Message encoding with irregular graphing

Claim 1

A method for encoding a message having a plurality of data items, comprising the steps of: forming a plurality of redundant data items including a first redundant data item and a second redundant data item; forming the first redundant data item to correspond to a first number of data items within the plurality of data items; forming the second redundant data item to correspond to a second number of data items within the plurality of data items, the first number being different than the second number; and encoding the plurality of data items with the plurality of redundant data items; wherein particular ones of the plurality of data items to which the first redundant data item corresponds are selected randomly; and wherein particular ones of the plurality of data items to which the second redundant data item corresponds are selected randomly; and further wherein each of the plurality of redundant data items are formed to correspond to a number of the plurality of data items within a range of numbers, and particular data items within the plurality of data items to which each of the redundant data items corresponds are selected randomly.

Claim 2

A method for encoding a message having a plurality of data items, comprising the steps of: forming a plurality of redundant data items including a first redundant data item and a second redundant data item; forming the first redundant data item to correspond to a first number of data items within the plurality of data items; forming the second redundant data item to correspond to a second number of data items within the plurality of data items, the first number being different than the second number; and encoding the plurality of data items with the plurality of redundant data items; wherein particular ones of the plurality of data items to which the first redundant data item corresponds are selected randomly; and wherein particular ones of the plurality of data items to which the second redundant data item corresponds are selected randomly; and further wherein each of the plurality of redundant data items are formed to correspond to a number of the plurality of data items within a range of numbers, and particular data items within the plurality of data items to which each of the redundant data items corresponds are selected randomly.

Claim 8

A method of encoding a message having a plurality of data items, comprising the steps of: identifying a maximum number of redundant data items and a minimum number of redundant data items to be associated with each data item within the plurality of data items; establishing a number of redundant data items to be associated with each data item within the plurality of data items, the number associated with each data item equaling at least the minimum number of redundant data items and no more than the maximum number of redundant data items, a first data item having a first number of redundant data items associated therewith and a second data item having a second number of redundant data items, different than the first number of redundant data items, associated therewith; forming a plurality of redundant data items, each of the plurality of redundant data items corresponding to the associated data items within the plurality of data items; and encoding a message with the plurality of redundant data items; wherein the number of redundant data items associated with each data item within the plurality of data items is established such that data items within a first fractional portion of the plurality of data items have the first number of redundant data items associated therewith and data items within a second fractional portion of the plurality of data items have the second number of redundant data items associated therewith; and wherein the maximum number of redundant data items equals D+1; a numeric N=1+(1/D); the first number of redundant data items equals i; the second number of redundant data items equals i'; the first fractional portion of the plurality of data items is computed by N/[i(i-1)]; and the second fractional portion of the plurality of data items is computed by N/[i'(i'-1)].

Claim 9

A method of encoding a message having a plurality of data items, comprising the steps of: identifying a maximum number of redundant data items and a minimum number of redundant data items to be associated with each data item within the plurality of data items; establishing a number of redundant data items to be associated with each data item within the plurality of data items, the number associated with each data item equaling at least the minimum number of redundant data items and no more than the maximum number of redundant data items, a first data item having a first number of redundant data items associated therewith and a second data item having a second number of redundant data items, different than the first number of redundant data items, associated therewith; forming a plurality of redundant data items, each of the plurality of redundant data items corresponding to the associated data items within the plurality of data items; and encoding a message with the plurality of redundant data items; wherein the number of redundant data items associated with each data item within the plurality of data items is established such that data items within a first fractional portion of the plurality of data items have the first number of redundant data items associated therewith and data items within a second fractional portion of the plurality of data items have the second number of redundant data items associated therewith; and wherein the maximum number of redundant data items equals D+1; a numeric N=1+(1/D); the first number of redundant data items equals i; the second number of redundant data items equals i'; the first fractional portion of the plurality of data items is computed by N/[i(i-1)]; and the second fractional portion of the plurality of data items is computed by N/[i'(i'-1)].

Claim 19

A system comprising: an encoder for generating an encoded message, the encoded message comprising a plurality of data items and a plurality of redundant data items, a first of the plurality of redundant data items is associated with a first number of individual data items in the plurality of data items and a second of the plurality of redundant data items is associated with a second number of individual data items in the plurality of data items; and a transmitter connected to the encoder, the transmitter for transmitting the encoded message; wherein the first number of individual data items is different from the second number of individual data items and wherein the first number of individual data items is randomly selected; and further wherein the encoded message comprises: a second plurality of redundant data items, wherein a first of the second plurality of redundant data items is associated with a third number of individual data items in the plurality of redundant data items and a second of the plurality of redundant data items is associated with a fourth number of individual data items in the plurality of redundant data items wherein the third number of individual data items is different from the fourth number of individual data items.

Claim 20

A system comprising: an encoder for generating an encoded message, the encoded message comprising a plurality of data items and a plurality of redundant data items, a first of the plurality of redundant data items is associated with a first number of individual data items in the plurality of data items and a second of the plurality of redundant data items is associated with a second number of individual data items in the plurality of data items; and a transmitter connected to the encoder, the transmitter for transmitting the encoded message; wherein the first number of individual data items is different from the second number of individual data items and wherein the first number of individual data items is randomly selected; and further wherein the encoded message comprises: a second plurality of redundant data items, wherein a first of the second plurality of redundant data items is associated with a third number of individual data items in the plurality of redundant data items and a second of the plurality of redundant data items is associated with a fourth number of individual data items in the plurality of redundant data items wherein the third number of individual data items is different from the fourth number of individual data items.