Means and method for block encoding detection and decoding

Method of signalling on a communications channel comprising:

• from a stream of numeric signals,
• converting said signals in blocks of b signals into K message point coordinates C1, C2 . . . CK for 40.gtoreq.K.gtoreq.4,
• modulating a carrier signal in accord ance with the values of said message point coordinates,
• wherein said message point coordinates are determined as follows:
• for each block of b signals determining a number N identifying the sequence of digits in said block,
• determining for N/A a quotient M and a remainder C, where A is once or twice the number of selected alternate lattices in K dimensions and where A may equal 1 and hence M may equal N and C may equal 0,
• providing a table of K dimensional shells where each shell comprises message points with permissible value coordinates and permissible modulo sum totals of the coordinate values at the same distance from a datum, said shells have a predetermined number of points with permissible value coordinates,
• identifying M in terms of a predetermined shell S.sub.K and a number D less than the number of such points therein,
• using S.sub.K, D to provide values,
• S.sub.F, X.sub.F and S.sub.G, X.sub.G where S.sub.F identifies a shell in F dimensions and X.sub.F identifies a point having permissible coordinates on said F dimensional shell and S.sub.F, X.sub.F ;
• S.sub.G, X.sub.G collectively identify S.sub.K, D,
• for each S.sub.F, X.sub.F and each S.sub.G, X.sub.G developing a pair of lower dimension S, X values, dimensions which summed equal F and G respectively and where each pair of lower dimension S, X values identify the higher dimension S, X values from which they are developed,
• continuing the process of substituting S, X values for higher dimension S, X values which they identify until these are obtained K sets of SX values in one dimension,
• generating a coordinate of permissible value from each one dimensional S, X pair and identifying it,
• modifying the coordinates thus developed to other permissible coordinates which identify A and C as well as M.

Means for signalling on a communications channel, comprising:

• means for converting blocks of b signal from a stream of numeric signals into K message point coordinates C1, C2 . . . CK for 40.gtoreq.K.gtoreq.4,
• means for modulating a carrier signal in accord with the values of said message point coordinates,
• said means for converting including the following:
• means for each sequence of b digits determining a number N identifying the sequence of signals in said block,
• means for providing a table of K dimensional shells where each shell comprises message points with permissible value coordinates and permissible modulo sum totals of the coordinate values which points are at the same distance from a datum, said shells having a predetermined number of points with permissible value coordinates,
• means for identifying N in terms of a predetermined shell S.sub.K and a number D less than the number of said points thereon,
• means for using S.sub.K, D to provide sets of values S.sub.F, X.sub.F and S.sub.G, X.sub.G where S.sub.F identifies a shell in F dimensions and X.sub.F identifies a point having permissible value coordinates on said F dimensional shell and S.sub.F, X.sub.F ;
• S.sub.G, X.sub.G collectively identify S.sub.K D.sub.K,
• means responsive to each set S.sub.F, X.sub.F and each set S.sub.G, X.sub.G for providing two sets of lower dimension S, X values for dimensions which summed equal F and G respectively and where each two sets of lower dimension S, X values identify the higher dimension set of S, X values from which they are developed,
• means for continuing the process of substituting two pairs of lower dimension S, X values for higher dimension S, X values which they identify until there are K sets of S, X values in one dimension,
• means for generating a coordinate a permissible magnitude and sign, identifying each one dimensional S, X pair.

Means for signalling on a communications channel, comprising:

• means for converting blocks of b signals from a stream of numeric signals into K message point coordinates C1, C2 . . . CK for 40.gtoreq.K>4,
• means for modulating a carrier signal in accord with the values of said message point coordinates,
• where for suitable packing of said points in K dimensional space said coordinates are expressible in permissible integral values and the sum of the K coordinates so expressed has a permissible modulo value,
• said means for converting including the following;
• means for each sequence of b digits determining a number N identifying the sequence of b digits,
• means for determining for N/A a quotient M and a remainder C where A is the number of selected alternate lattices in K dimensions or double such number if even or odd coordinates may be used and where A may equal 1 and hence M may equal N and C may equal 0,
• means for consulting a table of K dimensional shells where each shell comprises message points and a permissible modulo sum total of the values of the coordinates, said shells having a perdetermined number of points with permissible value coordinates,
• means for identifying M in terms of a predetermined shell S.sub.K and a number D less than the number of said points thereon,
• means for using S.sub.K, D to ptovide sets of values S.sub.F, X.sub.F and S.sub.G, X.sub.G where S.sub.F identifies a shell in F dimensions and X.sub.F defines a point having permissible value coordinates on said F dimensional shell, and S.sub.F, X.sub.F ;
• S.sub.G X.sub.G collectively identify S.sub.K, D.sub.K,
• means responsive to each set S.sub.F, X.sub.F and each set S.sub.G, X.sub.G for providing two sets of lower dimension S, X values, for dimensions which summed equal F and G respectively and where each two sets of lower dimension S, X values identify the higher dimension set of S, X values from which they are developed,
• means for continuing the process of subtituting two pairs of lower dimension S, X values for higher dimension S, X values which they identify until there are K sets of S, X values in one dimension,
• means for generating a coordinate of permissible magnitude and sign, identifying each one dimensional S, X pair,
• means for modifying the coordinates thus developed to other permissible coordinates which identify A and C as well as M.

Means for signalling on a communications channel comprising:

• means for converting blocks of b signals into K message point coordinates C1, C2, . . . CK, for 40.gtoreq.K>4,
• where for suitable packing of the message points in K dimensional space, rules are provided for coordinate values and the modulo sum of the coordinates when the coordinates are expressed as integers,
• means for modulating a carrier signal in accord with said message point coordinates,
• means for transmitting said modulated carrier signal,
• wherein said means for converting blocks of b signals comprises:
• means for determining a number N identifying the numerical signal sequence in said block,
• means providing a table of the number of available coordinate values in 1 dimension which satisfy the coordinate value rules for K dimensions, for regular intervals of r.sup.2 where r.sup.2 is the square of the distance in coordinate units from a point, defined by the number of coordinates corresponding to the dimension, to a datum point,
• means providing the numbers of corresponding values in higher dimension for such regular values of r.sup.2 up to dimension K,
• where such numbers in higher dimension are calculated in accord with the algorithm, ##EQU7## where V.sub.H, V.sub.F, V.sub.G, V.sub.K are the number of available sets of message points in dimensions H, F, G, K, respectively, F+G=H and n is the number of regular intervals of r.sup.2,
• means for determining the value of n, for V.sub.K, n where the total of values of V.sub.K, in a predetermined sequence of such values preceeding V.sub.K, n, is as large as possible without exceeding N,
• means for determining the value of X.sub.K, being N less such total,
• means, for values of X.sub.K, n for determining K corresponding coordinates C1, C2 . . . CK identifying X.sub.K, n.

Means for signalling on a communications channel comprising:

• means for converting blocks of b signals into K message point coordinates C1, C2, . . . CK, for 40.gtoreq.K>4,
• where for suitable packing of the message points in K dimensional space, rules are provided for coordinate values and for the modulo sum of the coordinates when the coordinate values are expressed as integers,
• means for modulating a carrier signal in accord with said message point coordinates,
• means for transmitting said modulated carrier signal,
• wherein said means for converting blocks of b signals comprises:
• means for determining a number N identifying the signal sequence in said block,
• means for determining for N/A a quotient M and a remainder C where A is the product of the number of selected alternate lattices and choice as to positive and negative coordinates in K dimensions and where A may equal 1 in which event M will equal N and C will equal 0,
• means providing a table of the number of available coordinate values in 1 dimension which satisfy the coordinate value rules for the K coordinates, for regular intervals of r.sup.2, where r.sup.2 is the square of the distance in the coordinate units from a point defined by the number of coordinate values corresponding to a dimension, to a datum point,
• means providing the numbers of corresponding values in higher dimension for such regular values of r.sup.2 up to dimension K,
• where such numbers in higher dimension are calculated in accord with the algorithm, ##EQU8## where V.sub.H, V.sub.F, V.sub.G, V.sub.K, are the number of available sets of coordinate values in dimension H, F, G, K, respectively, F+G=H and n is the number of regular intervals of r.sup.2,
• means for determining the value of n, for V.sub.K, n where the total number of values of V.sub.K in a predetermined sequence of such values preceeding V.sub.K, n is as large as possible without exceeding M,
• means for determining the value of X.sub.K, being N less such total,
• means, for values of X.sub.K, n for determining K corresponding coordinates identifying X.sub.K, n,
• where A.noteq.1 C.noteq.0 modifying the coordinates in accord with C.

Means for signalling on a communications channel, comprising:

• means for converting numeric signals in blocks of b signals into K message point coordinates C1, C2, . . . CK, for 40.gtoreq.K>4,
• where for suitable packing of the message points in K dimensional space, rules are provided for coordinate values and for the modulo sum of the coordinates when the coordinate values are expressed as integers,
• means for modulating a carrier signal in accord with said message point coordinates,
• means for transmitting said modulated carrier signal,
• means for determining said message point coordinates as follows:
• means for determining, for each block of b signals, a number N identifying the numeric signal sequence in said block,
• means for determining, for each N, a value r.sup.2 and a value X.sub.K, where r.sup.2 is one of a set of specific values, a number of message points occur whose individual values and whose modulo sum satisfy the requirements for coordinates C1, C2, . . . CK and where ##EQU9## where d is integral, CD1, CD2, . . . CDK is a datum point and X.sub.K identifies a specific message point with such r.sup.2, and r.sup.2 and X.sub.K identify N,
• for r.sup.2 and X.sub.K means for determining K coordinates C1, C2, . . . CK, identifying r.sup.2, X.sub.K.

Means for signalling in a communications channel comprising:

• means for converting numeric signals in blocks of b signals into K message point coordinates C1, C2, . . . CK for 40.gtoreq.K>4, including means for determining a number N identifying the numeric signals in each block,
• means for transmitting said modulated carrier signal,
• means for determining said message point coordinates as follows:
• means for determining for N/A a quotient M and a remainder C where A is the product of selected alternate lattices and 2 if even and odd coordinates are permissible in K dimensions and where A may equal 1 and hence M may equal N and C may equal 0,
• means for determining for each M a value r.sup.2 and a value X.sub.K where a number of message points occur whose individual message points and said sum satisfy the requirements for coordinates C1, C2, . . . CK and ##EQU10## where d has integral values, CD1, CD2, . . . CDK are the coordinates of a datum point, and X.sub.K relates to a specific message point with such r.sup.2, and r.sup.2 and X.sub.K identify N,
• means, for values r.sup.2 and X.sup.K for determining K coordinates C1, C2, . . . CK,
• where A.noteq.0, C.noteq.0, modifying the coordinates in accord with C.

Means for signalling on a communications channel comprising:

• means for converting a block of b numeric signals into a number N identifying the numeric signal sequence in said block,
• means for converting said number N into 24 message point coordinates C1, C2, . . . C24, identifying said number N,
• wherein said coordinates may be expressed in integral form and in such integral form are chosen to have all even values with a sum of 0 modulo 8 or all odd values with a sum of 4 modulo 8,
• means for modulating carrier signal in accord with the value of said message point coordinates,
• means for transmitting said modulated carrier signal.

Means for signalling on a communications channel comprising:

• means for converting numeric signals in blocks of b signals into 24 message point coordinates C1, C2, . . . C24,
• means for modulating a carrier signal in accord with the value of said message point coordinates,
• means for transmitting said modulated carrier signal,
• wherein said means for converting said numeric signals comprises,
• means, for each block of b digits determining a number N identifying said block,
• means for assigning each number N to a shell of message points in K space, which message points have integral coordinates and satisfy the rules:
• that the coordinates are either all even with a sum of 0 modulo 8 or all odd with a sum of 4 modulo 8,
• where a shell comprises the number of message points where specific ##EQU14## where d has integral values;
• CD1, CD2, . . . CD24 represents a datum point, and r.sup.2 has regular values 0, 32, 64, . . .
• means for deriving from N and said shell in 24 space, a pair of shells in dimensions F and G each with an identifying value where F+G=H, and H in the first derivation=24, the value r.sup.2 is the square of the distance of the shell from the datum having points in common with CD1, CD2, . . . CDF in F space and CD1, CD2, . . . CDG in G space, respectively,
• means for continuing to effect such derivations to the pairs of shells and identifying values until 24 shells and identifying values are obtained in one dimension,
• means for deriving said coordinates C1, C2, . . . C24 from said 24 shell and identifying values.

Means for signalling on a communications channel comprising:

• means for converting numeric signals in blocks of b signals into 24 message point coordinates C1, C2, . . . C24,
• means for modulating a carrier signal in accord with with value of said message point coordinates,
• means for transmitting said modulated carrier signals,
• wherein said means for converting said numeric signals comprises,
• means for each block of b digits to determine a number N identifying said block,
• means for providing the result of N/8192 as a quotient M and remainder C where C represents the choice of one of 4096 Leech lattice vectors and the choice of whether the coordinates shall be even or odd,
• means for assigning each number M to a shell of message points in 24 space, which message points, have integral coordinates and satisfy the rules:
• that the coordinates are either all even with a sum of 0 modulo 8 or all odd with a sum of 4 modulo 8, where a shell comprises the number of message points where d has integral values for which ##EQU15## for a given r, means for deriving from M and said shell in 24 dimensional space, by a splitting algorithm, a pair of shells in dimensions F and G each shell with an identifying value where F+G=24 the value for r.sup.2 is the square of the distance of the shell from the origin in F space and G space respectively,
• means for continuing to apply said splitting algorithm to the pairs of shells in dimensions F and G and identifying values until 24 shells and identifying values are obtained in one dimension,
• means for deriving 24 message point coordinates from said 24 shells and identifying values,
• means for modifying said last mentioned 24 message point coordinates in accord with the value of C to produce message point coordinates C1, C2, . . . C24.

Means for detection of received carrier signals modulated in accord with coordinate values C1, C2, . . . C24 conforming to a pattern of vectors derived from a pattern vector from the Leech lattice,

• means for demodulating said signals,
• means for comparing the demodulation products modulo 4 with 4096 even and 4096 odd pattern vectors,
• means for determining the pattern vector for which the demodulation products show the smallest error,
• means for using said last mention pattern vector and said coordinates to determine a number N identified thereby,
• means for providing a block of b numeric signals identified by said number N.