Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: A method of encoding data for transmission from a source to a destination over a communications channel is provided. A plurality of redundant symbols are generated from an ordered set of input symbols to be transmitted. A plurality of output symbols are generated from a combined set of symbols including the input symbols and the redundant symbols, wherein the number of possible output symbols is much larger than the number of symbols in the combined set of symbols, wherein at least one output symbol is generated from more than one symbol in the combined set of symbols and from less than all of the symbols in the combined set of symbols, and such that the ordered set of input symbols can be regenerated to a desired degree of accuracy from any predetermined number, N, of the output symbols.

Abstract: 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.

Abstract: Signaling the sending of source blocks within multiple physical layer blocks is done for both streaming and object delivery applications, using minimal additional overhead, and in some cases no overhead, to signal interleaved source blocks within a physical layer block, signaling how symbols are related to the source blocks from which they are generated, and signaled sending and indications of prioritized data for source blocks. Organizing and sending streams over one more channels can be done to improve the quality of delivered streams, while minimizing or improving the needed amount of channel resources and receiver power resources needed.

Abstract: Disclosed is a method for wireless signal transmission of signals from an array of two or more antennas, in which each signal to be transmitted is selected from a constellation of unitary space-time signals. Each unitary space-time signal is a unitary matrix, in which each column represents a respective antenna, each row represents a respective time interval, and each element represents a complex amplitude to be transmitted by a given antenna during a given time interval. In specific embodiments of the invention, the matrices of the signal constellation form a non-Abelian group having a positive diversity product, or a coset of such a group. In other embodiments, the signal constellation is a subset of such a group, and its multiplicative closure forms a finite non-Abelian group having a positive diversity product.

Abstract: A method and apparatus for efficient list decoding of Reed-Solomon error correction codes. A polynomial for a predetermined target list size combining points of an error code applied to a message and points of a received word is determined for a k dimensional error correction code by a displacement method. The displacement method finds a nonzero element in the kernel of a structured matrix which determines the polynomial. From roots of the polynomial, it is determined if the number of errors in the code word is smaller than a predetermined number of positions for generating a list of candidate code words meeting the error condition. In one embodiment, parallel processing is used for executing the displacement method. The invention will be more fully described by reference to the following drawings.

Abstract: 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.

Abstract: 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.

Abstract: 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.