Trellis demapper of a convolutional decoder for decoding pragmatic trellis codes suitable for use in a multi-channel receiver of satellite, terrestrial and cable transmitted FEC compressed-digital television data

Claim 2

In a convolutional decoder of a plurality of pragmatic trellis codes each of which is defined by a series of convolutionally-encoded symbol packets applied as in-phase (I) and quadrature-phase (Q) digital input signals thereto; wherein said plurality of pragmatic trellis codes comprise a distinct code for each constellation set of symbols in the I,Q plane that includes an even power of 2 number of symbols arranged in a square-grid bit-to-symbol mapping to produce square-grid symbol constellations, with the largest of said square-grid symbol constellations including 2 2y symbols, where y is a first positive integer having a given value of at least 2; and wherein said convolutional decoder includes a trellis demapper for demapping each of said plurality of pragmatic trellis codes; the improvement wherein (1) the bit-to-symbol mapping of said square grid of each constellation set is such that alternate cells of odd rows of said square grid define a first subset of symbols, the remaining cells of odd rows of said square grid define a second subset of symbols, alternate cells of even rows of said square grid define a third subset of symbols, and the remaining cells of even rows of said square grid define a fourth subset of symbols, and (2) said trellis demapper comprises: an I-channel random access memory (RAM) having an effective depth of 2.sup.(x+2) storage locations, where x is a second positive integer having a given value larger than said first positive integer, each storage location having an effective width at least sufficient to store an entry of an I-defining lookup table of y-bits; a Q-channel RAM having an effective depth of 2.sup.(x+2) storage locations, each storage location having an effective width at least sufficient to store an entry of a Q-defining lookup table of y-bits; first means for applying a first x-bit input to said I-channel RAM to define the value of said in-phase (I) digital input signal and for applying a second x-bit input to said Q-channel RAM to define the value of said quadrature (Q) digital input signal; second means for applying a 2-bit input to both said I-channel RAM and said Q-channel RAM to define a selected one of said four subsets in accordance with the binary value of said applied 2-bit input; third means for preloading said lookup table of said I-channel RAM in accordance with a selected one of said constellation sets of symbols such that the bits mapping the I component of that symbol of the selected one of said four subsets of said selected one of said constellation sets which is closest in value to the value defined by the in-phase (I) digital input signal to said I-channel RAM is read out as the output of said I-channel RAM; and fourth means for preloading said lookup table of said Q-channel RAM in accordance with a selected one of said constellation sets of symbols such that the bits mapping the Q component of that symbol of the selected one of said four subsets of said selected one of said constellation sets which is closest in value to the value defined by the quadrature (Q) digital input signal to said Q-channel RAM is read out as the output of said Q-channel RAM.

Claim 3

The convolutional decoder defined in claim 1, wherein: said bit-to-symbol mapping of said square grid of each constellation set is such that said third means employs binary Gray-coded bits to bit map said preloaded lookup table of said I-channel RAM, and said fourth means employs Gray-coded binary bits to bit map said preloaded lookup table of said Q-channel RAM.

Claim 4

The convolutional decoder defined in claim 2, wherein: said constellation sets of symbols in the I,Q plane that include a different even power of 2 number of symbols arranged in a square grid include a 16 symbol QAM constellation, a 64 symbol QAM constellation and a 256 symbol QAM constellation; the value of y is 3; and the value of x is 6.

Claim 5

The convolutional decoder defined in claim 1, wherein: said plurality of pragmatic trellis codes also comprise a distinct code for each constellation set of symbols in the I,Q plane that includes an odd power of 2 number of symbols arranged in a cross-grid bit-to-symbol mapping to produce cross-grid symbol constellations, with the largest of said cross-grid symbol constellations including 2 z symbols, where z is a third positive integer having a given value of at least 5 such that the value x of said second positive integer is larger than the value of z/2, and the bit-to-symbol mapping of said cross grid of each constellation set being such that alternate cells of odd rows of said cross grid define a first subset of symbols, the remaining cells of odd rows of said cross grid define a second subset of symbols, alternate cells of even rows of said cross grid define a third subset of symbols, and the remaining cells of even rows of said cross grid define a fourth subset of symbols; and wherein: said lookup table of said I-channel RAM when preloaded by said third means in accordance with said selected one of said constellation sets being an odd power of 2 symbols (1) provides the same bit-to-symbol mapping for the I component of each of said 4 subsets and (2) this bit-to-symbol mapping comprises a given number of columns of a square grid in which the given number of columns is the maximum number of columns in a single one of the four subsets of the cross-grid of the selected one of said constellation sets of an odd power of 2 symbols; said lookup table of said Q-channel RAM when preloaded by said fourth means in accordance with said selected one of said constellation sets being an odd power of 2 symbols (1) provides the same bit-to-symbol mapping for the Q component of each of said 4 subsets and (2) this bit-to-symbol mapping comprises a given number of rows of a square grid in which the given number of rows is the maximum number of rows in a single one of the four subsets of the cross-grid of the selected one of said constellation sets of an odd power of 2 symbols; and said trellis demapper further comprises (1) a remapper RAM responsive to said 2-bit input, said output of said I-channel RAM and said output of said Q-channel RAM being applied as respective inputs thereto for remapping the bit-to-symbol mapping of the square grid of symbols defined by both said I component present at the output of said I-channel RAM and said Q component present at the output of said Q-channel RAM into a square-grid bit-to-symbol mapping at the output of said remapper which remapper output square grid includes both those given symbol cells making up any one of said 4 subsets and at least one additional symbol cell located at least one corner of said remapper output square grid, the bits mapping said one additional symbol cell being a duplicate of the bits mapping a given symbol cell that is contiguously-located with respect to said one corner of said square grid; and (2) select means (a) responsive to said selected one of said constellation sets being an odd power of 2 symbols for forwarding said output of said remapper RAM as the output of said trellis demapper and (b) responsive to said selected one of said constellation sets being an even power of 2 symbols for directly forwarding said respective outputs of said I-channel RAM and said Q-channel RAM as the output of said trellis demapper.

Claim 6

The convolutional decoder defined in claim 4, wherein: a certain constellation set of symbols exhibits an odd power of 2 number of symbols equal to 5; the output from said I-channel RAM consists of 2 bits that are limited to expressing only 3 of 4 possible binary values in which these 3 binary values define the 3 columns of a 3×3 square grid; the output from said Q-channel RAM consists of 2 bits that are limited to expressing only 3 of 4 possible binary values in which these 3 binary values define the 3 rows of said 3×3 square grid; whereby there is derived a non-symmetrical 8-symbol subset situated within a 3×3 square-grid having a different bit-to-symbol mapping for each one of said 4 subsets at the output of said remapper, in which the duplicate bits map a single additional symbol cell for each separate one of said 4 subsets, and the single additional symbol cell is located at a different one of the 4 corners of the individual 3×3 square grids corresponding, respectively, to each separate one of said 4 subsets.

Claim 7

The convolutional decoder defined in claim 4, wherein: a certain constellation set of symbols exhibits a given odd power of 2 number of symbols larger than 5, whereby the symbols of each of the four subsets of said certain constellation set of a given odd power of 2 number of symbols larger than 5 are arranged in a cross grid; the output from said I-channel RAM consists of a group of at least 3 bits, wherein the number of binary values expressed by said group of bits is limited to expressing the number k of columns in the cross grid of any one 4 subsets, where k is a fourth positive integer; the output from said Q-channel RAM consists of a group of at least 3 bits, wherein the number of binary values expressed by said group of bits is limited to expressing the number k of rows in the cross grid of any one 4 subsets;. whereby there is derived a symmetrical cross-grid symbol subset situated within a k×k square-grid having the same bit-to-symbol mapping for each one of said 4 subsets at the output of said remapper, in which the duplicate bits map at least one additional symbol cell located at each of the 4 corners of the k×k square grid for each of said 4 subsets.

Claim 8

The convolutional decoder defined in claim 4, wherein: said bit-to-symbol mapping appearing at each of the outputs of said of said I-channel RAM, said Q-channel RAM, and said remapper RAM consists of binary Gray-coded bits.

Claim 9

The convolutional decoder defined in claim 7, wherein: said constellation sets of symbols in the I,Q plane that include a different even power of 2 number of symbols arranged in a square grid include a 16 symbol QAM constellation, a 64 symbol QAM constellation and a 256 symbol QAM constellation; said constellation sets of symbols in the I,Q plane that include a different odd power of 2 number of symbols arranged in a cross grid include a 32 symbol QAM constellation and a 128 symbol QAM constellation; the value of y is 3; the value of z is 7; and the value of x is 6.

Claim 10

The convolutional decoder defined in claim 8, wherein: said plurality of pragmatic trellis codes also comprise a distinct code for an 8-PSK constellation set of 8 symbols in the I,Q plane in which said 8 symbols are radially distributed symmetrically about the origin of said I,Q plane with each of said 8 symbols being angularly offset by substantially 22.5° with respect to an axis of said I,Q plane, and said 8-PSK constellation set of 8 symbols has a 3-bit bit-to-symbol mapping such that said 8-PSK constellation set is divided into 4 subsets of 2 symbols each in accordance with the binary value-expressed by the 2 least significant bits of said 3 bits, and the 2 symbols of each of these 4 subsets are differentiated from one another in accordance with the binary value expressed by the 1 highest significant bit of said 3 bits; said trellis demapper further comprises an 8-PSK demapper logic means responsive to (1) said first x-bit input being applied as a first input thereto to define the value of said in-phase (I) digital input signal, (2) said second x-bit input being applied as a second input thereto to define the value of said quadrature (Q) digital input signal, and (3) said 2-bit input being applied as a third input thereto to select one of said 4 subsets of said 8-PSK constellation set in accordance with the binary value expressed by said 2-bit input being applied, and in response to said first, second and third inputs thereto said 8-PSK demapper logic means derives a 1-bit output therefrom that expresses the binary value of said 1 highest significant bit of said 3 bits of said bit-to-symbol mapping which is indicative of that one of the 2 symbols of said selected one of said 4 subsets of said 8-PSK constellation that is closest in (I+Q) distance to the position of a symbol in said I,Q plane defined by the respective values of the in-phase (I) digital input signal applied as a first input thereto and the quadrature (Q) digital input signal applied as a second input thereto; and said select means being also responsive to a selection of said 8-PSK constellation set forwarding said 1-bit output from said 8-PSK demapper logic means as the output of said trellis demapper.

Claim 11

The convolutional decoder defined in claim 9, wherein: the bit-to-symbol mapping of the 8 symbols of the 8-PSK constellation set is such that a symbol in the first quadrant of the I,Q plane oriented at substantially 22.5° with respect to the I axis is mapped with the binary value 000, a symbol in the first quadrant of the I,Q plane oriented at substantially 22.5° with respect to the Q axis is mapped with the binary value 001, a symbol in the second quadrant of the I,Q plane oriented at substantially 22.5° with respect to the I axis is mapped with the binary value 010, a symbol in the second quadrant of the I,Q plane oriented at substantially 22.5° with respect to the Q axis is mapped with the binary value 011, a symbol in the third quadrant of the I,Q plane oriented at substantially 22.5° with respect to the I axis is mapped with the binary value 100, a symbol in the third quadrant of the I,Q plane oriented at substantially 22.5° with respect to the Q axis is mapped with the binary value 101, a symbol in the fourth quadrant of the I,Q plane oriented at substantially 22.5° with respect to the I axis is mapped with the binary value 110, and a symbol in the fourth quadrant of the I,Q plane oriented at substantially 22.5° with respect to the Q axis is mapped with the binary value 111; and said 8-PSK demapper logic means including means for deriving a binary value of "1" for said 1-bit output therefrom only if the product of the numerical value of said in-phase (I) digital input signal times the numerical value of I 1 is less than the product of the numerical value of said quadrature (Q) digital input signal times the numerical value of Q 2 , where the numerical value of I 1 is 9 for subset 00, 4 for subset 01, -9 for subset 10 and -4 for subset 11, and the numerical value of Q 2 is -4 for subset 00, -9 for subset 01, -4 for subset 10 and -9 for subset 11.

Claim 12

The convolutional decoder defined in claim 10, wherein: said convolutional decoder is a component of a multi-channel receiver.

Claim 13

The convolutional decoder defined in claim 11, wherein: said multi-channel receiver is a digital television receiver for receiving forward-error-corrected compressed-digital television data transmitted thereto.

Claim 14

In a convolutional decoder of a plurality of pragmatic trellis codes each of which is defined by a series of convolutionally-encoded symbol packets applied as-in-phase (I) and quadrature-phase (Q) digital input signals thereto; wherein said plurality of pragmatic trellis codes comprise a distinct code for each constellation set of symbols in the I,Q plane that includes an odd power of 2 number of symbols arranged in a cross-grid bit-to-symbol mapping to produce cross-grid symbol constellations, with the largest of said cross-grid symbol constellations including 2 z symbols, where z is a first positive integer having a given value of at least 5; and wherein said convolutional decoder includes a trellis demapper for demapping each of said plurality of pragmatic trellis codes; the improvement wherein (1) the bit-to-symbol mapping of said cross grid of each constellation set is such that alternate cells of odd rows of said cross grid define a first subset of symbols, the remaining cells of odd rows of said cross grid define a second subset of symbols, alternate cells of even rows of said cross grid define a third subset of symbols, and the remaining cells of even rows of said cross grid define a fourth subset of symbols, and (2) said trellis demapper comprises: an I-channel random access memory (RAM) having an effective depth of 2.sup.(x+2) storage locations, where x is a second positive integer having a given value larger than one-half said first positive integer, each storage location having an effective width at least sufficient to store an entry of an I-defining lookup table of b-bits, where b=z/2+1/2; a Q-channel RAM having an effective-depth of 2.sup.(x+2) storage locations, each storage location having an effective width at least sufficient to store an entry of a Q-defining lookup table of b-bits; first means for applying a first x-bit input to said I-channel RAM to define the value of said in-phase (I) digital input signal and for applying a second x-bit input to said Q-channel RAM to define the value of said quadrature (Q) digital input signal; second means for applying a 2-bit input to both said I-channel RAM and said Q-channel RAM to define a selected one of said four subsets in accordance with the binary value of said applied 2-bit input; third means for preloading said lookup table of said I-channel RAM in accordance with a selected one of said constellation sets of an odd power of 2 symbols such that the bits mapping the I component of that symbol of the selected one of said four subsets of said selected one of said constellation sets which is closest in value to the value defined by the in-phase (I) digital input signal to said I-channel RAM is read out as the output of said I-channel RAM to (1) provide the same bit-to-symbol mapping for the I component of each of said 4 subsets and (2) this bit-to-symbol mapping comprises a given number of columns of a square grid in which the given number of columns is the maximum number of columns in a single one of the four subsets of the cross-grid of the selected one of said constellation sets of an odd power of 2 symbols; fourth means for preloading said lookup table of said Q-channel RAM in accordance with a selected one of said constellation sets of an odd power of 2 symbols such that the bits mapping the Q component of that symbol of the selected one of said four subsets of said selected one of said constellation sets which is closest in value to the value defined by the quadrature (Q) digital input signal to said Q-channel RAM is read out as the output of said Q-channel RAM to (1) provide the same bit-to-symbol mapping for the Q component of each of said 4 subsets and (2) this bit-to-symbol mapping comprises a given number of rows of a square grid in which the given number of rows is the maximum number of rows in a single one of the four subsets of the cross-grid of the selected one of said constellation sets of an odd power of 2 symbols; and a remapper RAM responsive to said 2-bit input, said output of said I-channel RAM and said output of said Q-channel RAM being applied as respective inputs thereto for remapping the bit-to-symbol mapping of the square grid of symbols defined by both said I component present at the output of said I-channel RAM and said Q component present at the output of said Q-channel RAM into a square-grid bit-to-symbol mapping at the output of said remapper which remapper output square grid includes both those given symbol cells making up any one of said 4 subsets and at least one additional symbol cell located at at least one corner of said remapper output square grid, the bits mapping said one additional symbol cell being a duplicate of the bits mapping a given symbol cell that is contiguously-located with respect to said one corner of said square grid.

Claim 15

In a convolutional decoder of a plurality of pragmatic trellis codes each of which is defined by a series of convolutionally-encoded symbol packets applied as-in-phase (I) and quadrature-phase (Q) digital input signals thereto; wherein said plurality of pragmatic trellis codes comprise a distinct code for each constellation set of symbols in the I,Q plane that includes an odd power of 2 number of symbols arranged in a cross-grid bit-to-symbol mapping to produce cross-grid symbol constellations, with the largest of said cross-grid symbol constellations including 2 z symbols, where z is a first positive integer having a given value of at least 5; and wherein said convolutional decoder includes a trellis demapper for demapping each of said plurality of pragmatic trellis codes; the improvement wherein (1) the bit-to-symbol mapping of said cross grid of each constellation set is such that alternate cells of odd rows of said cross grid define a first subset of symbols, the remaining cells of odd rows of said cross grid define a second subset of symbols, alternate cells of even rows of said cross grid define a third subset of symbols, and the remaining cells of even rows of said cross grid define a fourth subset of symbols, and (2) said trellis demapper comprises: an I-channel random access memory (RAM) having an effective depth of 2.sup.(x+2) storage locations, where x is a second positive integer having a given value larger than one-half said first positive integer, each storage location having an effective width at least sufficient to store an entry of an I-defining lookup table of b-bits, where b=z/2+1/2; a Q-channel RAM having an effective-depth of 2.sup.(x+2) storage locations, each storage location having an effective width at least sufficient to store an entry of a Q-defining lookup table of b-bits; first means for applying a first x-bit input to said I-channel RAM to define the value of said in-phase (I) digital input signal and for applying a second x-bit input to said Q-channel RAM to define the value of said quadrature (Q) digital input signal; second means for applying a 2-bit input to both said I-channel RAM and said Q-channel RAM to define a selected one of said four subsets in accordance with the binary value of said applied 2-bit input; third means for preloading said lookup table of said I-channel RAM in accordance with a selected one of said constellation sets of an odd power of 2 symbols such that the bits mapping the I component of that symbol of the selected one of said four subsets of said selected one of said constellation sets which is closest in value to the value defined by the in-phase (I) digital input signal to said I-channel RAM is read out as the output of said I-channel RAM to (1) provide the same bit-to-symbol mapping for the I component of each of said 4 subsets and (2) this bit-to-symbol mapping comprises a given number of columns of a square grid in which the given number of columns is the maximum number of columns in a single one of the four subsets of the cross-grid of the selected one of said constellation sets of an odd power of 2 symbols; fourth means for preloading said lookup table of said Q-channel RAM in accordance with a selected one of said constellation sets of an odd power of 2 symbols such that the bits mapping the Q component of that symbol of the selected one of said four subsets of said selected one of said constellation sets which is closest in value to the value defined by the quadrature (Q) digital input signal to said Q-channel RAM is read out as the output of said Q-channel RAM to (1) provide the same bit-to-symbol mapping for the Q component of each of said 4 subsets and (2) this bit-to-symbol mapping comprises a given number of rows of a square grid in which the given number of rows is the maximum number of rows in a single one of the four subsets of the cross-grid of the selected one of said constellation sets of an odd power of 2 symbols; and a remapper RAM responsive to said 2-bit input, said output of said I-channel RAM and said output of said Q-channel RAM being applied as respective inputs thereto for remapping the bit-to-symbol mapping of the square grid of symbols defined by both said I component present at the output of said I-channel RAM and said Q component present at the output of said Q-channel RAM into a square-grid bit-to-symbol mapping at the output of said remapper which remapper output square grid includes both those given symbol cells making up any one of said 4 subsets and at least one additional symbol cell located at at least one corner of said remapper output square grid, the bits mapping said one additional symbol cell being a duplicate of the bits mapping a given symbol cell that is contiguously-located with respect to said one corner of said square grid.

Claim 16

The convolutional decoder defined in claim 13, wherein: a certain constellation set of symbols exhibits an odd power of 2 number of symbols equal to 5; the output from said I-channel RAM consists of 2 bits that are limited to expressing only 3 of 4 possible binary values in which these 3 binary values define the 3 columns of a 3×3 square grid; the output from said Q-channel RAM consists of 2 bits that are limited to expressing only 3 of 4 possible binary values in which these 3 binary values define the 3 rows of said 3×3 square grid; whereby there is derived a non-symmetrical 8-symbol subset situated within a 3×3 square-grid having a different bit-to-symbol mapping for each one of said 4 subsets at the output of said remapper, in which the duplicate bits map a single additional symbol cell for each separate one of said 4 subsets, and the single additional symbol cell is located at a different one of the 4 corners of the individual 3×3 square grids corresponding, respectively, to each separate one of said 4 subsets.

Claim 17

The convolutional decoder defined in claim 13, wherein: a certain constellation set of symbols exhibits a given odd power of 2 number of symbols larger than 5, whereby the symbols of each of the four subsets of said certain constellation set of a given odd power of 2 number of symbols larger than 5 are arranged in a cross grid; the output from said I-channel-RAM consists of a group of at least 3 bits, wherein the number of binary values expressed by said group of bits is limited to expressing the number k of columns in the cross grid of any one 4 subsets, where k is a fourth positive integer; the output from said Q-channel RAM consists of a group of at least 3 bits, wherein the number of binary values expressed by said group of bits is limited to expressing the number k of rows in the cross grid of any one 4 subsets; whereby there is derived a symmetrical cross-grid symbol subset situated within a k×k square-grid having the same bit-to-symbol mapping for each one of said 4 subsets at the output of said remapper, in which the duplicate bits map at least one additional symbol cell located at each of the 4 corners of the k×k square grid for each of said 4 subsets.

Claim 18

The convolutional decoder defined in claim 13, wherein: said-bit-to-symbol mapping appearing at each of the outputs of said of said I-channel RAM, said Q-channel RAM, and said remapper RAM consists of binary Gray-coded bits.

Claim 19

The convolutional decoder defined in claim 16, wherein: said constellation sets of symbols in the I,Q plane that include a different odd power of 2 number of symbols arranged in a cross grid include a 32 symbol QAM constellation and a 128 symbol QAM constellation; the value of z is 7; and the value of x is 6.

Claim 20

The convolutional decoder defined in claim 17, wherein: said plurality of pragmatic trellis codes also comprise a distinct code for an 8-PSK constellation set of 8 symbols in the I,Q plane in which said 8 symbols are radially distributed symmetrically about the origin of said I,Q plane with each of said 8 symbols being angularly offset by substantially 22.5° with respect to an axis of said I,Q plane, and said 8-PSK constellation set of 8 symbols has a 3-bit bit-to-symbol mapping such that said 8-PSK constellation set is divided into 4 subsets of 2 symbols each in accordance with the binary value expressed by the 2 least significant bits of said 3 bits, and the 2 symbols of each of these 4 subsets are differentiated from one another in accordance with the binary value expressed by the 1 highest significant bit of said 3 bits; said trellis demapper further comprises an 8-PSK demapper logic means responsive to (1) said first x-bit input being applied as a first input thereto to define the value of said in-phase (I) digital input signal, (2) said second x-bit input being applied as a second input thereto to define the value of said quadrature (Q) digital input signal, and (3) said 2-bit input being applied as a third input thereto to select one of said 4 subsets of said 8-PSK constellation set in accordance with the binary value expressed by said 2-bit input being applied, and in response to said first, second and third inputs thereto said 8-PSK demapper logic means derives a 1-bit output therefrom that expresses the binary value of said 1 highest significant bit of said 3 bits of said bit-to-symbol mapping which is indicative of that one of the 2 symbols of said selected one of said 4 subsets of said 8-PSK constellation that is closest in (I+Q) distance to the position of a symbol in said I,Q plane defined by the respective values of the in-phase (I) digital input signal applied as a first input thereto and the quadrature (Q) digital input signal applied as a second input thereto; and select means (a) responsive to said selected one of said constellation sets being an odd power of 2 symbols for forwarding said output of said remapper RAM as the output of said trellis demapper and (b) responsive to a selection of said 8-PSK constellation set forwarding said 1-bit output from said 8-PSK demapper logic means as the output of said trellis demapper.

Claim 21

The convolutional decoder defined in claim 18, wherein: the bit-to-symbol mapping of the 8 symbols of the 8-PSK constellation set is such that a symbol in the first quadrant of the I,Q plane oriented at substantially 22.5° with respect to the I axis is mapped with the binary value 000, a symbol in the first quadrant of the I,Q plane oriented at substantially 22.5° with respect to the Q axis is mapped with the binary value 001, a symbol in the second quadrant of the I,Q plane oriented at substantially 22.5° with respect to the I axis is mapped with the binary value 010, a symbol in the second quadrant of the I,Q plane oriented at substantially 22.5° with respect to the Q axis is mapped with the binary value 011, a symbol in the third quadrant of the I,Q plane oriented at substantially 22.5° with respect to the I axis is mapped with the binary value 100, a symbol in the third quadrant of the I,Q plane oriented at substantially 22.5° with respect to the Q axis is mapped with the binary value 101, a symbol in the fourth quadrant of the I,Q plane oriented at substantially 22.5° with respect to the I axis is mapped with the binary value 110, and a symbol in the fourth quadrant of the I,Q plane oriented at substantially 22.5° with respect to the Q axis is mapped with the binary value 111; and said 8-PSK demapper logic means including means for deriving a binary value of "1" for said 1-bit output therefrom only if the product of the numerical value of said in-phase (I) digital input signal times the numerical value of I 1 is less than the product of the numerical value of said quadrature (Q) digital input signal times the numerical value of Q 2 , where the numerical value of I 1 is 9 for subset 00, 4 for subset 01, -9 for subset 10 and -4 for subset 11, and the numerical value of Q2 is -4 for subset 00, -9 for subset 01, -4 for subset 10 and -9 for subset 11.