Patent Publication Number: US-2005129094-A1

Title: Communication system using wavelength spread-spectrum coding

Description:
BACKGROUND  
      Wavelength division multiplexing (WDM) is employed in optical communication systems to enable information signals to be transmitted at multiple wavelengths over a single optical fiber, thereby increasing the number of information signals that can be transmitted by the fiber. The theoretical minimum optical loss for glass optical fiber is about 0.16 decibels per kilometer (dB/km), and this theoretical minimum occurs at a wavelength of about 1550 nanometers (nm). Erbium-doped amplifiers, which currently are the most common type of amplifier used for amplifying optical signals carried on optical fibers, perform best in the wavelength range of approximately 1520 to 1565 nm. Therefore, these amplifiers have the best gain characteristics over a wavelength range that includes the wavelength at which optical attenuation in optical fibers is at a minimum.  
       FIG. 1  illustrates a graph  1  on which two curves  10  and  11  are plotted. The axis labeled FIBER LOSS (dB) of graph  1  indicates the optical loss in decibels (dB) for a typical optical fiber as a function of transmission wavelength. The axis labeled AMPLIFIER GAIN (dB) indicates the optical gain in dB of a typical erbium-doped amplifier as a function of wavelength. Curve  10  represents optical loss as a function of wavelength for a typical optical fiber. Curve  11  represents gain as a function of wavelength for a typical erbium-doped amplifier. Curves  10  and  11  are not intended to illustrate precise relationships, but illustrate an approximate relationship between the loss and gain characteristics of a typical optical fiber and a typical erbium-doped amplifier, respectively.  
      The shape of curve  11  in the graph  1  indicates that a typical erbium-doped amplifier has its highest gain in a wavelength range that is approximately 43 nm wide. This range includes the 1550 nm wavelength and wavelengths slightly less than and greater than 1550 nm. The shape of curve  11  also indicates that the gain of the erbium-doped amplifier drops off rapidly outside the 43 nm-wide range. The shape of curve  10  indicates that the optical fiber has its lowest optical loss at approximately 1550 nm. Therefore, optimum optical performance is obtained in an optical communication system by using transmission wavelengths in the 43 nm-wide wavelength range. Two other wavelength ranges exist that are used less commonly than the 43 nm range described above. These are the long band (L-band) and short band (S-band) wavelength ranges. For illustrative purposes, only the 43 nm-wide wavelength range at approximately 1550 nm will be discussed herein due to the fact that the majority of optical fiber communication occur in this wavelength range.  
      The ability of WDM to increase the capacity of optical communication systems is limited by the above-described constraint on usable transmission wavelengths and by the need for the transmission wavelengths to be spaced sufficiently in wavelength to prevent interference between the optical signals in adjacent channels. This need for wavelength spacing decreases the number of usable transmission wavelengths, and thereby further limits capacity.  
      In optical communication systems employing WDM, the above-mentioned 43 nm-wide wavelength range is typically divided into 80 channels, i.e., transmission wavebands, each of which carries an optical signal modulated at a bit rate of 10 Gigabits per second (Gb/s). Adjacent channels differ in center frequency by 50 Gigahertz (GHz). The 80 channels collectively occupy a frequency range of approximately 4,000 GHz, i.e., 80 channels×50 GHz. The aggregate bit rate when information signals are transmitted on all channels is 800 Gb/s, i.e., 80 channels×10 Gb/s. A good figure of merit for the spectral efficiency of an optical communication system is the bit rate divided by the bandwidth of the system. The 80-channel system, therefore, has a figure of merit equal to approximately ((80×10 Gb/s)/(4,000 GHz)) or 0.20 bits.sec −1 /Hz. This figure of merit is very close to the limit of what can be achieved with current WDM systems. The limit is a practical limit dictated by a number of factors including laser drift and drift of the optical filters used in the WDM demultiplexers.  
      Optical filters are used in the wavelength division demultiplexer of the optical receivers used in optical communication systems to separate the WDM channels at the receiver and prevent interference between the optical signals in adjacent channels. The optical filters that are currently used in such receivers have a pass bandwidth of approximately 30 GHz, which is much less than the channel spacing of 50 GHz. Wider filter bandwidths would enable the bit rate of the optical signals to be increased, but would produce unacceptable levels of inter-channel interference because of the gradual roll-off of the out-of-band rejection characteristic of the optical filters. In addition, factors such as temperature drift of both the laser frequency and the center frequency of the optical filters, aging of the filter components, etc., further reduce the possibility that the usable bandwidth of the channels can be increased by conventional approaches. The factors just described combine to limit the maximum bit rate per channel in such systems to the 10 Gb/s rate mentioned above. This bit rate is small compared with the channel spacing between the channels.  
      Also, in a conventional optical communication system, if the transmitter or the receiver associated with one of the information signals fails or is otherwise impaired, transmission of the information signal through the optical communication system stops until the failed component is repaired or replaced.  
      Accordingly, a need exists for an alternative way of increasing the transmission capacity and reliability of an optical transmission system.  
     SUMMARY  
      In accordance with the present invention, wavelength spread-spectrum encoding is used to enable a multi-channel communication system such as a WDM optical communication system to transmit more full-bandwidth information signals than the number of channels of the communication system. In such wavelength spread-spectrum communication system, each information signal is carried by all of the channels of the communication system and each of the channels carries part of all the information signals.  
      Applying wavelength spread-spectrum encoding to the information signals in accordance with the invention gives the additional advantage that all of the information signals can be successfully recovered at the receiver even if one or more channels of the multi-channel communication system become inoperable or subject to high levels of interference. In other words, wavelength spread-spectrum encoding in accordance with the invention provides redundancy with respect to transmission of the information signals. Wavelength spread-spectrum encoding in accordance with the invention is suitable for use in any wired, wireless or optical multi-channel communication system.  
      In a first aspect, the invention provides a method for transmitting information signals via multiple transmission channels. In an embodiment of the method, each information signal is encoded with a respective spreading code to generate a coded signal corresponding to each bit of the spreading code. The spreading codes are mutually different. The coded signals corresponding to the same bit of the spreading codes are allocated to a respective transmission channel. Then, in each transmission channel, the coded signals allocated to the transmission channel are analog summed to generate a modulation signal, and a transmission signal is modulated in response to the modulation signal.  
      In a second aspect, the invention provides a method for recovering information signals from channel signals received via respective transmission channels. The channel signals are generated by encoding the information signals with respective spreading codes. In an embodiment of the method, each of the information signals is recovered by multiplying the channel signal from each transmission channel by a respective bit of the spreading code assigned to the information signal to generate a respective product signal, summing the product signals to generate a sum signal, and subjecting the sum signal to thresholding.  
      In a third aspect, the invention provides apparatus for transmitting information signals via multiple transmission channels. An embodiment of the apparatus comprises a spread-spectrum encoder for each of the information signals, a signal allocator and, in each transmission channel, an analog summer and a transmitter. Each spread-spectrum encoder comprises coded signal outputs and is operable to encode the information signal with a respective spreading code to provide a coded signal corresponding to each bit of the spreading code at a respective one of the coded signal outputs. The spreading codes are mutually different. The signal allocator is connected to the coded signal outputs of the spread-spectrum encoders and structured to allocate the coded signals corresponding to the same bit of the spreading codes to a respective one of the transmission channels. Each analog summer comprises an output, and inputs connected to the signal allocator to receive therefrom the coded signals allocated to the transmission channel. The transmitter comprises a modulation input connected to the output of the analog summer.  
      In a fourth aspect, the invention provides apparatus for recovering information signals from channel signals received via respective transmission channels. The channel signals are generated by encoding the information signals with respective spreading codes. An embodiment of the apparatus comprises a spread-spectrum decoder for each information signal. The spread-spectrum decoder comprises a multiplying circuit, an analog summer and a threshold circuit. The multiplier circuit is connected to receive the channel signals from the transmission channels and is for multiplying each channel signal by a respective bit of the spreading code assigned to the information signal to generate a respective product signal. The analog summer comprises an output, and inputs connected to receive the product signals from the multiplying circuit. The threshold circuit comprises an input connected to the output of the analog summer and additionally comprises an output that provides the recovered information signal.  
      Other features and advantages of the invention will become apparent from the following description, drawings and claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  is a graph illustrating a general loss versus wavelength characteristic for an optical fiber and a general gain versus wavelength characteristic for an erbium-doped amplifier.  
       FIG. 2  is a block diagram of an exemplary embodiment of the transmitter of a wavelength spread-spectrum communication system in accordance with the invention.  
       FIGS. 3A-3D  are block diagrams of an exemplary embodiment of the spread-spectrum encoders of the transmitter shown in  FIG. 2 .  
       FIG. 4  is a table showing the 64 possible states of the coded signals generated by the spread-spectrum encoders of the transmitter shown in  FIG. 2  in response to all 16 possible combinations of the states of four information signals.  
       FIG. 5  is a block diagram of an exemplary embodiment of the receiver of a wavelength spread-spectrum communication system in accordance with the invention.  
       FIG. 6  is a block diagram of an exemplary first embodiment of one of the spread-spectrum decoders of the receiver shown in  FIG. 5 .  
       FIG. 7  is a table showing the operation of the spread-spectrum decoders of the receiver shown in  FIG. 5  in response to all 16 possible combinations of the states of the channel signals.  
       FIG. 8  is a block diagram of an alternative embodiment of one of the spread-spectrum encoders of the transmitter shown in  FIG. 2 .  
       FIGS. 9A and 9B  are block diagrams of another alternative embodiment of two of the spread-spectrum encoders of the transmitter shown in  FIG. 2 .  
       FIG. 10  is a block diagram of an alternative embodiment of one of the spread-spectrum decoders of the receiver shown in  FIG. 5 .  
       FIG. 11  is a flow chart of an embodiment of a method in accordance with the invention for transmitting information signals via multiple transmission channels.  
       FIG. 12  is a flow chart of an embodiment of a method in accordance with the invention for recovering information signals from channel signals received via respective transmission channels. 
    
    
     DETAILED DESCRIPTION  
      In accordance with the invention, wavelength spread-spectrum encoding is used to increase the transmission capacity of a multi-channel communication system such as an optical communication system employing wavelength division multiplexing (WDM). The invention will be described below with reference to an example in which the multi-channel communication system is a WDM optical communication system. However, the invention may be applied to any type of multi-channel communication system, including wired, wireless and optical communication systems.  
      In accordance with the invention, each information signal is encoded with a respective spreading code to produce a coded signal corresponding to each bit of the spreading code. The spreading codes used to encode all the information signals are mutually different. The coded signals corresponding to the same bit of the spreading codes are then allocated to a respective one of the transmission channels. In each of the transmission channels, the coded signals allocated to the transmission channel are analog summed to generate a modulation signal, and a transmission signal is modulated in response to modulation signal.  
      In the transmitter of an exemplary WDM optical communication system employing wavelength spread-spectrum encoding, each transmission channel includes an optical transmitter in which light generated by a laser is intensity modulated in response to the modulation signal. The lasers generate light at mutually-different carrier wavelengths. The intensity of the single wavelength optical signal resulting from intensity modulating the light generated by the laser in each transmission channel represents to the analog sum of the coded signals allocated to the channel. The single-wavelength optical signals are wavelength division multiplexed to form a multi-wavelength optical signal for transmission via an optical path.  
      At the receiver, the multi-wavelength optical signal received from the optical path is demultiplexed according to wavelength into its constituent single-wavelength optical signals, each of which occupies a respective transmission channel. The single-wavelength optical signals are converted into respective electrical signals that will be called channel signals. The channel signals are then subject to spread-spectrum decoding to recover the original information signals. Each information signal is recovered by multiplying the channel signal from each of the transmission channels by a respective bit of the spreading code with which the information signal was encoded. The multiplying generates a product signal. The product signals are analog summed to generate a sum signal. The sum signal is subject to thresholding to recover the information signal. The other information signals are similarly recovered by multiplying the channel signals with respective bits of the spreading codes assigned to encode the respective information signals.  
      The channel signals subject to spread-spectrum decoding include coded components of all the information signals. However, with mutually-orthogonal spreading codes, the result of applying the multiplication and summing operations to the components coded using other spreading codes will be zero, or very close to zero. Therefore, the spread-spectrum decoding performed in each spread-spectrum decoder in the receiver recognizes and recovers only the information signal that was coded with the same spreading code as that used in the decoder.  
       FIG. 2  is a block diagram of an exemplary embodiment of the transmitter  20  of a multi-channel communication system in which wavelength spread-spectrum encoding is applied in accordance with the invention. The example shown is highly simplified in that it transmits only four information signals using four transmission channels. Practical examples transmit substantially more than four information signals using substantially more than four transmission channels. In embodiments using quasi-orthogonal spreading codes, the transmission channels are fewer in number than the information signals so that the communication system will have a greater figure of merit than a conventional communication system in which each information signal is transmitted in its own transmission channel.  
      Transmitter  20 , in accordance with this embodiment, is composed of spread-spectrum encoders  21 ,  22 ,  23  and  24  that apply spread-spectrum encoding to information signal  1 , information signal  2 , information signal  3  and information signal  4 , respectively. The transmitter is additionally composed of a signal allocating circuit  25 , transmission channels  31 ,  32 ,  33  and  34  and an optical multiplexer  26 . Transmission channel  31  is composed of an analog summer  36  and an optical transmitter  41  connected in series. Transmission channel  32  is composed of an analog summer  37  and an optical transmitter  42  connected in series. Transmission channel  33  is composed of an analog summer  38  and an optical transmitter  43  connected in series. Transmission channel  34  is composed of an analog summer  39  and an optical transmitter  44  connected in series. Each of the optical transmitters  41 ,  42 ,  43  and  44  incorporates a laser (not shown). The lasers of the optical transmitters generate light at mutually-different wavelengths.  
      Each of the spread-spectrum encoders  21 ,  22 ,  23  and  24  encodes the information signal it receives with a spreading code assigned to it to generate coded signals equal in number to the number of bits in the spreading codes, as will be described in detail below. The coded signals are output by the spread-spectrum encoders  21 - 24  at coded signal outputs labelled B 1 , B 2 , B 3  and B 4 . The coded signals will be identified herein by the letter S and a number corresponding to the number of the coded signal output of the spread-spectrum encoder at which it is output. Thus, coded signals S 1 , S 2 , S 3  and S 4  are output by the spread-spectrum encoders at coded signal outputs B 1 , B 2 , B 3  and B 4 , respectively.  
      Each of the analog summers  36 - 39  has four inputs. Signal allocating circuit  25  has 16 inputs and 16 outputs. Four of the inputs of signal allocating circuit  25  are connected to the coded signal outputs B 1  of spread-spectrum encoders  21 - 24 . These four inputs connect to four of the outputs that are connected to the inputs of analog summer  36 . Another four of the inputs of the signal allocating circuit are connected to the coded signal outputs B 2  of the spread-spectrum encoders. These four inputs connect to another four of the outputs that are connected to the inputs of analog summer  37 . Another four of the inputs of the signal allocating circuit are connected to the coded signal outputs B 3  of the spread-spectrum encoders. These four inputs connect to another four of the outputs that are connected to the inputs of analog summer  38 . A final four of the inputs of the signal allocating circuit are connected to the coded signal outputs B 4  of the spread-spectrum encoders. These four inputs connect to a final four of the outputs that are connected to the inputs of analog summer  38 . Thus, signal allocating circuit  25  allocates to transmission channel  31  the coded signals S 1  generated by encoding information signals  1 ,  2 ,  3  and  4  with respective spreading codes. Similarly, signal allocating circuit  25  allocates the coded signals S 2  generated by encoding information signals  1 ,  2 ,  3  and  4  with the respective spreading codes to transmission channel  32 , the coded signals S 3  generated by encoding information signals  1 ,  2 ,  3  and  4  with the respective spreading codes to transmission channel  33  and the coded signals S 4  generated by encoding information signals  1 ,  2 ,  3  and  4  with respective spreading codes to transmission channel  34 .  
      In transmission channel  31 , analog summer  36  analog sums the four coded signals S 1  generated by encoding the information signals  1 ,  2 ,  3  and  4  to generate a respective modulation signal. The output of analog summer  36  is connected to the modulation input of optical transmitter  41 . The modulation signal output by analog summer  36  modulates the intensity of the light generated by the laser (not shown) of optical transmitter  41  to provide a single-wavelength optical signal as the output of transmission channel  31 .  
      In transmission channel  32 , analog summer  37  sums the coded signals S 2  generated by encoding the information signals  1 ,  2 ,  3  and  4  to generate a respective modulation signal. The output of analog summer  37  is connected to the modulation input of optical transmitter  42 . The modulation signal generated by analog summer  37  modulates the intensity of the light output by the laser (not shown) of optical transmitter  42  to provide a single-wavelength optical signal as the output of transmission channel  32 .  
      In transmission channel  33 , analog summer  38  sums the coded signals S 3  generated by encoding the information signals  1 ,  2 ,  3  and  4  to generate a respective modulation signal. The output of analog summer  38  is connected to the modulation input of optical transmitter  43 . The modulation signal generated by analog summer  38  modulates the intensity of the light generated by the laser (not shown) of optical transmitter  43  to provide a single-wavelength optical signal as the output of the transmission channel  33 .  
      In transmission channel  34 , analog summer  39  sums the coded signals S 4  generated by encoding the information signals  1 ,  2 ,  3  and  4  to generate a respective modulation signal. The output of analog summer  39  is connected to the modulation input of optical transmitter  44 . The modulation signal generated by analog summer  39  modulates the intensity of the light generated by the laser (not shown) of optical transmitter  44  to provide a single-wavelength optical signal as the output of the transmission channel  34 .  
      The intensity of the light generated by the lasers (not shown) of optical transmitters  4144  is modulated by modulating the drive current to the laser in response to the modulation signal. Alternatively, the intensity of the light may be modulated by passing the light generated by the laser through a modulator that operates in response to the modulation signal.  
      The intensity-modulated single-wavelength optical signals output by transmission channels  31 - 34  pass to optical multiplexer  26 . Optical multiplexer  26  has inputs connected to the outputs of optical transmitters  41 - 44  and multiplexes the single-wavelength optical signals generated by the optical transmitters to form a multi-wavelength optical signal for transmission via a single optical transmission path  28  connected to the output of the optical multiplexer. Typically, an optical fiber provides the optical transmission path  28 .  
      Each of the spread-spectrum encoders  21 ,  22 ,  23  and  24  encodes the information signal it receives with a spreading code assigned to it. The spreading codes assigned to spread-spectrum encoders  21 - 24  are mutually different. In the example shown, the spreading codes are mutually orthogonal. Alternatively, the spreading codes may be mutually quasi-orthogonal.  
       FIG. 3A  is a block diagram of an exemplary embodiment of spread-spectrum encoder  21  that encodes information signal  1 . Spread-spectrum encoder  21  is composed of a spreading code source  50  and multipliers  51 ,  52 ,  53  and  54 . The spreading code source has outputs each of which provides a respective bit of the spreading code assigned to spread-spectrum encoder  21 . The bits of the spreading code will be identified as C 1 , C 2 , C 3  and C 4  in this example in which the spreading codes each have four bits.  
      One input of each of the multipliers  51 - 54  is connected to receive the information signal  1 . The other inputs of the multipliers  51 ,  52 ,  53  and  54  are connected to the outputs of spreading code source  50  to receive bit C 1 , bit C 2 , bit C 3  and bit C 4 , respectively, of the spreading code assigned to spread-spectrum encoder  21 . The outputs of the multipliers  51 ,  52 ,  53  and  54  are connected to the coded signal outputs B 1 , B 2 , B 3  and B 4 , respectively, of spread-spectrum encoder  21 . The outputs of the multipliers  51 ,  52 ,  53  and  54  provide the coded signals S 1 , S 2 , S 3  and S 4 , respectively, generated by spread-spectrum encoder  21 .  
      Multipliers  51 ,  52 ,  53  and  54  multiply information signal  1  by bit C 1 , bit C 2 , bit C 3  and bit C 4 , respectively, of the spreading code received from spreading code source  50 . The multiplication by multipliers  51 ,  52 ,  53  and  54  generates the four coded signals S 1 , S 2 , S 3  and S 4 , respectively, that collectively represent information signal  1 . The coded signals are output by spread-spectrum encoder  21  at coded signal outputs B!, B 2 , B 3  and B 4 , respectively.  
      The remaining spread-spectrum encoders  22 - 24  are shown in  FIGS. 3B-3D  and are structurally identical to spread-spectrum encoder  21  except for the spreading code output by spreading code source  50 .  FIGS. 3A-3D  also show two consecutive states of the coded signals S 1 -S 4  that each spread-spectrum encoder  21 - 24  generates in response to two consecutive bits of the respective information signal. The consecutive bits are in a −1 state and a +1 state. The bits of the information signals in the +1 state and the states of the coded signals generated in response to the bits of the information signals in the +1 state are shown in parentheses.  
      The way in which the transmitter  20  applies wavelength spread-spectrum encoding to information signals  1 ,  2 ,  3  and  4  will be described with reference to the simplified example shown in  FIGS. 2 , and  3 A- 3 D, which uses 4-bit spreading codes. The only mutually-orthogonal 4-bit spreading codes are spreading code  1 : {−1,−1,+1,+1}; spreading code  2 : {−1,−1,−1,−1}; spreading code  3 : {−1,+1,−1,+1}; spreading code  4 : {−1,+1,+1,−1}. The orthogonality of two spreading codes is defined by taking the discrete cross-correlation of the spreading codes. If w q  and x q  are the qth elements of two L-bit bipolar spreading codes wand x, then the cross-correlation of any two of the spreading codes may be determined by the operation:  
             y   k     ≡       w   k     *     x   k         =       ∑     m   =   0       L   -   1       ⁢       w   m     ⁢     x     m   +   k             ,       
 
 where w k  and x k  have non-zero values between 0 and L−1 inclusive. The cross-correlation y has length 2L−1 running from 1-L to L−1. To define orthogonality, the only term of interest is the zero offset term (k=0). The two spreading codes are orthogonal if the zero-offset cross-correlation is zero (y 0 =0). The autocorrelation is defined by x k *x k  is always L for bipolar L-bit spreading codes. 
 
      The mutual orthogonality of spreading code  1 ={−1,−1,+1,+1}, spreading code  2 ={−1,−1,−1,−1}, spreading code  3 ={−1,+1,−1,+1,−1} and spreading code  4 ={−1,+1,+1,−1} may be confirmed by direct substitution of the spreading codes into the cross-correlation formula set forth above.  
      In accordance with the invention, for each information signal to be transmitted, the information signal is encoded with the spreading code assigned to encode the information signal to generate a coded signal corresponding to each bit of the spreading code. Then, the coded signals corresponding to the same bit of the spreading codes are assigned to a respective one of the transmission channels. In each transmission channel, the coded signals allocated to the channel are analog summed to provide a modulation signal and a transmission signal is modulated in response to the modulation signal. For example, to transmit a bit of an information signal encoded with a four-bit spreading code needs four transmission channels.  
      Spreading code  1  is assigned to encode information signal  1  and is stored in code word source  50  of spread-spectrum encoder  21  shown in  FIGS. 2 and 3 A. Spreading code  2  is assigned to encode information signal  2  and is stored in code word source  50  of spread-spectrum encoder  22  shown in  FIGS. 2 and 3 B. Spreading code  3  is assigned to encode information signal  3  and is stored in the code word source of spread-spectrum encoder  23  shown in  FIGS. 2 and 3 C. Spreading code  4  is assigned to encode information signal  4  and is stored in the code word source of spread-spectrum encoder  24  shown in  FIGS. 2 and 3 D.  
      Referring to  FIG. 3A , in spread-spectrum encoder  21  for information signal  1 , multipliers  51 ,  52 ,  53  and  54  multiply information signal  1  by the four bits {C 1 =−1, C 2 =−1, C 3 =+1, C 4 =+1}, respectively, of spreading code  1  to generate the four coded signals S 1 , S 2 , S 3  and S 4 , respectively. For each bit of information signal  1  in the −1 state, multipliers  51 ,  52 ,  53  and  54  generate coded signals S 1 , S 2 , S 3  and S 4  with states +1,+1,−1 and −1, respectively. For each bit of information signal  1  in the +1 state, multipliers  51 ,  52 ,  53  and  54  generate coded signals S 1 , S 2 , S 3  and S 4  with states −1,−1,+1 and +1, respectively. Spread-spectrum encoder  21  outputs to signal allocator  25  coded signals S 1 , S 2 , S 3  and S 4  with states +1,+1,−1 and −1, respectively for each bit of information signal  1  in the −1 state and with states −1,−1,+1 and +1, respectively, for each bit of information signal  1  in the +1 state.  
      Referring now to  FIG. 3B , in spread-spectrum encoder  22  for information signal  2 , multipliers  51 ,  52 ,  53  and  54  multiply information signal  2  by the four bits {C 1 =−1, C 2 =−1, C 3 =−1, C 4 =−1}, respectively, of spreading code  2  to generate the four coded signals S 1 , S 2 , S 3  and S 4 , respectively. For each bit of information signal  2  in the −1 state, multipliers  51 ,  52 ,  53  and  54  generate coded signals S 1 , S 2 , S 3  and S 4  with states +1,+1,+1 and +1, respectively. For each bit of information signal  2  in the +1 state, multipliers  51 ,  52 ,  53  and  54  generate coded signals S 1 , S 2 , S 3  and S 4  with states −1,−1,−1, and −1, respectively. Spread-spectrum encoder  22  outputs to signal allocator  25  coded signals S 1 , S 2 , S 3  and S 4  with states +1,+1,+1 and +1, respectively for each bit of information signal  2  in the −1 state and with states −1,−1,−1 and −1, respectively, for each bit of information signal  2  in the +1 state.  
      Referring now to  FIG. 3C , in spread-spectrum encoder  23  for information signal  3 , multipliers  51 ,  52 ,  53  and  54  multiply information signal  3  by the four bits {C 1 =−1, C 2 =+1, C 3 =−1, C 4 =+1}, respectively, of spreading code  3  to generate four coded signals S 1 , S 2 , S 3  and S 4 , respectively. For each bit of information signal  3  in the −1 state, multipliers  51 ,  52 ,  53  and  54  generate coded signals S 1 , S 2 , S 3  and S 4  with states +1,−1,+1 and −1, respectively. For each bit of information signal  3  in the +1 state, multipliers  51 ,  52 ,  53  and  54  generate coded signals S 1 , S 2 , S 3  and S 4  with states −1,+1,−1 and +1, respectively. Spread-spectrum encoder  23  outputs to signal allocator  25  coded signals S 1 , S 2 , S 3  and S 4  with states +1,−1,+1 and −1, respectively for each bit of information signal  3  in the −1 state and with states −1,+1,−1 and +1, respectively, for each bit of information signal  3  in the +1 state.  
      Referring now to  FIG. 3D , in spread-spectrum encoder  24  for information signal  4 , multipliers  51 ,  52 ,  53  and  54  multiply information signal  4  by the four bits {C 1 =−1, C 2 =+1, C 3 =+1, C 4 =−1}, respectively, of spreading code  4  to generate four coded signals S 1 , S 2 , S 3  and S 4 , respectively. For each bit of information signal  4  in the −1 state, multipliers  51 ,  52 ,  53  and  54  generate coded signals S 1 , S 2 , S 3  and S 4  with states +1,−1,−1 and +1, respectively. For each bit of information signal  3  in the +1 state, multipliers  51 ,  52 ,  53  and  54  generate coded signals S 1 , S 2 , S 3  and S 4  with states −1,+1,+1 and −1, respectively. Spread-spectrum encoder  24  outputs to signal allocator  25  coded signals S 1 , S 2 , S 3  and S 4  with states +1,−1,−1 and +1, respectively for each bit of information signal  4  in the −1 state and with states −1,+1,+1 and −1, respectively, for each bit of information signal  4  in the +1 state.  
      Referring again to  FIG. 2 , signal allocator  25  connects the outputs B 1  of spread-spectrum encoders  21 ,  22 ,  23  and  24  to the inputs of analog summer  36  in transmission channel  31 . Analog summer  36  generates a modulation signal whose level is the analog sum of the coded signals S 1  received from the spread-spectrum encoders. The signal allocator also connects the outputs B 2  of spread-spectrum encoders  21 ,  22 ,  23  and  24  to the inputs of analog summer  37  in transmission channel  32 . Analog summer  37  generates a modulation signal whose level is the analog sum of the coded signals S 2  received from the spread-spectrum encoders. The signal allocator also connects the ouputs B 3  of spread-spectrum encoders  21 ,  22 ,  23  and  24  to the inputs of analog summer  38  transmission channel  33 . Analog summer  38  generates a modulation signal whose level is the analog sum of the coded signals S 3  received from the spread-spectrum encoders. The signal allocator connects the outputs B 4  of spread-spectrum encoders  21 ,  22 ,  23  and  24  to the inputs of analog summer  39  in transmission channel  34 . Analog summer  39  generates a modulation signal whose level is the analog sum of the coded signals S 4  received from the spread-spectrum encoders.  
       FIG. 4  is a table showing the 64 possible states of the coded signals generated by spread-spectrum encoders  21 ,  22 ,  23  and  24  in response to all 16 possible combinations of the states of the information signals  1 - 4 .  FIG. 4  is divided by vertical double lines into three columnar panels. The panels are divided by horizontal double lines into blocks each of which shows one combination of the states of the information signals. The left-hand columnar panel indicates the reference numerals of the spread-spectrum encoders in a column labelled S-S Enc. and the spreading code assigned to each spread-spectrum encoder in a column labelled Spread. Code. The center panel shows, in columns labelled S 1  through  54 , the states of the coded signal indicated by the label generated by the spread-spectrum encoders for each combination of states of information signals  1 - 4  in the range −1−1−1−1 through −1+1+1+1. The states of the information signals are shown in a column labelled IS. State. The center panel also shows, in a row labelled Mod, the level of the modulation signal obtained by analog summing the four coded signal states shown in the same column. The right-hand panel shows, in columns labelled S 1  through S 4 , the states of the coded signal indicated by the label generated by the spread-spectrum encoders for each combination of states of information signals  1 - 4  in the range +1−1−1−1 through +1+1+1+1. The states of the information signals are shown in a column labelled IS. State. The right-hand panel also shows, in a row labelled Mod, the level of the modulation signal obtained by analog summing the four coded signal states shown in the same column.  
      Referring additionally to  FIG. 2 , in an example in which the combination of states of information signals  1 - 4 , respectively, is {−1,−1,+1,−1}, the states of coded signals S 1 -S 4  generated by spread-spectrum encoders  21 ,  22 ,  23  and  24 , respectively, are {+1,+1,−1,−1}, {+1,+1,+1,+1}, {−1,+1,−1,+1} and {1,−1,−1,+1}, respectively. The states of the coded signals are shown in order from coded signal S 1  through coded signal S 4 .  
      Analog summer  36  receives the states {−1,−1,+1,−1} of coded signals S 1  from spread-spectrum encoders  21 ,  22 ,  23  and  24 , respectively. Analog summer  36  generates a modulation signal whose level is the analog sum of the states of coded signals S 1 . In this example, the modulation signal output by analog summer  36  has a level of (1+1−1+1)=2. Analog summer  37  receives the states {+1,+1,+1,−1} of coded signals S 2  from spread-spectrum encoders  21 ,  22 ,  23  and  24 , respectively. Analog summer  37  generates a modulation signal whose level is the analog sum of the states of the coded signals S 1 . In this example, the modulation signal output by analog summer  37  has a level of (+1+1+1−1)=2. Analog summer  38  receives the states {+1,+1,−1,−1} of coded signals S 3  from spread-spectrum encoders  21 ,  22 ,  23  and  24 , respectively. Analog summer  38  generates a modulation signal whose level is the analog sum of the states of coded signals S 3 . In this example, the modulation signal output by analog summer  38  has a level of (−1+1−1−1)=−2. Analog summer  38  receives the states {−1,+1,+1,+1} of coded signals S 4  from spread-spectrum encoders  21 ,  22 ,  23  and  24 , respectively. Analog summer  39  generates a modulation signal whose level is the analog sum of the states of the coded signals S 4 . In this example, the modulation signal output by analog summer  39  has a level of (−1+1+1+1)=2.  
      In transmission channel  31 , the modulation signal generated by analog summer  36  is fed to the modulation input of optical transmitter  41  where it sets the single-wavelength optical signal output by optical transmitter  41  to an intensity representing a transmission signal level of +2. In transmission channel  32 , the modulation signal generated by analog summer  37  is fed to the modulation input of optical transmitter  42  where it sets the single-wavelength optical signal output by optical transmitter  42  to an intensity representing a transmission signal level of +2. In transmission channel  33 , the modulation signal generated by analog summer  38  is fed to the modulation input of optical transmitter  43  where it sets the single-wavelength optical signal output by optical transmitter  43  to an intensity representing a transmission signal level of −2. In transmission channel  34 , the modulation signal generated by analog summer  39  is fed to the modulation input of optical transmitter  44  where it sets the single-wavelength optical signal output by optical transmitter  44  to an intensity representing a transmission signal level of +2.  
      Since light cannot have a negative intensity, the modulation signals do not directly modulate the intensity of the single-wavelength optical signals generated by optical transmitters  41 - 44 . Instead, the optical transmitters each incorporate a level coder (not shown) that converts the bipolar range of levels of the modulation signals generated by analog summers  31 - 34  to a unipolar range of levels that set the intensity of the single-wavelength optical signal output by the optical transmitter. In one embodiment, the level coder increases the level of the modulation signal by four to convert the −4 to +4 range of the modulation signal to a range of 0 to +8. In this case, the single-wavelength optical signal output by the optical transmitter has possible intensities of 0, +2, +4, +6 and +8. In another embodiment, the coder increases each negative level of the modulation signal by five to convert the −4 to +4 range in steps of two of the modulation signal to a range of 0 to +4 in steps of one. In this case, the single-wavelength optical signal output by the optical transmitter has possible intensities of 0, +1, +2, +3 and +4. Thus, the single-wavelength optical signals output by the optical transmitters  41 - 44  of the transmission channels  31 - 34 , respectively, have intensities dependent on the levels of the modulation signals output by the analog summers  36 - 39 , respectively. In the above description, the levels of the modulation signals and the intensities of the single-wavelength optical signals are expressed in respective arbitrary units.  
      Optical multiplexer  26  multiplexes the single-wavelength optical signals output by the transmission channels  31 ,  32 ,  33  and  34  to generate a WDM optical signal for transmission via transmission path  28 . Transmission path  28  transmits the WDM optical signal to a wavelength spread-spectrum receiver (not shown in  FIG. 2 ) at its distal end.  
      Embodiments of transmitters  41 - 44  that generate an electrical signal for transmission via transmission path  28  are typically capable of modulation in response to a negative modulation signal, and so can be directly modulated by the modulation signals generated by analog summers  31 - 34 . Moreover, such embodiments may employ modulation schemes other than the intensity modulation scheme exemplified above.  
      In the above-described examples, analog summers  31 - 34  sum the −1 and +1 states of coded signals S 1 -S 4  with a weight of 1. However, this is not critical to the invention. The analog summers may alternatively sum the −1 and +1 states of the coded signals with a weight different from 1 to generate the modulation signal with a dynamic range compatible with the dynamic range requirements of optical transmitters  41 - 44 . In the example described above, embodiments of analog summers  31 - 34  that sum the −1 and +1 states of the coded signals with a weight of ¼ will generate the modulation signals with a dynamic range from −1 to +1.  
       FIG. 5  is a block diagram of an exemplary embodiment  60  of the receiver of a wavelength spread-spectrum communication system in accordance with the invention. As with the wavelength spread-spectrum transmitter described above with reference to  FIG. 2 , the wavelength spread-spectrum receiver is a highly simplified example with only four transmission channels. A practical embodiment would receive optical signals in more than the four transmission channels shown and would recover information signals substantially greater in number than the transmission channels.  
      Receiver  60  is composed of an optical demultiplexer  62 , a channel signal distributor  64 , transmission channels  71 ,  72 ,  73  and  74  and spread-spectrum decoders  81 ,  82 ,  83  and  84 . Receiver  60  is additionally composed of optical receivers  76 ,  77 ,  78  and  79  located in transmission channels  71 ,  72 ,  73  and  74 , respectively.  
      Optical demultiplexer  62  located at the end of optical transmission path  28  remote from transmitter  20  described above with reference to  FIG. 2 . The optical demultiplexer receives the WDM optical signal from optical transmission path  28  and demultiplexes the WDM optical signal into its constituent single-wavelength optical signals.  
      Optical demultiplexer  62  has an optical output through which it delivers a respective one of the single-wavelength optical signals to each the transmission channels  71 ,  72 ,  73  and  74 . Each of the transmission channels  71 ,  72 ,  73  and  74  has an optical receiver  76 ,  77 ,  78  and  79 , respectively, optically coupled to a respective one of the outputs of optical demultiplexer  62 . Each of the optical receivers  76 - 79  receives the single-wavelength optical signal delivered to the respective one of transmission channels  71 - 74  and converts the single-wavelength optical signal to an analog electrical signal that will be called a channel signal. Each of the optical receivers  76 - 79  typically includes a photodiode (not shown) or some other suitable device to effect the above-described optical-to-electrical conversion.  
      Each of the optical receivers  76 ,  77 ,  78  and  79  additionally includes a level decoder (not shown) that converts the unipolar analog electrical signal generated by the photo-diode (not shown) to a bipolar analog electrical signal having a range of levels that corresponds to the range of levels of the modulation signal generated by the corresponding one of the analog summers  36 - 39  ( FIG. 2 ) of transmitter  20  ( FIG. 2 ). In an example, the level decoder converts a unipolar analog electrical signal having levels ranging from 0 to +8 to a bipolar analog electrical signal having levels ranging from −4 to +4.  
      Referring additionally to  FIG. 2 , the levels of the analog electrical signals respectively output by the optical receivers  76 - 79  are proportional to the levels of the modulation signals in the corresponding one of the transmitter channels  31 - 34  of transmitter  20 . Thus, the analog electrical signal output by optical receiver  76  represents the analog sum of the coded signals S 1  generated by the analog summer  31  and will be called the channel signal X 1 ; the analog electrical signal output by optical receiver  77  represents the analog sum of the coded signals S 2  generated by the analog summer  32  and will be called the channel signal X 2 ; the analog electrical signal output by optical receiver  78  represents the analog sum of the coded signals S 3  generated by the analog summer  33  and will be called the channel signal X 3  and the analog electrical signal output by the optical receiver  79  represents the analog sum of the coded signals S 4  generated by the analog summer  34  and will be called the channel signal X 4 . Channel signal X 1 , channel signal X 2 , channel signal X 3  signal and channel signal X 4  signal are referred to collectively as channel signals. Each of the channel signals is composed of concatenated temporal segments each having a temporal duration equal to the bit period of information signals  1  through  4 .  
      The output of each of the optical receivers  76 - 79  is connected to a respective one of the inputs of the channel signal distributor  64 . The channel signal distributor is a four-in, 16-out distribution circuit. The four inputs of the channel signal distributor receive the channel signal X 1  from optical receiver  76 , the channel signal X 2  from optical receiver  77 , the channel signal X 3  from optical receiver  78  and the channel signal X 4  from optical receiver  79 . The outputs of the channel signal distributor are divided into groups of four, an exemplary one of which is shown at  66 . Each input of the channel signal distributor is connected to a different one of the outputs in each group of four outputs. Each of the spread-spectrum decoders  81 - 84  has four channel signal inputs labelled Z 1 , Z 2 , Z 3  and Z 4 . The electrical inputs of each spread-spectrum decoder are electrically connected to a respective one of the groups of four outputs of channel signal distributor  64 , with the inputs Z 1 , Z 2 , Z 3  and Z 4  each connected to a respective output in the group of four outputs. Accordingly, the four electrical inputs of each spread-spectrum decoder collectively receive all the channel signals.  
      Each of the spread-spectrum decoders  81 - 84  decodes one of the information signals represented by the four channel signals received at its inputs Z 1 -Z 4 . Each of the spread-spectrum decoders has assigned to it the spreading code that was used to encode a respective one of the information signals. Each spread-spectrum decoder decodes the information signal whose spreading code is assigned to it by multiplying the channel signals X 1  through X 4  by the corresponding bit C 1  through C 4  of the spreading code assigned to it to generate respective product signals. The four product signals are then analog summed to generate a sum signal. The sum signal is then subject to thresholding to convert it into a digital signal. The digital signal is logically identical to the information signal that was encoded using the spreading code assigned to the spread-spectrum decoder and is output as a recovered information signal.  
       FIG. 6  is a block diagram of an exemplary first embodiment of spread-spectrum decoder  81  of the receiver shown in  FIG. 5 . The spreading code that was used to encode information signal  1  in transmitter  20  ( FIG. 2 ) is assigned to spread-spectrum decoder  81 . Spread-spectrum decoder  81  is composed of a multiplying circuit  86 , a spreading code source  90 , an analog summer  95  and threshold circuit  96 . The spreading code source has outputs each providing a respective bit C 1 , C 2 , C 3  and C 4  of the spreading code assigned to spread-spectrum decoder  81 .  
      Multiplying circuit  86  is connected to the inputs Z 1 , Z 2 , Z 3  and Z 4  of spread-spectrum decoder  81  to receive the channel signals X 1 , X 2 , X 3  and X 4  from transmission channels  71 ,  72 ,  73  and  74 , respectively, and performs the function of multiplying each channel signal by a respective bit C 1 , C 2 , C 3  and C 4  of the spreading code assigned to information signal  1  to generate a respective product signal P 1 , P 2 , P 3  and P 4 . In the example shown, the multiplying circuit is composed of multipliers  91 ,  92 ,  93  and  94 . One input of the multipliers  91 ,  92 ,  93  and  94  is connected to the inputs Z 1 , Z 2 , Z 3  and Z 4 , respectively, of spread-spectrum decoder  81  to receive channel signal X 1 , channel signal X 2 , channel signal X 3  and channel signal X 4 , respectively. The other inputs of the multipliers  91 ,  92 ,  93  and  94  are connected to the outputs of spreading code source  90  to receive bit C 1 , bit C 2 , bit C 3  and bit C 4 , respectively, of the spreading code assigned to spread-spectrum decoder  81 . The outputs of multipliers  91 ,  92 ,  93  and  94  are connected to the inputs of analog summer  95 . The output of the analog summer is connected to the input of threshold circuit  96 . The output of the threshold circuit provides the recovered information signal  1  output by spread-spectrum decoder  81 .  
      Multipliers  91 ,  92 ,  93  and  94  multiply the channel signal X 1 , the channel signal X 2 , the channel signal X 3  signal and the channel signal X 4 , respectively, by bit C 1 , bit C 2 , bit C 3  and bit C 4 , respectively, of the spreading code received from spreading code source  90 . Multiplication of the channel signals X 1 , X 2 , X 3  and X 4  by multipliers  91 ,  92 ,  93  and  94  generates product signals P 1 , P 2 , P 3  and P 4 , respectively. Analog summer  95  analog sums product signals P 1 , P 2 , P 3  and P 4  generated by multipliers  91 ,  92 ,  93  and  94 , respectively, to generate a sum signal. The sum signal output by the analog summer in response to product signals P 1 , P 2 , P 3  and P 4  is an analog signal that replicates the logical states of information signal  1 . Threshold circuit  96  receives the sum signal from analog summer  95  and subjects the sum signal to thresholding. This converts the sum signal into a digital signal that constitutes recovered information signal  1 . Threshold circuit  96  outputs a bit in a −1 state when the sum signal it receives is less than a first threshold and outputs a bit in a +1 state when the sum signal it receives is greater than a second threshold, greater than the first threshold. The thresholding eliminates the noise that originates from the components in the channel signals resulting from encoding information signals  2 - 4 .  
      The remaining spread-spectrum decoders  82 - 84  are structurally identical to spread-spectrum decoder  81  except for the spreading code provided by spreading code source  90 . Spread-spectrum decoders  82 - 84  will therefore not be separately described.  
       FIG. 7  is a table showing the operation of the spread-spectrum decoders  81 - 84  in response to all 16 possible combinations of the states of channel signal X 1 , channel signal X 2 , channel signal X 3  and channel signal X 4  output by optical receivers  76 - 79 .  FIG. 7  is divided by double lines into three columnar panels. The left-hand panel indicates the reference numerals of the spread-spectrum decoders in a column labelled S-S Dec., and the spreading codes assigned to each spread-spectrum encoder in a column labelled Spread. Code. The center panel shows the levels of the channel signals received by the spread-spectrum decoders and the corresponding levels of the product signals for each combination of channel signal levels representing states of information signals  1 - 4  in the range −1−1−1−1 through −1+1+1+1. The right-hand panel shows the levels of the channel signals received by the spread-spectrum decoders and the corresponding levels of the product signals for each combination of channel signal levels representing states of information signals  1 - 4  in the range +1−1−1−1 through +1+1+1+1.  FIG. 7  is additionally divided by horizontal double lines into blocks of five rows. In the top row of each block, the levels of channel signals X 1 , X 2 , X 3  and X 4  are respectively shown in columns labelled P 1 , P 2 , P 3  and P 4 , respectively. In the remaining four rows, the levels of the product signals P 1 , P 2 , P 3 , and P 4  output by each of spread-spectrum decoders  81 ,  82 ,  83 , and  84  are indicated in the columns labelled P 1 , P 2 , P 3  and P 4 , respectively. Finally, each of the center and right-hand panels shows, in the column labelled Sum, the level of the sum signal generated in each of the spread-spectrum decoders  81 - 84  by the analog summer  95  analog summing product signals P 1 , P 2 , P 3  and P 4 . The sum signal has two levels: −4 and +4. These levels correspond to the −1 state and the +1 state, respectively, of information signals  1 - 4  shown in  FIG. 4 .  
      In an example in which the levels of the channel signals X 1 , X 2 , X 3  and X 4  are {+2,+2,−2,+2},  FIG. 7  shows that the levels of the product signals P 1 , P 2 , P 3  and P 4  generated by multipliers  91 ,  92 ,  93  and  94  of spread-spectrum decoder  81  are {−2,−2,−2,+2}, those generated by multipliers  91 ,  92 ,  93  and  94  of spread-spectrum decoder  82  are {−2,−2,+2,−2} those generated by multipliers  91 ,  92 ,  93  and  94  of spread-spectrum decoder  83  are {−2,+2,+2,+2) and those generated by multipliers  91 ,  92 ,  93  and  94  of spread-spectrum decoder  84  are {−2,+2,−2,−2}. The resulting levels of the sum signals generated by analog summers  95  of spread-spectrum decoders  81 ,  82 ,  83  and  84  are {−4,−4,+4,−4}. These levels correspond to states of {−1,−1,+1,−1} of recovered information signals  1  through  4  respectively.  
      The levels of the channel signals X 1 -X 4  shown in  FIG. 7  assume that the communication system gain between the modulation inputs of optical transmitters  41 - 44  of transmitter  20  shown in  FIG. 2  and the outputs of optical receivers  76 - 79  of receiver  60  shown in  FIG. 5  is unity. The difference between the two levels of the sum signals output by analog summers  95  depends linearly on the gain of the communication system. Thus, the difference between the two levels of the sum signals will differ from that shown in embodiments in which the communication system has a gain different from unity.  
      In the above-described examples, analog summer  95  in each of the spread-spectrum decoders  81 - 84  sums product signals P 1 -P 4  with a weight of 1. However, this is not critical to the invention. Analog summer may alternatively sum the product signals with a weight different from unity to generate the sum signal with a dynamic range compatible with the dynamic range requirements of threshold circuit  96 . In the example described above, an embodiment of analog summer  95  that sums the product signals with a weight of ¼ will generate the sum signal with a dynamic range from −1 to +1.  
      An alternative embodiment of receiver  60  lacks optical receivers  76 - 79 . In such alternative embodiment, channel signal distributor  64  operates in the optical domain and has its inputs connected to the outputs of demultiplexer  62 . The outputs of the channel signal distributor are connected to the inputs Z 1 -Z 4  of spread-spectrum decoders  81 - 84  as described above. Each of the spread-spectrum decoders additionally has an optical-to-electrical converter (not shown) and a level decoder (not shown) connected in series between each of the inputs Z 1 -Z 4  and the inputs of multiplying circuit  86  ( FIG. 6 ) or  286  ( FIG. 10 ).  
      The multipliers shown in  FIGS. 3A-3D  may be implemented using exclusive-NOR (XNOR) gates.  FIG. 8  is a block diagram of an alternative embodiment  121  of spread-spectrum encoder  21  shown in  FIG. 3A .  
      In spread-spectrum encoder  121  shown in  FIG. 8 , multipliers  51 ,  52 ,  53  and  54  shown in  FIG. 3A  are implemented by exclusive-NOR gates  151 ,  152 ,  153  and  154 . One input of each of XNOR gates  151 ,  152 ,  153  and  154  is connected to receive information signal  1 . The other input of each of XNOR gates  151 ,  152 ,  153  and  154  is connected to the outputs of spreading code source  50  to receive a respective one of bits C 1 , C 2 , C 3  and C 4  of spreading code  1 . The outputs of XNOR gates  151 ,  152 ,  153  and  154  are connected to outputs B 1 , B 2 , B 3  and B 4  of spread-spectrum encoder  121  to which they provide the coded signals S 1 , S 2 , S 3  and S 4 , respectively, output by spread-spectrum encoder  121 .  
       FIG. 8  also shows two consecutive states of the coded signals S 1 -S 4  that spread-spectrum encoder  121  generates in response to two consecutive bits of information signal  1 . The consecutive bits are in a −1 state and a +1 state, respectively. The bit of the information signal  1  in the +1 state and the states of the coded signals generated in response to the bit of information signal  1  in the +1 state are shown in parentheses.  
      Exclusive-OR gates may be used in spread-spectrum encoder  121  instead of the exclusive-NOR gates shown, and the term exclusive-NOR as used herein will be understood to encompass exclusive-OR.  
      Alternative embodiments of spread-spectrum encoders  22 ,  23  and  24  ( FIGS. 3B, 3C  and  3 D, respectively) are identically structured to spread-spectrum encoder  121  shown in  FIG. 8 , except that XNOR gates  151 ,  152 ,  153  and  154  receive different spreading codes from spreading code source  50 .  
      In the embodiments described above, the spread-spectrum encoders  21 - 24  and spread-spectrum decoders  81 - 84  each include a spreading code source that provides the assigned spreading code to the multipliers or, in the case of the spread-spectrum encoders, to the XNOR gates that perform multiplication. This arrangement allows the spreading code assigned to encode and decode a given information signal to be changed simply by changing the spreading code stored in the spreading code source of the spread-spectrum encoder and the spread-spectrum decoder that encode and decode the information signal. Embodiments in which an ability to change the spreading code used to encode a given information signal is not needed can incorporate the alternative spread-spectrum encoders shown in  FIGS. 9A and 9B  and the alternative spread-spectrum decoder shown in  FIG. 10 .  
       FIG. 9A  is a block diagram of an alternative embodiment  221  of spread-spectrum encoder  21  shown in  FIG. 3A  and  FIG. 9B  is a block diagram of an alternative embodiment  222  of spread-spectrum encoder  22  shown in  FIG. 3B . Spread-spectrum encoders  221  and  222  are each composed of four parallel signal paths  231 ,  232 ,  233  and  234 . The signal paths are interconnected at one end, where they are additionally connected to receive the respective information signal. The other ends of signal paths  231 ,  232 ,  233  and  234  are connected the outputs B 1 , B 2 , B 3  and B 4 , respectively. The information signal on each of the signal paths is encoded by a different one of the bits C 1 , C 2 , C 3  and C 4  of the spreading code assigned to the spread-spectrum encoder to generate the coded signals S 1 , S 2 , S 3  and S 4 , respectively. An inverter is connected in series with those of the signal paths for which the respective bit of the spreading code is in the −1 state.  
      The bits of spreading code  1  assigned to spread-spectrum encoder  221  shown in  FIG. 9A  are {C 1 =−1, C 2 =−1, C 3 =+1, C 4 =+1}. The bits of spreading code  1  corresponding to outputs B 1  and B 2  are in the −1 state. Accordingly, an inverter  236  is connected in series with signal path  231  connected to output B 1  and an inverter  237  is connected in series with signal path  232  connected to output B 2 . The bits of spreading code  1  corresponding to outputs B 3  and B 4  are in the +1 state, so no inverters are connected in series with signal paths  233  and  234  connected to outputs B 3  and B 4 , respectively. The bits of spreading code  2  assigned to spread-spectrum encoder  222  shown in  FIG. 9B  are {C 1 =−1, C 2 =−1, C 3 =−1, C 4 =−1}. The bits of spreading code  2  corresponding to outputs B 1 , B 2 , B 3  and B 4  are all in the −1 state. Accordingly, an inverter  236  is connected in series with signal path  231  connected to output B 1 , an inverter  237  is connected in series with signal path  233  connected to output B 2 , an inverter  238  is connected in series with signal path  234  connected to output B 3  and an inverter  239  is connected in series with signal path  235  connected to output B 4 . An alternative embodiment of spread-spectrum encoder  23  ( FIG. 3C ) has inverters connected in series with signal paths  231  and  233 , and an alternative embodiment of spread-spectrum encoder  24  ( FIG. 3D ) has inverters connected in series with signal paths  231  and  234 .  
       FIGS. 9A and 9B  also show two consecutive states of the coded signals S 1 -S 4  that spread-spectrum encoders  221  and  222  generate in response to two consecutive bits of information signal  1  and information signal  2 , respectively. The consecutive bits are a −1 state and a +1 state. The bits of the information signals in the +1 state and the states of the coded signals generated in response to the bits of the information signals in the +1 state are shown in parentheses.  
       FIG. 10  is a block diagram of an alternative embodiment  281  of spread-spectrum decoder  81  of the wavelength spread-spectrum receiver shown in  FIG. 5 . Elements of spread-spectrum decoder  281  that correspond to elements of spread-spectrum decoder  81  described above with reference to  FIG. 6  have the same reference numerals and will not be described again in detail.  
      In spread-spectrum decoder  281 , multiplying circuit  286  is connected to the inputs Z 1 , Z 2 , Z 3  and Z 4  to receive the channel signals X 1 , X 2 , X 3  and X 4  from transmission channels  71 ,  72 ,  73  and  74 , respectively, and performs the function of multiplying each channel signal by a respective bit C 1 , C 2 , C 3  and C 4  of the spreading code assigned to information signal  1  to generate a respective product signal P 1 , P 2 , P 3  and P 4 . In the example shown, multiplying circuit  286  is composed of four parallel signal paths  241 ,  242 ,  243  and  244 . At one end, signal paths  241 ,  242 ,  243  and  244  are connected to inputs Z 1 , Z 2 , Z 3  and Z 4  to receive channel signals X 1 , X 2 , X 3  and X 4 , respectively. The other ends of signal paths  241 ,  242 ,  243  and  244  are connected to the inputs of analog summer  95  to which they deliver the product signals P 1 , P 2 , P 3  and P 4 , respectively. The channel signal on each of the signal paths  241 ,  242 ,  243  and  244  is multiplied by a different one of the bits C  1 , C 2 , C 3  and C 4 , respectively, of spreading code  1  assigned to spread-spectrum decoder  281  by an inverter connected in series with those of signal paths  241 ,  242 ,  243  and  244  for which the respective bit of the spreading code is in the −1 state.  
      The bits of spreading code  1  assigned to spread-spectrum decoder  281  shown in  FIG. 10  are {C 1 =−1, C 2 =−1, C 3 =+1, C 4 =+1}. The bits of spreading code  1  corresponding to channel signals X 1  and X 2  are in the −1 state. Accordingly, an inverter  246  is connected in series with signal path  241  connected to input Z 1  and an inverter  247  is connected in series with signal path  242  connected to input Z 2 . The bits of spreading code  1  corresponding to channel signals X 3  and X 4  are in the +1 state, so no inverters are connected in series with signal paths  243  and  244  connected to inputs X 3  and X 4 , respectively. An alternative embodiment of spread-spectrum decoder  82  ( FIG. 2 ) has inverters connected in series with signal paths  241 ,  242 ,  243  and  244 , an alternative embodiment of spread-spectrum decoder  83  has inverters connected in series with signal paths  241  and  243 , and an alternative embodiment of spread-spectrum encoder  84  has inverters connected in series with signal paths  241  and  244 .  
      In the embodiments described above, the information signals have states of −1 and +1 and the spreading codes have states of −1 and +1. However, this is not critical to the invention. The information signals may alternatively have states of 0 and 1 and the spreading codes may alternatively have states of 0 and 1. In an embodiment of transmitter  20  in which the information signals and spreading codes have states of 0 and 1, embodiments of spread-spectrum encoders  21 - 24  use XNOR gates to multiply such information signals with such spreading codes as described above. In such embodiments, analog summers  31 - 34  are structured to sum the 0 states of the coded signals with a weight of −1 and the 1 states of the coded signals in with a weight of +1. In an embodiment of receiver  60  in which the information signals and spreading codes have states of 0 and 1, spread-spectrum decoders  81 - 84  multiply the channel signals by the spreading codes by inverting those of the channel signals for which the corresponding bit of the spreading code is a zero 0, and do not invert those of the channel signals for which the corresponding bit of the spreading code is a 1. Additionally, thresholding circuit  96  in each of the spread-spectrum decoders  81 - 84  is configured to output the recovered information signal with states of 0 and 1.  
      The examples described above are highly simplified in that four information signals are encoded using four mutually-orthogonal spreading codes each of four bits and are transmitted via four transmission channels. The above-described figure of merit of this simplified example is no higher than that of a conventional multi-channel communication system in which each information signal is transmitted in a respective transmission channel. However, the simplified example is potentially more reliable than a conventional multi-channel communication system in that all information signals can be recovered at the receiver even if one of the transmission channels fails.  
      A practical embodiment of the wavelength spread-spectrum communication system uses more than four transmission channels and, hence, spreading codes of more than four bits. Even with spreading codes of more than four bits, the number of purely orthogonal spreading codes is equal to the number of bits. Consequently, a wavelength spread-spectrum communication system using purely orthogonal spreading codes is only capable of transmitting the same number of information signals as the number of transmission channels. Such embodiments provide an increase in reliability, as described above, but no increase in the figure of merit compared with a conventional multi-channel communication system. However, by additionally or alternatively using quasi-orthogonal spreading codes, of which more exist than the number of bits, a wavelength spread-spectrum communication system can transmit more information signals than the number of transmission channels. Such a communication system has a higher figure of merit than a conventional multi-channel communication system.  
      Embodiments of the wavelength spread-spectrum communication system described above may be constructed from one or more of discrete components, small-scale or large-scale integrated circuits, suitably-configured application-specific integrated circuits (ASICs) and other suitable hardware. Alternatively, embodiments of the apparatus and the modules thereof may be constructed using a digital signal processor (DSP), microprocessor, microcomputer, computer or other programmable device with internal or external memory operating in response to a program fixed in a computer-readable medium. A programmable device, such as a DSP, a microprocessor, microcomputer or computer, capable of executing a program will be referred to herein as a computer.  
      In computer-based embodiments of the wavelength spread-spectrum communication, one or more of the modules described above may be ephemeral, and may only exist temporarily as the program executes. In such embodiments, the program is conveyed to the computer on which it is to run by embodying the program in a suitable computer-readable medium, such as a set of floppy disks, a CD-ROM, a DVD-ROM, flash memory or other memory device. Alternatively, the program could be transmitted to such computer by a suitable data link and be stored in a memory device in the computer.  
       FIG. 11  is a flow chart of an embodiment  300  of a method in accordance with the invention for transmitting information signals via multiple transmission channels. In the method, in block  301 , each information signal is encoded with a respective spreading code to generate a coded signal corresponding to each bit of the spreading code. The spreading codes used to encode the information signals are mutually different. In block  303  the coded signals corresponding to the same bit of the spreading codes are allocated to a respective one of the transmission channels. Blocks  305  and  307  are performed in each of the transmission channels. In block  305  the coded signals allocated to the transmission channels are analog summed to generate a modulation signal. In block  307 , a transmission signal is modulated in response to the modulation signal.  
      In an embodiment, the spreading codes are mutually orthogonal. In another embodiment, the spreading codes are mutually quasi-orthogonal.  
      In an embodiment, each information signals is encoded by multiplying it by each bit of the respective spreading code. Each multiplication may be performed by exclusively-NORing the information signal with the bit of the respective spreading code. In another embodiment, each spreading code comprises bits each in one of a first state and a second state, e.g., bits each in one of a −1 state and a +1 state. Each information signal is encoded by outputting the information signal as the coded signal for each bit of the spreading code in the first state and inverting the information signal and outputting the inverted information signal as the coded signal for each bit of the spreading code in the second state.  
       FIG. 12  is a flow chart of an embodiment  320  of a method in accordance with the invention for recovering information signals from channel signals received via respective transmission channels. The channel signals have been generated by encoding the information signals with respective spreading codes. The method is performed for each of the information signals. In the method, in block  321 , the channel signal from each of the transmission channels is multiplied by a respective bit of the spreading code assigned to the information signal to generate a respective product signal. In block  323 , the product signals are summed to generate a sum signal. In block  325 , the sum signal is subject to thresholding to recover the information signal.  
      In an embodiment, each spreading code comprises bits each in one of a first state and a second state. Each channel signal is multiplied by outputting the channel signal as the product signal for each bit of the spreading code in the first state and inverting the channel signal and outputting the inverted channel signal as the product signal for each bit of the spreading code in the second state.  
      In an embodiment, the spreading codes are mutually orthogonal. In another embodiment, the spreading codes are mutually quasi-orthogonal.  
      Orthogonal spreading codes are preferred because they have a cross-correlation of zero. This means that the sum signal from which each information signal is recovered is free of noise contributions originating from the other information signals. However, the number of orthogonal spreading codes of a given number of bits is limited, as described above. If quasi-orthogonal spreading codes are used, the sum signal from which each information signal is recovered includes noise contributions originating from the other information signals. However, such noise contributions are discarded by the thresholding applied to the sum signal provided that their level is low enough. Using quasi-orthogonal spreading codes increases the number of useable spreading codes, which enables the communication system to transmit more information signals than the number of transmission channels. Welch Bound Equality (WBE) codes can be used as the spreading codes to increase the number of information signals that can be transmitted beyond one per transmission channel. The manner in which WBE codes can be generated is known in the art. The increase in transmission capacity provided by using WBE codes as the spreading codes is limited by the lower bound of the WBE codes for cross-correlation, as is also known in the art.  
      While the invention has been described with reference to exemplary embodiments, the invention is not limited to the precise embodiments described, and is defined exclusively by the appended claims and their equivalents.