Qualcomm Incorporated

Other

Digital Equipment Corporation

Compaq Computer Corporation, Inc.

Digital Fountain, Inc.

Mohammad Amin Shokrollahi

Michael G Luby

Lorenz Christoph Minder

Michael David Mitzenmacher

Daniel A Spielman

Volker Stemann

Mark Watson

Payam Pakzad

Lorenzo Vicisano

Encoding of a plurality of encoded symbols is provided wherein an encoded symbol is generated from a combination of a first symbol generated from a first set of intermediate symbols and a second symbol generated from a second set of intermediate symbols, each set having at least one different coding parameter, wherein the intermediate symbols are generated based on the set of source symbols. A method of decoding data is also provided, wherein a set of intermediate symbols is decoded from a set of received encoded symbols, the intermediate symbols organized into a first and second sets of symbols for decoding, wherein intermediate symbols in the second set are permanently inactivated for the purpose of scheduling the decoding process to recover the intermediate symbols from the encoded symbols, wherein at least some of the source symbols are recovered from the decoded set of intermediate symbols.

Methods and apparatus employing FEC codes with permanent inactivation of symbols for encoding and decoding processes

Data can be encoded by assigning source symbols to base blocks, assigning base blocks to source blocks and encoding each source block into encoding symbols, where at least one pair of source blocks is such they have at least one base block in common with both source blocks of the pair and at least one base block not in common with the other source block of the pair. The encoding of a source block can be independent of content of other source blocks. Decoding to recover all of a desired set of the original source symbols can be done from a set of encoding symbols from a plurality of source blocks wherein the amount of encoding symbols from the first source block is less than the amount of source data in the first source block and likewise for the second source block.

Encoding and decoding using elastic codes with flexible source block mapping

A method of encoding data into a chain reaction code includes generating a set of input symbols from input data. Subsequently, one or more non-systematic output symbols is generated from the set of input symbols, each of the one or more non-systematic output symbols being selected from an alphabet of non-systematic output symbols, and each non-systematic output symbol generated as a function of one or more of the input symbols. As a result of this encoding process, any subset of the set of input symbols is recoverable from (i) a predetermined number of non-systematic output symbols, or (ii) a combination of (a) input symbols which are not included in the subset of input symbols that are to be recovered, and (b) one or more of the non-systematic output symbols.

Systematic encoding and decoding of chain reaction codes

A system, computer program, and/or method for encoding data that can correct r/2 errors. The original symbols are transformed using a Fourier transform of length p. Generator polynomials are used to encode the p blocks separately, and an inverse Fourier transform is applied to obtain the redundant symbol. In a decoding system, Fourier transforms are applied to every set of p consecutive symbols of the received vector, to obtain p blocks of symbols which in total have the same size as the received vector. Next, a syndrome calculator is applied to each of these blocks to produce p syndromes. The syndromes are forwarded to a Berlekamp-Massey unit and an error locator polynomial is decimated into p parts and a Chien search is applied concurrently. A Fourier transform of length p is applied to values calculated by the Chien search, and the positions of the zeros obtained are error positions.

Encoding and decoding of generalized Reed-Solomon codes using parallel processing techniques

A method of encoding data for transmission from a source to a destination over a communications channel is provided. A plurality of encoded symbols are generated from a set of input symbols including source symbols and redundant symbols, wherein the input symbols are organized such that at least one of the input symbols is not used for a first encoding process, so that it is permanently inactivated for the purposes of scheduling a decoding process. A method of decoding data is also provided, wherein encoded symbols generated from a set of input symbols are used to recover source symbols, wherein the input symbols are organized such that at least one of the input symbols is not used for a first decoding process, so that it is permanently inactivated for the purpose of scheduling the decoding process.

An encoded message, includes a plurality of data items and a plurality of redundant data items. Each of the plurality of redundant data items corresponds to a number of the data items, with respective redundant data items corresponding to different numbers of data items.

Message encoding with irregular graphing

A method of encoding a message including a plurality of data items, includes identifying maximum and minimum numbers of first edges to be associated with data items. A first distribution of different numbers of first edges, ranging from the maximum to the minimum number of first edges, to be associated with the data items is computed. A first associated number of first edges, within the range, is established for each data item, the different numbers of first edges being associated with the data items according to the computed first distribution. A maximum and minimum number of second edges to be associated with redundant data items are identified. A second distribution of numbers of second edges, ranging from the maximum to the minimum number of second edges, to be associated with the redundant data items is computed. An associated number of second edges, within the range, is established for each redundant data item, the different numbers of second edges being associated with the redundant data items according to the determined second distribution. A threshold number of potentially lost/corrupted data items is established. An encoded message is formed with the redundant data items associated with the data items according to the first distribution and with the data items associated with the redundant data items according to the second distribution only if the number of data items which are recoverable or correctable exceeds the threshold.

Irregularly graphed encoding technique

An encoded message includes a plurality of data items and a plurality of redundant data items. Each of the redundant data items is associated with more than one of the data items. To decode the encoded message, a reduced first redundant data item is reduced to correspond to only one data item. This data item is replaced with the reduced first redundant data item. A second redundant data item is reduced, using the replaced data item, to correspond to only a second of data item. The second data item is replaced with the second redundant data item to decode the encoded message.

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Preverenges, Switzerland

Mohammad Amin Shokrollahi