Methods and systems for efficient multi-wire communications and crosstalk cancellation

Abstract

Methods and systems are disclosed for efficient cancellation of crosstalk between signals transmitted over multiple signal paths. Symmetry is induced on the signals transmitted over the signal paths such that the crosstalk matrix becomes a matrix with structure. Such structured matrix may be a circulant matrix of which the inverse may be applied efficiently to transmitted symbols or received symbols. Application of such inverse may comprise the fast Fourier transform. Applications of the methods and systems disclosed include chip-to-chip communications, on-chip communications, communication over cables and storage of information.

1 . An apparatus for conveying symbols representing information where the crosstalk between the symbols is described by a crosstalk matrix, the apparatus comprising:
 a plurality of signal paths arranged in such a way that the crosstalk matrix is circulant; and   a receiver configured to:
 receive a first set of symbols; and 
 form a second set of symbols based at least in part on the first set of symbols and the inverse of the circulant sampled crosstalk matrix. 
   
     
     
         2 . The apparatus of  claim 1  where the crosstalk matrix is circulant by arranging the signal paths in such a way that the cross section of the signal paths has a discrete rotational symmetry of order equal to the number of signal paths. 
     
     
         3 . The apparatus of  claim 1  where the crosstalk matrix is circulant by arranging the signal paths in a twisted configuration. 
     
     
         4 . The apparatus of  claim 1  where the circulant sampled crosstalk matrix is applied to part of the first set of symbols and comprises a fast Fourier transform. 
     
     
         5 . The apparatus of  claim 1  where the signal paths are electrical conductors or optical waveguides. 
     
     
         6 . A method of transmitting symbols representing information over a channel comprising n signal paths with at least n pulse amplitude modulation signals where the crosstalk between the symbols due to transmission on the channel is described by a crosstalk matrix, the method comprising:
 providing n signal paths in a configuration where the cross section of the signal paths has a discrete rotational symmetry of order n, wherein n is an integer larger than three;   receiving a first set of symbols representing the information;   forming a first set of signals by pulse amplitude modulation of a pulse shape where the pulse amplitudes are based at least in part on the first set of symbols; and   providing the first set of signals for transmission over the signal paths such causing the crosstalk matrix to be circulant, wherein crosstalk between the symbols is cancelled by a transmitter or receiver with less than quadratic complexity with respect to the number of signal paths.   
     
     
         7 . The method of  claim 6 , where the first set of symbols is formed by application of the inverse of the circulant sampled crosstalk matrix to a second set of symbols representing information. 
     
     
         8 . The method of  claim 6  where the pulse shape is a non-return-to-zero pulse shape or return-to-zero pulse shape. 
     
     
         9 . The method of  claim 7  where the inverse of the circulant sampled crosstalk matrix comprises a fast Fourier transform. 
     
     
         10 . The method of  claim 6  where the signal paths are one of electrical conductors, electrical waveguides, or optical waveguides. 
     
     
         11 . The method of  claim 6  where the crosstalk matrix has become circulant by arranging the signal paths in such a way that the cross section of the signal paths has a discrete rotational symmetry of order equal to the number of signal paths. 
     
     
         12 . The method of  claim 6  where the crosstalk matrix is circulant by providing the signal paths in a twisted configuration. 
     
     
         13 . The method of  claim 6  where the crosstalk matrix is circulant by providing extension signal paths on which part of the first set of signals are transmitted. 
     
     
         14 . A method of transmitting symbols representing information on a plurality of signal paths where crosstalk between the symbols is described by a crosstalk matrix, the method comprising:
 receiving a first set of symbols representing the information;   forming a first set of signals based at least in part on the first set of symbols;   forming a second set of signals based at least in part on the first set of signals;   providing the first set of signals for transmission over a first group of signal paths; and   providing the second set of signals for transmission over a second group of signal paths causing the crosstalk matrix to be circulant.   
     
     
         15 . The method of  claim 14  where the second set of signals is equal to part of the first set of signals. 
     
     
         16 . The method of  claim 14  where the first set of signals is formed by pulse amplitude modulation of a pulse shape with the first set of symbols as the amplitudes of the pulses. 
     
     
         17 . The method of  claim 16  where the pulse shape is a non-return-to-zero pulse shape. 
     
     
         18 . A method of transmitting information in accordance with  claim 14 , where the first set of symbols is formed by application of the inverse of the circulant sampled crosstalk matrix to a second set of symbols representing information. 
     
     
         19 . The method of  claim 18  where the application of the inverse of the circulant sampled crosstalk matrix comprises a fast Fourier transform. 
     
     
         20 . The method of  claim 14  where the signals paths comprise electrical conductors or optical waveguides.