Block coding into 24 coordinates and detection of transmitted signals

Means for detecting received coordinates transmitted as 24 coordinates modulated on a carrier which coordinate values were 0 mod 4 and modified in accord with a selected pattern vector of a Leech matrix and in accord with whether even or odd coordinates would be used, to provide:

• for even coordinates, 0's and 2's mod 4 determined by the presence of 0's or 1's in the selected pattern vector and a mod sum of the coordinate values which is 0 and mod 8,
• for odd coordinates, 1's and 3's mod 4 determined by the presence of 0's or 1's in the selected pattern vectors and a sum of the coordinate values which is 4 mod 8,
• means on demodulating the received coordinate values and storing such demodulated values,
• means providing such demodulated values mod 4 and a measure of error of such value relative to possible coordinate values 0,1,2,3,
• where an octuple is the first, second or third eight places of a 24 place coordinate set or Leech matrix pattern vector and three such octuples make up 24 places,
• where the Leech matrix was selected to produce octuples which may all be classified in complementary pairs,
• means for determining the 256 possible values of octuples mod 4 present in possible Leech matrix pattern vectors, being 128 arrangements each of which may be even or odd,
• means for comparing complementary pairs of such octuples to determine which octuple in a pair has a lower total error measure relative to the relevant received values, storing the preferred candidate from each complementary pair,
• where the possible combinations of three rows of the said Leech matrix determine the complementary pairs,
• means using the possible combinations of a further three rows of the Leech matrix and the choice of even or odd coordinates to produce 128 groups of eight triple octuples, even group having candidates determined by the eight possible combinations of the further three rows,
• means determining for each group of eight the triple octuple with lowest sum of errors whereby the lowest triple octuples in each group of eight together comprise 128 candidates,
• means determining for each of the 128 candidates the sum of the error measures for the 24 coordinates, of the triple octuple,
• and means determining the triple octuple with the lowest sum of error measures,
• means deriving from the determination lowest sum triple octuple the directions as to the remaining bits of the pattern vector to define the pattern vector, and even or odd,
• means for producing from the preceding determinations for determining the transmitted coordinates.

In means for signalling including means for encoding numeric data into coordinate sets of 24 modified in accord with a selected pattern vector derived from a Leech matrix wherein the coordinates had values which were 0 mod 4, modified to be all even or all odd and so that:

• (a) even coordinates are 0 or 2 mod 4;
• (b) odd coordinates are 1 or 3 mod 4;
• in each of (a) and (b) dependant upon whether the pattern vector has a 1 or a 0 in the place corresponding to the coordinate,
• and where the sum of the coordinate values is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,
• wherein the pattern vectors are derived from a Leech matrix obtained by placing the columns of a conventional Leech matrix in the order (using numbering of odd matrix columns)
• 1, 18, 24, 22, 19, 10, 23, 3, 6, 8, 21, 16, 12, 15, 17, 7, 9, 13, 2, 4, 14, 5, 20, 11,
• means for modulating a carrier in accord with said modified coordinate values and means for transmitting said modulated carrier.

In means for signalling including means for encoding numeric data into sets of 24 coordinates in accord with pattern vectors derived from a Leech matrix wherein the coordinates have values which were 0 mod 4, modified to be all even or all odd and so that:

• (a) even coordinates are 0 mod 4 or 2 mod 4,
• (b) odd coordinates are 1 mod 4 or 3 mod 4,
• in each of (a) or (b) dependant upon whether the pattern vector has a 1 or a 0 in the place corresponding to the coordinate,
• and where the sum of the coordinate values is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,
• wherein the pattern vectors are those deriveable from aa modified Leech matrix of the form:
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• means for modulating said coordinates on a carrier and means for transmitting said modulated carrier.

In means for signalling including means for encoding numeric data into coordinate sets of 24 in accord with pattern vectors derived from a Leech matrix wherein the coordinates have values which are 0 mod 4, modified to be all even or all odd and so that:

• (a) even coordinates are 0 or 2 mod 4,
• (b) odd coordinates are 1 or 3 mod 4,
• in each of (a) or (b) dependant upon whether the pattern vector has a 1 or a 0 in the place corresponding to the coordinate,
• and where the sum of the coordinate values is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,
• wherein the pattern vectors are deriveable from a modified Leech matrix including the row patterns:
• ______________________________________ 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 ______________________________________
• as three of the 12 rows,
• means for modulating said coordinates on a carrier, means for transmitting said carrier.

Means for detecting and decoding signals containing numeric data modulated on a carrier in coordinate sets of 24 which signals were derived from 24 coordinate values 0 mod 4, modified to be all even or all odd and modified in accord with a pattern vector of a Leech matrix so that:

• (a) even coordinates being 0 mod 4 or 2 mod 4;
• (b) odd coordinates being 1 mod 4 or 3 mod 4;
• in each of (a) and (b) dependant upon whether the pattern vector has a 1 or a 0 in the place corresponding to the coordinates,
• and where the sum of the coordinate values is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,
• wherein the pattern vectors are derived from a Leech matrix obtained by placing the columns of a conventional Leech lattice in the order (using numbering of old matric columns):
• 1, 18, 24, 22, 19, 10, 23, 3, 6, 8, 21, 16, 12, 15, 17, 7, 9, 13, 2, 4, 14, 5, 20, 11,
• means for receiving and demodulating such signals to provide 24 coordinate values, constituting 3 receive octuples,
• means for determining for each received octuple and each possible octuple provided by the encoding system used, a measure the error involved in accepting its coordinate values as the corresponding octuple of transmitted values and from this which of each of 128 pairs of complementary candidate octuples is a more likely candidate to represent the corresponding received octuple conditionally including in said measure of error the smallest increase in the event that a coordinate must be altered or a complementary octuple substituted to change the modulo sum of the coordinates,
• with such more likely pair candidates determining which permissible combination of 3 octuples has the lowest sum of measures of error, when the mod 8 sum rule is satisfied;
• on this basis determining the best 24 coordinates mod 4 to represent the received coordinates,
• means for determining the pattern vector therefrom,
• means for deriving the 0 mod 4 coordinates from the values of the received coordinates and the determined pattern vector and the choice of even or odd,
• means for deriving the numeric data represented by the 24 coordinates modulated on the carrier.

Means for detecting and decoding numeric data signals modulated on a carrier in coordinate sets of 24 which signals were derived from 24 coordinate values 0 mod 4, modified to be all even or all odd and modified in accord with a pattern vector of a Leech matrix so that:

• (a) even coordinates are 0 mod 4 or 2 mod 4;
• (b) odd coordinates are 1 mod 4 or 3 mod 4;
• in each of (a) and (b) dependant upon whether the pattern vector has a 1 or a 0 in the place corresponding to the coordinate,
• and where the sum of the coordinate values is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,
• wherein the pattern vectors are deriveable from a modified Leech matrix:
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• means for receiving and demodulating the transmitted signal,
• means for determining for each octuple of the received coordinates and for each octuple deriveable from a pattern vector and the choice of even or odd, a measure of the error involved in accepting the deriveable octuples coordinates values mod 4 as the values of the received octuple and the penalty for the lowest increase in measure of error if the candidate octuple must be altered or substituted for to correct the module 8 sum,
• means for comparing said deriveable octuples in complementary pairs to determine which of the pairs has the lower error measure,
• means with such lower error measure of a pair candidates for determining which permissable combination of three octuples has the lowest sum of measure of error,
• means if the sum modulo 8 does not satisfy the modulo sum rules, to increase the octuple of the three with the smallest error by the corresponding penalty, on this basis determining the best 24 coordinates mod 4 to represent the received coordinates,
• means for determining therefrom the pattern vector employed,
• means for deriving the 0 mod 4 coordinates from the values of the received coordinates and the selected pattern vector,
• means for deriving the numeric data from the coordinates, the pattern vector and the choice of even or odd.

Means for detecting and decoding information containing signals mdoulated on a carrier in coordinate sets of 24 which signals were derived from 24 coordinate values 0 mod 4, modified to be all even or all odd and modified in accord with a pattern vector of a Leech matrix so that:

• (a) even coordinates are 0 or 2 mod 4;
• (b) odd coordinates are 1 or 3 mod 4;
• in each of (a) and (b) dependant upon whether the pattern vector has a 1 or a 0 in the place corresponding to the coordinates,
• and where the sum of the coordinate values is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,
• wherein the pattern vectors are deriveable from a conventional Leech matrix with or without the interchange of rows,
• means for receiving and demodulating said signals to produce 24 received coordinate signals,
• means at the receiver to make the place changes in said 24 coordinate signals required to convert the Leech matrix used into a matrix deriveable from the matrix,
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• by row changes only,
• means for determining each octuple of the place changed received coordinates and each octuple deriveable from the last mentioned matrix and a choice of even or odd, a measure of the error involved in accepting its coordinate values mod 4 and the penalty for the lowest increase in measure of error of the candidate octuple must be altered or substituted for, to correct the modulo 8 sum,
• means for comparing said deriveable pair octuples in complementary pairs to determine which of the pairs has the lower error measure,
• means with lower measure of a pair candidate determining which permissable combination of three octuples has the lowest sum of measures of error,
• means if the sum modulo 8 does not satisfy the modulo sum rules to increase the octuple of the three with the smallest error,
• on the basis of this determining the best 24 coordinates mod 4 to represent the received coordinates in the revised column order,
• means for determining therefrom the pattern vector employed and the coordinates transmitted both with the original place order of the coordinates,
• means for deriving the information from the coordinate pattern vector and the choice of even or odd.

Means for receiving, detecting and decoding information containing signals, modulated on a carrier, encoded in 24 coordinates, 0 mod 4 modified in accord with a pattern vector derived from a Leech matrix,

• means for demodulating said signals,
• means for arranging the places of such signals to correspond to the column changes required to convert the matrix used at the transmitter to a matrix which will produce the same pattern vectors as the matrix:
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• considering a set of 24 signal values as three consecutive octuples,
• where there are 128 possible even coordinate mod 4 octuples mod 4 and 128 possible odd coordinate octuples and where said possible octuples may be arranged in 64 even pairs which are complements and 64 odd pairs of octuples with each pair having complementary values,
• means for calculating the measure of the error between the received coordinate value mod 4 and the possible octuple, for each pair,
• means for designating the one of the pairs with lower error measure, and a measure of the penalty being the increase in the error and the better candidate of the two if coordinate or octuple must be replaced with the smallest increased error to correct the modulo sum of the octuple,
• means for determining for the 1024 even and 1024 odd combinations of three consecutive octuples the candidate with the lowest sum of such measure of error with necessary correction for module sum of the coordinate values,
• means for deriving from such three octuple candidates the pattern vector used,
• means for converting the pattern vector to reverse the column changes between the encoding matrix and the detecting matrix,
• means for converting the pattern vector to reverse the row changes between the encoding matrix and the detecting matrix, to produce the encoding pattern vector,
• means for modifying the received values of the received coordinates to reverse the effect of the encoding pattern vector,
• means for deriving the information from the derived coordinates, the encoding pattern vector and the choice of even or odd.

Means for detecting transmitted value sets of 24 coordinates which had values 0 mod 4 and were modified place by place in accord with a selected pattern vector of a Leech matrix to be 0 or 2 mod 4 or 1 or 3 mod 4 in accord with the 1's or 0's in the pattern vector, and to sum to 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,

• means for arranging the places of the received coordinates to correspond to the column changes applicable to the Leech matrix used to produce a Leech matrix which will produce the same pattern vectors as the matrix:
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• means for producing the transmitted values of the 24 coordinates mod 4,
• means for determining the relationship of each octuple of the 24 received values, and complementary pairs of the possible transmitted octuples using the available pattern vectors of the matrix set out above, to determine for each of the possible octuples a measure of the sum of the errors from the received values and a measure of the smallest penalty being the increase of error for altering the modulo sum of the octuple or for substituting its complement,
• means, for possible combinations of three octuples with the smaller error, for determining the sum of such errors, if the modulo sum is correct, and the sum of the errors plus the smallest penalty if the modulo sum is not correct and determining the pattern vector used in encoding and whether the coordinates are even or odd,
• means for rearranging received, detected coordinate places to reverse the previous changes,
• means for altering the received values of the coordinates to reverse the modification by the pattern vector at the encoder,
• means for deriving the information transmitted from the coordinates the pattern vector and the choice of even or old.

Means for detecting and decoding a set of 24 coordinates containing information and modulated on a carrier signal, which have encoded values 0 mod 4 modified in accord with a selected pattern vector derived from a Leech matrix, to provide all even values 0 or 2 mod 4 or all odd values 1 or 3 mod 4 in each case determined by whether the pattern vector has a 1 or a 0 at the corresponding coordinate place and having a sum of the coordinates which is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates, and which, so modified have been modulated on a carrier and transmitted, comprising:

• means for demodulating said carrier signal to produce values corresponding to the modified coordinates,
• means for interchanging places of the received coordinates mod 4 to correspond to the column changes between the Leech matrix used at the encoder and the modified Leech matrix:
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• means for determining measures of the errors corresponding to the assumption that octuples of the column changed received coordinates modulo 4 correspond respectively to complementary pairs of possible octuples derived from the modified Leech matrix and selecting the octuple from each pair with the lower error, and the octuple with the lowest error to alter with the other modulo sum,
• means for determining from possible 24 coordinate sets made of said selected octuples, the set with the lowest total of three octuple errors with the correct modulo sum,
• means for determining therefrom the corresponding pattern vector of the modified Leech lattice,
• means for determining therefrom the pattern vector used at the encoder, means for modifying the received coordinates to reverse the modification at the encoder and recover the information from the coordinates, the encoder pattern vector and the choice of even or odd.

Means for communicating information, comprising:

• means for converting a block of information to a number N,
• means for producing the value N/8192=quotient M and the remainder C,
• means for selecting a Leech pattern vector and the choice of even or odd coordinates on the basis of C,
• means for encoding M into 24 coordinates which are 0 modulo 4,
• means for modifying said coordinates in accord with the 24 corresponding places of the pattern vector and the choice of even or odd coordinates to produce 24 coordinates which are 0 or 2 mod 4 or 1 or 3 mod 4,
• means for modulating said modified coordinates on a carrier,
• means for transmitting said coordinates,
• means for receiving and demodulating said coordinates,
• means for making any alteration in the places to correspond to the column changes required to convert the matrix used at the encoder to the modified Leech matrix:
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• for each octuple of said coordinates, means for determining a measure of the error relative to each octuple available from use of the modified Leech matrix and the choice of even or odd coordinates and a measure of the smallest increase in error involved in changing one coordinate by 4 or replacing the octuple by the complementary octuple,
• means for the possible sets of three available octuples, determining the set with the smallest error and the correct modulo sum,
• means for said set determining the corresponding pattern vector,
• means for converting said pattern vector to that used at the encoder,
• means for modifying the received coordinate values in accord with the modified pattern vector,
• means for determining from the modified received coordinate values the number N.

Method of encoding numeric data into coordinate sets of 24 modified in accord with a selected pattern vector derived from a Leech matrix wherein the coordinates had values which were 0 mod 4, modified to be all even or all odd and so that:

• (a) even coordinates are 0 or 2 mod 4;
• (b) odd coordinates are 1 or 3 mod 4;
• in each of (a) and (b) dependant upon whether the pattern vector has a 1 or a 0 in the place corresponding to the coordinate,
• and where the sum of the coordinate values is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,
• wherein the pattern vectors are derived from a Leech matrix obtained by placing the columns of a conventional Leech matrix in the order (using numbering of old matrix columns):
• 1,18,24,22,19,10,23,3,6,8,21,16,12,15,17,7,9,13,2,4, 14,15,20,11,
• modulating said coordinates on a carrier and transmitting said modulated carrier.

Method of signalling comprising:

• encoding numeric data into sets of 24 coordinates in accord with pattern vectors derived from a Leech matrix wherein the coordinates have values which were 0 mod 4, modified to be all even or all odd and so that:
• (a) even coordinates are 0 or 2 mod 4;
• (b) odd coordinates are 1 or 3 mod 4;
• in each of (a) or (b) dependant upon whether the pattern vector has a 1 or a 0 in the place corresponding to the coordinates,
• and where the sum of the coordinate values is 0 mod 8 for even coordinates and 4 mod 8 for odd coordinates,
• wherein the pattern vectors are those deriveable from a modified Leech matrix of the form:
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• modulating said coordinates on a carrier and transmitting said modulated carrier.

Method of communicating information comprising:

• converting a block of information into a number N,
• producing the value N/8192=quotient M and remainder C,
• selecting a Leech pattern vector and the choice of even or odd coordinates on the basis of C,
• encoding M into 24 coordinates which are 0 modulo 4,
• modifying said coordinates in accord with the 24 corresponding places of the pattern vector and the choice of even or odd coordinates to produce 24 coordinates which are 0 or 2 mod 4 or 1 or 3 mod 4,
• modulating said modified coordinates on a carrier,
• transmitting said coordinates,
• receiving and demodulating said coordinates,
• making any alteration in the places of the demodulated coordinates to correspond to the column changes required to convert the matrix used to the encoder, the modified Leech matrix:
• ______________________________________ 1 11111111 00000000 00000000 2 00000000 11111111 00000000 3 00000000 00000000 11111111 4 00001111 00001111 00000000 5 00110011 00110011 00000000 6 01010101 01010101 00000000 7 00000000 00001111 00001111 8 00000000 00110011 00110011 9 00000000 01010101 01010101 10 01001101 01001101 01001101 11 01010011 01010011 01010011 12 01110100 01110100 01110100 ______________________________________
• for used octuple of said coordinates, determining a measure of the error relative to each octuple available from use of the modified Leech matrix and the choice of even or odd coordinates and a measure of the smallest increase in error involved in changing one coordinates by for or replacing the octuple by the complementary octuple,
• from the possible sets of three available octuples, determining the set with the smallest error and the correct modulo sum,
• determining the corresponding pattern vector,
• converting said pattern vector to that used at the encoder,
• modifying the pattern vector to that used at the encoder,
• modifying the received coordinate values in accord with the modified pattern vector,
• determining from the modified received coordinate values the number N.