of the codebook, denoted by Card(AFEC).

Any two different codeword vectors in the codebook AFEC may be associated with a distance metric known as the 'Hamming distance', expressed previously in equation (<NUM>). The Hamming distance indicates the number of bits in which these codewords are different. Based on the definition of the Hamming distance, the forward error correcting code <IMG> may be associated with a second parameter, known as the minimum distance, previously expressed in equation (<NUM>). The minimum distance, denoted by dmin,FEC, represents the minimum value of the Hamming distance metrics over all pairs of different codeword vectors in the codebook AFEC.

In the following description of certain embodiments, a FEC code <IMG> will be represented by a set of error correction parameters comprising the set of codeword vectors or codebook AFEC, the error correction coding rate rFEC, and the minimum distance dmin,FEC. The FEC code will be accordingly denoted by <IMG>(AFEC, rFEC, dmin,FEC).

A Space-Time code <IMG> of Space-Time coding rate <MAT> encodes a sequence s = (s<NUM>, s<NUM>,. , sQ) of Q modulated symbols to be sent through the optical transmission channel during T channel uses into a codeword matrix <MAT> composed on Nt row vectors and T column vectors. Nt designates the space dimension of the Space-Time code <IMG> and T represents the temporal length of the code that may depend on the total transmission time during which the optical transmitter is configured to transmit the optical signal to the optical receiver(s). For the different values taken by the modulated symbols, the corresponding codeword matrices are different and take values in a set of codeword matrices values, the codebook, denoted by AST. The total number of the different codeword matrices represents the cardinality of the codebook, denoted by Card(AST).

Similarly to the FEC code, any two different codeword matrices in the codebook AST may be associated with a distance metric known as the 'Euclidean distance', expressed previously in equation (<NUM>). The Euclidean distance (hereinafter referred to `Euclidean distance metric') indicates the distance between any two different codewords in the Euclidean Space. Based on the definition of the Euclidean distance, the ST code <IMG> may be associated with a second parameter, known as the minimum Euclidean distance, previously expressed in equation (<NUM>). The minimum Euclidean distance, denoted by dmin,ST, represents the minimum value of the Euclidean distance metrics over all pairs of different codeword matrices in the codebook AST.

In the following description of certain embodiments, an ST code <IMG> will be represented by a set of Space-Time code parameters comprising the set of codeword matrices or codebook AST, the Space-Time coding rate rST, and the minimum Euclidean distance dmin,ST. The ST code will be accordingly denoted by <IMG>(AST, rST, dmin,ST).

Step <NUM> may be performed to determine at least one parameter of a forward error correcting code <IMG> and at least one parameter of a Space-Time code <IMG> depending on at least one input parameter and according to a criterion related to the predefined value of the mode-dependent loss, MDL, impacting the transmission system.

The optical transmission system may be represented by an optical multiple-input multiple-output system described by the relation: <MAT> In equation (<NUM>):.

According to some embodiments, the channel noise may be modeled by a White Gaussian variable of <NUM>σ<NUM> variance per complex dimension.

According to some embodiments, the channel matrix may be given by: <MAT>.

In equation (<NUM>), D designates a diagonal matrix of diagonal components uniformly selected from the interval [λmin, λmax] and represent the different losses experienced by the different propagation modes. U denotes a unitary matrix modeling the coupling between the different propagation modes and α characterizes the mode average propagation loss according to the expression: <MAT>.

The channel matrix accordingly satisfies (HH*) = Nt, with Tr(A) designating the trace of a given matrix A and the operator (. )* designating the Hermitian conjugate operation.

The determination of at least one parameter for the FEC code and the ST code based on a criterion related to the mode-dependent loss has been elaborated by the inventors from a decoding error optimization problem which assumes a concatenation of maximum likelihood (ML) Space-Time decoding at the Space-Time decoder <NUM> and hard-decision FEC decoding at the FEC decoder <NUM>. The determination of the FEC code and the ST code parameters based on such decoding error optimization problem provides an efficient joint FEC code and ST code design enabling the minimization of the decoding error probability with a complete mitigation of the mode-dependent loss affecting the transmission channel.

In the first decoding stage, a Space-Time ML decoding provides an estimate of the transmitted codeword matrix according to the minimization of the Euclidean distance between the received signal Y and the different possible values of the codeword matrices. A ST codeword decoding error occurs if the estimated codeword matrix is different from the transmitted codeword matrix.

The analysis of the codeword error probability under ML ST decoding can be performed based on the pair-wise error probability corresponding to the error probability that for a transmitted codeword, a different codeword matrix is estimated.

In some embodiments assuming that the channel matrix is known at the optical receiver using for example one or more training sequences, the pair-wise error probability denoted by Pr(Xl → Xp) and corresponding to the error probability of estimating a codeword Xp while a codeword Xl was transmitted is expressed by: <MAT>.

In equation (<NUM>), Q(. ) designates the Q function (not to be confused with the number of modulated symbols) defined by: <MAT>.

Using the Chernoff's bound and by averaging over the channel realizations, the pair-wise error probability may be upper bounded according to: <MAT>.

Each pair of different codeword matrices Xl and Xp for l ≠ p, may be associated with a difference codeword matrix Dlp determined by computing the difference between the different codeword matrices such that Dlp = Xl - Xp. In addition, each difference codeword matrix may be associated with a distance metric given by dST(Xl, Xp) = ∥Dlp∥ = ∥Xl - Xp∥.

Using the difference codeword matrix notation, inequality (<NUM>) may be equivalently written as: <MAT>.

Using the law of total probability, the pair-wise error probability can be written as:<MAT>(<NUM>).

The upper bound expression in equation (<NUM>) may be accordingly divided into two terms T<NUM> and T<NUM> such that: <MAT>.

The first term T<NUM> comprises the pairs of different codeword matrices associated with unitary difference codeword matrices, while the second term T<NUM> comprises the pairs of different codeword matrices associated with non-unitary difference codeword matrices.

Using the properties of unitary matrices and the minimum Euclidean distance of the code, the first term may be upper bounded according to the expression: <MAT>.

In equation (<NUM>), p<NUM>,min designates the probability that the codeword difference matrix Dlp between two codeword matrices Xl and Xp is unitary and is associated with a distance metric equal to the minimum Euclidean distance of the ST code, that is dST(Xl, Xp) = ∥Dlp∥ = ∥Xl - Xp∥ = dmin,ST.

The second term T<NUM> may be simplified as follows. First, using the property that <MAT>, this term may be upper bounded according to: <MAT>.

In equation (<NUM>), the upper bound is computed by averaging over the diagonal entries of the matrix D and the components of the unitary matrix U.

Using the property that the product matrix <MAT> is a square Hermitian matrix, there exists a unitary matrix V and a diagonal matrix Σ = diag(Σ<NUM>, Σ<NUM>,. , ΣNt) such that <MAT> VΣV*. Inequality (<NUM>) may be accordingly written as: <MAT>.

Given that the matrix U is randomly drawn from the unitary matrices ensemble, the product matrix UV follows the same distribution as the matrix U. Then, inequality (<NUM>) can be equivalently expressed as: <MAT>.

By developing the product matrix DUΣU*, the upper bound on the pairwise error probability in inequality (<NUM>) can be written according to: <MAT> <MAT> <MAT>.

In inequalities (<NUM>)-(<NUM>), Ukt designates the component of the unitary matrix U at the kth row and tth column. Given the uniform distribution of the experienced losses λk over the interval [λmin, λmax], averaging the upper bound in equation (<NUM>) over the different values of λk gives: <MAT>.

In inequality (<NUM>), P(λk) denotes the probability distribution function of λk and is given by: <MAT>.

Using the probability distribution function of the experienced losses, inequality (<NUM>) can be expressed by: <MAT> <MAT>.

Using the approximation of the hyperbolic sine function at high signal-to-noise ratio, the upper bound in inequality (<NUM>) can be expressed as: <MAT> <MAT> <MAT> <MAT>.

In inequality (<NUM>), the term MDL corresponds to the value of the mode-depend loss on the optical transmission system given by the ratio between the maximum and the minimum eigenvalues of the channel matrix such that <MAT>.

The upper bound in inequality (<NUM>) is independent of the unitary matrix U, then the term T<NUM> can be upper bounded according to: <MAT>.

Using the properties the minimum Euclidean distance of the ST code, inequality (<NUM>) may be equivalently written as: <MAT>.

In equation (<NUM>), p<NUM>,min designates the probability that the codeword difference matrix Dlp between two codeword matrices Xl and Xp is non-unitary and is associated with a distance metric equal to the minimum Euclidean distance of the ST code, that is dST(Xl, Xp) = ∥Dlp∥ = ∥Xl - Xp∥ = dmin,ST.

Combining the results of inequalities (<NUM>) and (<NUM>), the pair-wise error probability inequality (<NUM>) may be written as: <MAT>.

Finally, the pair-wise error probability can be approximated by: <MAT>.

In the second decoding stage, Hard-decision FEC decoding provides firm decisions for each component ci for i = <NUM>,. ,n of the codeword vector c carried by the received signal to whether the component corresponds to zero (i.e. the bit ci is equal to '<NUM>') or one (i.e. the bit ci is equal to '<NUM>'). A FEC codeword decoding error occurs if at least one bit of the estimated codeword is different from the corresponding bit in the transmitted codeword vector.

The analysis of the codeword error probability under binary FEC decoding can be performed based on the equivalent binary-symmetric channel (BSC) with crossover probability p. The BSC is a transmission channel with binary input and binary output and probability of error p and corresponds to a transmission of binary values equal to zero or to one and a reception of a correct bit with a probability equal to <NUM> - p. Accordingly, the probability of having m errors in a block of n bits comprised in the transmitted codeword vector c maybe expressed as: <MAT>.

In equation (<NUM>), <MAT> designates the binomial coefficient denoting m combinations among n.

The addition of redundant bits to the original data by FEC coding aims at providing the receiver the capability of detecting and possibly correcting the errors that occurred randomly during the transmission. The correction capability of the code, denoted by t is expressed, as a function of the minimum distance of the code dmin,FEC according to: <MAT>.

The FEC code decoder can correct up to t transmission errors. When the number of errors exceeds the correction capability of the code, a decoding error may be declared at the receiver. Accordingly, the bit error probability after hard-decision decoding can be upper bounded by: <MAT> <MAT>.

In the high regime of the signal-to-noise ratio, the crossover probability tends to zero (<NUM>). The upper bound on the bit error probability in inequality (<NUM>) is consequently dominated by the first term of the summation such that: <MAT>.

Replacing the correction capability term by its expression given in equation (<NUM>), inequality (<NUM>) may be equivalently written as: <MAT> In inequality (<NUM>), <MAT>.

Combining now the two-stages of the decoding process, and given that a ST codeword error occurs when at least one bit in the transmitted codeword vector c is in error, the decoding decisions at the level of the FEC hard-decision decoding may be expressed based on the pair-wise error probability on the codeword matrices. First, the crossover probability may be written as: <MAT>.

And by using the upper bound on the pair-wise error probability in inequality (<NUM>), the bit error probability in inequality (<NUM>) can be expressed according to: <MAT>.

Using the relation Es = Eb × rFEC × rST × q involving the FEC code error correction coding rate rFEC, the ST coding rate rST, the average bit energy Eb, the average symbol energy Es, and the number of bits per modulated symbol q, the bit error probability can be upper bounded as: <MAT>.

According to some embodiments, the determination of the parameters of the FEC code <IMG>(AFEC, rFEC, dmin,FEC) and/or the parameters of the Space-Time code <IMG>(AST, rST, dmin,ST) may be based on the minimization of the bit error probability in inequality (<NUM>) depending on the value of the mode-dependent loss, MDL.

Determining the parameters of the FEC code may be equivalent to:.

Determining the parameters of the ST code may be equivalent to:.

According to certain embodiments, at least one parameter of the error correcting code and/or at least one parameter of the Space-Time code may be determined according to a criterion based on the minimization of the bit error probability in inequality (<NUM>) for a predefined value of the mode-dependent loss, the criterion being satisfied if the following inequality holds: <MAT>.

In inequality (<NUM>), f(. ) designates any function of the predefined value of the MDL.

In particular embodiments based on the complete removal of the MDL effect while minimizing the error probability, the function f(. ) may be a multiplicative function expressed by: <MAT>.

In such embodiments, the slope coefficient is given by <MAT> and depends on the signal-to-noise ratio.

Further, according to some embodiments, at least one parameter of the error correcting code and/or at least one parameter of the Space-Time code may be determined depending on a predefined coding gain ΔG that may be received among the input parameters. The coding gain indicates the gain that may be provided by a coded system over an uncoded system (i.e. without FEC coding and without ST coding). It indicates the reduction in signal-to-noise ratio for a coded system to achieve the same error probability as an uncoded system. For deriving the expression of the coding gain, first the bit error probability Pe,NC for an uncoded system may be formulated based on inequality (<NUM>) such that: <MAT>.

In inequality (<NUM>), dmin,NC designates the minimum distance of the modulation used to modulate the encoded vector prior to Space-Time coding and depends on the modulation scheme received among the input parameters.

According to inequalities (<NUM>) and (<NUM>), the coding gain in the logarithm scale may be given by: <MAT>.

In equation (<NUM>), GdB,FEC and GdB,ST designate respectively the coding gain of an only FEC coded scheme and an only ST coded scheme over an uncoded scheme.

According to some embodiments, at least one parameter of the error correcting code and/or at least one parameter of the Space-Time code may be determined such that a predefined coding gain ΔG (or its equivalent in the logarithm domain ΔGdB) can be achieved by concatenating the corresponding FEC code and ST code.

Further, according to some embodiments, at least one parameter of the forward error correcting code may be determined depending on a group of error correcting codes comprising binary FEC codes, non-binary FEC codes, Hamming codes, the Reed-Solomon codes, the convolutional codes, the BCH codes, the Turbo codes, binary Low-Density Parity Check (LDPC) codes, and non-binary LDPC codes.

Further, according to some embodiments, at least one parameter of the Space-Time code may be determined depending on a group of Space-Time codes comprising orthogonal codes, quasi-orthogonal codes, the Perfect codes, and the TAST code. Exemplary orthogonal codes comprise the Alamouti code.

At step <NUM>, the received input binary sequence b may be encoded into a codeword vector c selected from the codebook AFEC of the considered FEC code depending on the values of the different bits comprised in the binary sequence.

At step <NUM>, a sequence of Q modulated symbols s<NUM>, s<NUM>,. , sQ may be determined by applying a modulation scheme to the codeword determined in step <NUM>. The symbols may take complex values selected in a set of values depending on the predefined modulation scheme. Different modulation schemes may be implemented such as <NUM>q-QAM or <NUM>q-PSK with <NUM>q symbols or states. Each modulated symbol comprises q bits (not to be confused with the order of the Galois Field GF(q)). A symbol sp has an average symbol energy Es and can be written in the form: <MAT>.

In equation (<NUM>), i denotes the complex number such that i<NUM> = -<NUM> and the Re(. ) operators output respectively the real and imaginary parts of an input value. When modulation formats such as <NUM>q-QAM are used, the <NUM>q symbols or states represent a sub-set of the integer field <MAT>. The corresponding constellation is composed of <NUM>q points representing the different states or symbols. In addition, in the case of squared modulations, the real and imaginary parts of the information symbols belong to the same finite alphabet A = [- (q - <NUM>), (q - <NUM>)].

Step <NUM> may be performed to determine a codeword matrix by encoding the set of modulated symbols using the considered Space-Time code. A codeword matrix may be accordingly selected from the ST codebook depending on the values of the different modulated symbols.

An analysis of the decoding error probability of the concatenation of existing FEC codes and ST codes has been carried out to validate the performance of the joint FEC and ST coding method according to some embodiments. In particular, the error performances of the BCH code (k = <NUM>, n = <NUM>, <MAT>,t = <NUM>) and the TAST code (Nt = <NUM>, T = <NUM>, rST = <NUM>/c. u) have been evaluated for different MDL values using <NUM>-QAM modulations. ML ST decoding is performed at the receiver side, in addition to demodulation, de-interleaving and hard-decision FEC decoding.

<FIG> depicts the Bit Error Rate (BER) performance as a function of the signal-to-noise ratio (SNR) for uncoded schemes, coded schemes using only a FEC coding based on the BCH code, coded schemes using only a ST coding based on the TAST code, and a joint FEC and ST coding by concatenating a BCH code and the TAST code. Depicted performance results in <FIG> are obtained according to some embodiments of the invention in a <NUM>-mode fiber-based transmission system affected by a mode-dependent loss of <NUM>-decibles. ML ST decoding is performed at the receiver side, in addition to demodulation, de-interleaving and hard-decision FEC decoding. Plotted results confirm the efficiency of concatenating a FEC code and a ST code for mitigating the effects of the mode-dependent loss. A joint FEC and ST coded scheme in the presence of a <NUM>-dB MDL approaches the bit error performance of an MDL-free uncoded scheme. In addition, the coding gain reached by the concatenation of the BCH code and the TAST code is approximately equal to the coding gain provided by each code separately, which confirms the results of equation (<NUM>).

<FIG> depicts the Bit Error Rate (BER) performance as function of the signal-to-noise ratio for the same uncoded and coded schemes evaluated in <FIG> obtained in a <NUM>-mode fiber-based transmission system affected by a mode-dependent loss of <NUM>-decibles. Similarly to the results of <FIG>, plotted results in <FIG> show the outperformance of a joint FEC and ST coding scheme over the uncoded scheme and over coded schemes using either a FEC code or a ST code alone. Furthermore, results show the capability of such combined coding design in mitigating even high values of mode-dependent losses.

Although the various embodiments have been detailed in the case of single-core multi-mode fibers in which a single polarization, a single wavelength and single-carrier modulation are used, it should be noted that the invention can also be applied in multi-core multi-mode fibers in combination with polarization multiplexing using two polarizations and/or in combination with the use of wavelength multiplexing using several wavelengths, and/or using multi-carrier modulation formats. The application of the invention in such optical-fiber systems may be based on a system model obtained from the generalization of the system provided in this application in equation (<NUM>).

Claim 1:
An optical transmitter configured to transmit a data sequence over at least two spatial propagation modes through an optical transmission channel in a multi-mode optical fiber transmission system, the transmission system being associated with a predefined value of a mode-dependent loss, the optical transmitter comprising:
- a forward error correcting code encoder (<NUM>) configured to encode said data sequence into a codeword vector by applying at least one error correcting code represented by a set of error correcting code parameters;
- a modulator (<NUM>) configured to determine a set of modulated symbols by applying a modulation scheme to said codeword vector; and
- a Space-Time encoder (<NUM>) configured to determine a codeword matrix by applying a Space-Time code to said set of modulated symbols said Space-Time code being represented by a set of Space-Time code parameters,
wherein said set of error correcting code parameters comprises at least a number of codeword vectors, an error correction coding rate, and an error correction minimum distance value and said set of Space-Time code parameters comprises at least a number of codeword matrices, a Space-Time coding rate, and a Space-Time code Euclidean distance value,
wherein the optical transmitter comprises a processing unit (<NUM>) configured to determine at least one parameter of said set of error correcting code parameters and at least one parameter of said set of Space-Time code parameters depending on said predefined value of mode-dependent loss.