PASM and TASM forward error correction and detection code method and apparatus

Claim 2

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, by setting the parity-check symbol for each of the first set of parity-check symbols for each parity line equal to the modulo-2 p sum of the data symbols along each parity line, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells, and said first set of parity-check symbols forms a first parity row located in said parity-check memory cells; calculating at least a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, by setting the parity-check symbol for each of the second set of parity-check symbols for each parity line equal to the modulo-2 p sum of the data symbols and parity-check symbols along each parity line, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row, and said second set of parity-check symbols form a second parity row located in said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 3

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, by setting the parity-check symbol for each of the first set of parity-check symbols for each parity line equal to the modulo-2 p sum of the data symbols along each parity line, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells, and said first set of parity-check symbols forms a first parity row located in said parity-check memory cells; calculating a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, by setting the parity-check symbol for each of the second set of parity-check symbols for each parity line equal to the modulo-2 p sum of the data symbols and parity-check symbols along each parity line, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row, and said second set of parity-check symbols form a second parity row located in said parity-check memory cells; calculating at least a third set of parity-check symbols from the data symbols and parity-check symbols along a third set of parity lines, by setting the parity-check symbol for each of the third set of parity-check symbols for each parity line equal to the modulo-2 p sum of the data symbols and parity-check symbols along each parity line, wherein each parity line of the third set of parity lines has a path with a third slope traversing through said information-memory cells and through said first and second parity rows, and said third set of parity-check symbols form a third parity row located in said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 4

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, by setting the parity-check symbol for each of the first set of parity-check symbols for each parity line equal to the modulo-2 p sum of the data symbols along each parity line, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells, and said first set of parity-check symbols forms a first parity row located in said parity-check memory cells; calculating a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, by setting the parity-check symbol for each of the second set of parity-check symbols for each parity line equal to the modulo-2 p sum of the data symbols and parity-check symbols along each parity line, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row, and said second set of parity-check symbols form a second parity row located in said parity-check memory cells; calculating at least a third set of parity-check symbols from the data symbols and parity-check symbols along a third set of parity lines, by setting the parity-check symbol for each of the third set of parity-check symbols for each parity line equal to the modulo-2 p sum of the data symbols and parity-check symbols along each parity line, wherein each parity line of the third set of parity lines has a path with a third slope traversing through said information-memory cells and through said first and second parity rows, and said third set of parity-check symbols form a third parity row located in said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 5

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells; calculating at least a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 6

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells; calculating at least a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 7

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells; calculating a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said parity-check memory cells; calculating at least a third set of parity-check symbols from the data symbols and parity-check symbols along a third set of parity lines, wherein each parity line of the third set of parity lines has a path with a third slope traversing through said information-memory cells and through said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 8

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells; calculating a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said parity-check memory cells; calculating at least a third set of parity-check symbols from the data symbols and parity-check symbols along a third set of parity lines, wherein each parity line of the third set of parity lines has a path with a third slope traversing through said information-memory cells and through said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 9

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells; storing said first set of parity-check symbols in a first parity row located in said parity-check memory cells; calculating at least a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row; storing said second set of parity-check symbols in a second parity row located in said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 10

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells; storing said first set of parity-check symbols in a first parity row located in said parity-check memory cells; calculating at least a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row; storing said second set of parity-check symbols in a second parity row located in said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 11

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells; storing said first set of parity-check symbols in a first parity row located in said parity-check memory cells; calculating a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row; storing said second set of parity-check symbols in a second parity row located in said parity-check memory cells; calculating at least a third set of parity-check symbols from the data symbols and parity-check symbols along a third set of parity lines, wherein each parity line of the third set of parity lines has a path with a third slope traversing through said information-memory cells and through said first and second parity rows; storing said third set of parity-check symbols in a third parity row located in said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 12

A process for encoding a PASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells; storing said first set of parity-check symbols in a first parity row located in said parity-check memory cells; calculating a second set of parity-check symbols from the data symbols and parity-check symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row; storing said second set of parity-check symbols in a second parity row located in said parity-check memory cells; calculating at least a third set of parity-check symbols from the data symbols and parity-check symbols along a third set of parity lines, wherein each parity line of the third set of parity lines has a path with a third slope traversing through said information-memory cells and through said first and second parity rows; storing said third set of parity-check symbols in a third parity row located in said parity-check memory cells; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 13

The process of encoding a PASM error correcting and detecting code as set forth in claim 1, 2, 3, 4, 5, or 6, wherein the step of storing a block of a data-symbol sequence includes storing the data-symbol sequence in g rows by h columns of information-memory cells.

Claim 14

A process for encoding a TASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; calculating a first parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells by adding modulo 2 p the data symbols and parity-check symbols along the first parity path; storing said first parity-check symbol in a first parity row located in said parity-check memory cells; calculating a second parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope by adding modulo 2 p the data symbols and parity-check symbols along the second parity path, wherein said second parity path traverses through said first parity-check symbol; storing said second parity-check symbol in said second parity row; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check sequence.

Claim 15

A process for encoding a TASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; calculating a first parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells by adding modulo 2 p the data symbols and parity-check symbols along the first parity path; storing said first parity-check symbol in a first parity row located in said parity-check memory cells; calculating a second parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope by adding modulo 2 p the data symbols and parity-check symbols along the second parity path, wherein said second parity path traverses through said first parity-check symbol; storing said second parity-check symbol in said second parity row; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check sequence.

Claim 16

A process for encoding a TASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; calculating a first parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells by adding modulo 2 p the data symbols and parity-check symbols along the first parity path; storing said first parity-check symbol in a first parity row located in said parity-check memory cells; calculating a second parity-check symbols from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope by adding modulo 2 p the data symbols and parity-check symbols along the second parity path, wherein said second parity path traverses through said first parity-check symbol; storing said second parity-check symbol in said second parity row; calculating at least a third parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a third parity path having a third slope passing through the second parity-check row, and through the information memory cells and parity-check memory cells, by adding modulo 2 p the data symbols and parity-check symbols along the third parity path, wherein said third parity path traverses through said second parity-check symbol; storing said third parity-check symbol in a third parity row located in said parity-memory cells; and outputting an encoded-data symbol sequence.

Claim 17

A process for encoding a TASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; calculating a first parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells by adding modulo 2 p the data symbols and parity-check symbols along the first parity path; storing said first parity-check symbol in a first parity row located in said parity-check memory cells; calculating a second parity-check symbols from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope by adding modulo 2 p the data symbols and parity-check symbols along the second parity path, wherein said second parity path traverses through said first parity-check symbol; storing said second parity-check symbol in said second parity row; calculating at least a third parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a third parity path having a third slope passing through the second parity-check row, and through the information memory cells and parity-check memory cells, by adding modulo 2 p the data symbols and parity-check symbols along the third parity path, wherein said third parity path traverses through said second parity-check symbol; storing said third parity-check symbol in a third parity row located in said parity-memory cells; and outputting an encoded-data symbol sequence.

Claim 18

A process for encoding a TASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; calculating a first parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells; calculating at least a second parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope, wherein said second parity path traverses through said first parity-check symbol; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check sequence.

Claim 19

A process for encoding a TASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; calculating a first parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells; calculating at least a second parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope, wherein said second parity path traverses through said first parity-check symbol; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check sequence.

Claim 20

A process for encoding a TASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; calculating a first parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells; calculating a second parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope, wherein said second parity path traverses through said first parity-check symbol; calculating at least a third parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a third parity path having a third slope passing through the second parity-check row, and through the information memory cells and parity-check memory cells, wherein said third parity path traverses through said second parity-check symbol in the second parity row; and outputting an encoded-data symbol sequence.

Claim 21

A process for encoding a TASM error correcting and detecting code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; calculating a first parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells; calculating a second parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope, wherein said second parity path traverses through said first parity-check symbol; calculating at least a third parity-check symbol from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a third parity path having a third slope passing through the second parity-check row, and through the information memory cells and parity-check memory cells, wherein said third parity path traverses through said second parity-check symbol in the second parity row; and outputting an encoded-data symbol sequence.

Claim 22

The process for encoding a TASM error correcting and detecting code as set forth in claim 8, 9, 10, or 11, wherein the step of storing a block of a data-symbol sequence includes storing the data-symbol sequence in g rows by h columns of information memory cells.

Claim 23

A process for communicating in an ARQ system with the PASM FEC and detection code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first block of parity-check symbols from the data symbols along at least two sets of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope, and each parity line of the second set of parity lines has a path with a second slope, traversing through said information-memory cells; calculating at least a second block of parity-check symbols from the data symbols and parity-check symbols along at least a third set of parity lines, wherein each parity line of the third set of parity lines has a path with a third slope traversing through said information-memory cells and through said parity-check memory cells; and transmitting encoded-data-symbol sequence comprising the data-symbol sequence and the first block of parity-check symbols, over a communications channel having a feedback channel; storing the encoded-data-symbol sequence in receiver-memory means having receiver-information-memory cells and receiver-parity-memory cells, wherein said encoded-data-symbol sequence includes a received-parity-check-symbol sequence having received-parity-check symbols stored in the receiver-parity-memory cells, and a receiver-data-symbol sequence blocked and stored in the receiver-information-memory cells; finding the parity-check bits and the parity-line bits along the parity lines in receiver-information-memory cells, having an error; incrementing the count of each composite cell on a composite-error graph traversed by the path of each of the parity lines having an error; determining the largest-number cell in the composite-error graph having the largest number; comparing the largest number to a threshold; inverting, provided the largest number exceeds the threshold, the data bit in the receiver-information-memory cells corresponding to the largest-number cell in the composite-error graph having the largest number, thereby the new-data symbol minimizes the count in the largest-number cell; sending a retransmit request to the transmitter if some errors are not correctable; sending the second block of parity-check symbols over the communications channel; and using the second set of parity-check symbols, repeating the steps of finding the parity-check bits and the parity-line bits along the parity lines in the g rows by h columns of receiver-information-memory cells, having an error; incrementing the count of each composite cell on a composite-error graph traversed by the path of each of the parity lines having an error; determining the largest-number cell in the composite-error graph having the largest number; comparing the largest number to a threshold; inverting, provided the largest number exceeds the threshold, the data bit in the receiver-information-memory cells corresponding to the largest-number cell in the composite-error graph having the largest number, thereby the new-data symbol minimizes the count in the largest-number cell.

Claim 24

A process for communicating in an ARQ system with the PASM FEC and detection code comprising the steps of: storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information-memory cells and parity-check memory cells; calculating a first block of parity-check symbols from the data symbols along at least two sets of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope, and each parity line of the second set of parity lines has a path with a second slope, traversing through said information-memory cells; calculating at least a second block of parity-check symbols from the data symbols and parity-check symbols along at least a third set of parity lines, wherein each parity line of the third set of parity lines has a path with a third slope traversing through said information-memory cells and through said parity-check memory cells; and transmitting encoded-data-symbol sequence comprising the data-symbol sequence and the first block of parity-check symbols, over a communications channel having a feedback channel; storing the encoded-data-symbol sequence in receiver-memory means having receiver-information-memory cells and receiver-parity-memory cells, wherein said encoded-data-symbol sequence includes a received-parity-check-symbol sequence having received-parity-check symbols stored in the receiver-parity-memory cells, and a receiver-data-symbol sequence blocked and stored in the receiver-information-memory cells; finding the parity-check bits and the parity-line bits along the parity lines in receiver-information-memory cells, having an error; incrementing the count of each composite cell on a composite-error graph traversed by the path of each of the parity lines having an error; determining the largest-number cell in the composite-error graph having the largest number; comparing the largest number to a threshold; inverting, provided the largest number exceeds the threshold, the data bit in the receiver-information-memory cells corresponding to the largest-number cell in the composite-error graph having the largest number, thereby the new-data symbol minimizes the count in the largest-number cell; sending a retransmit request to the transmitter if some errors are not correctable; sending the second block of parity-check symbols over the communications channel; and using the second set of parity-check symbols, repeating the steps of finding the parity-check bits and the parity-line bits along the parity lines in the g rows by h columns of receiver-information-memory cells, having an error; incrementing the count of each composite cell on a composite-error graph traversed by the path of each of the parity lines having an error; determining the largest-number cell in the composite-error graph having the largest number; comparing the largest number to a threshold; inverting, provided the largest number exceeds the threshold, the data bit in the receiver-information-memory cells corresponding to the largest-number cell in the composite-error graph having the largest number, thereby the new-data symbol minimizes the count in the largest-number cell.

Claim 25

A PASM error correcting and detecting code encoding apparatus comprising: memory means coupled to a data source for storing a block of a data-symbol sequence; and processor means coupled to said memory means for calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells, and said first set of parity-check symbols forms a first parity row located in said parity-check memory cells, calculating at least a second set of parity-check symbols from the data symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row, and said second set of parity-check symbols form a second parity row located in said parity-check memory cells, and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 26

A PASM error correcting and detecting code encoding apparatus comprising: memory means coupled to a data source for storing a block of a data-symbol sequence; and processor means coupled to said memory means for calculating a first set of parity-check symbols from the data symbols along a first set of parity lines, wherein each parity line of the first set of parity lines has a path with a first slope traversing through said information-memory cells, and said first set of parity-check symbols forms a first parity row located in said parity-check memory cells, calculating at least a second set of parity-check symbols from the data symbols along a second set of parity lines, wherein each parity line of the second set of parity lines has a path with a second slope traversing through said information-memory cells and through said first parity row, and said second set of parity-check symbols form a second parity row located in said parity-check memory cells, and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check symbols.

Claim 27

A TASM error correcting and detecting code encoding apparatus comprising: memory means coupled to a data source for storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; and processor means for calculating a first set of parity-check symbols from data symbols located in the information memory cells, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells by adding modulo 2 p the data symbols and parity-check symbols along the first parity path; storing said first set of parity-check symbols in a first parity row located in said parity-check memory cells; calculating at least a second set of parity-check symbols from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope by adding modulo 2 p the data symbols and parity-check symbols along the second parity path, wherein said second parity-check symbols are located at said second slope with reference to the first parity-check symbols, in a second parity row located in said parity-check memory cells; storing said second parity-check symbols in said second parity row; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check sequence.

Claim 28

A TASM error correcting and detecting code encoding apparatus comprising: memory means coupled to a data source for storing a block of a data-symbol sequence having data symbols with p-bits per symbol, in memory means having information memory cells and parity-check memory cells; and processor means for calculating a first set of parity-check symbols from data symbols located in the information memory cells, along a first parity path having a first slope passing through the information memory cells and parity-check memory cells by adding modulo 2 p the data symbols and parity-check symbols along the first parity path; storing said first set of parity-check symbols in a first parity row located in said parity-check memory cells; calculating at least a second set of parity-check symbols from data symbols and parity-check symbols located in the information memory cells and parity-check memory cells, respectively, along a second parity path having a second slope by adding modulo 2 p the data symbols and parity-check symbols along the second parity path, wherein said second parity-check symbols are located at said second slope with reference to the first parity-check symbols, in a second parity row located in said parity-check memory cells; storing said second parity-check symbols in said second parity row; and outputting an encoded-data-symbol sequence comprising the data-symbol sequence and the parity-check sequence.