In an illustrative example, a method includes receiving data that includes a set of data symbols. The method further includes generating a set of parity symbols based on the set of data symbols using an erasure correcting code. The set of parity symbols includes at least a first parity symbol that is generated based on a first proper subset of the set of data symbols. The first parity symbol enables recovery of a data symbol of the first proper subset independently of a second proper subset of the set of data symbols.

The present disclosure is based on erasure coding, information dispersal, secret sharing and ramp schemes to assure reliability and security. More precisely, the present disclosure combines ramp threshold secret sharing and systematic erasure coding.

Methods and apparatus for transmitting and receiving broadcast signals are provided. The method for transmitting a broadcast signal includes encoding mobile data for forward error correction (FEC), encoding signaling data, forming data groups including the encoded mobile data and the encoded signaling data and transmitting a signal frame that includes the data groups.

A memory controller system includes error correction circuitry and erasure decoder circuitry. A retry flow is triggered when the memory controller's error checking and correction (ECC) detects an uncorrectable codeword. Error correction circuitry generates erasure codewords from the codeword with uncorrectable errors. The memory controller computes the syndrome weight of the erasure codewords. For example, the erasure decoder circuitry receives the erasure codewords and computes the syndrome weights. Error correction circuitry orders the erasure codewords based on their corresponding syndrome weights. Then error correction circuitry selects a subset of the codewords, and sends them to erasure decoder circuitry. Erasure decoder circuitry receives the selected codewords and decodes them.

Distributed storage systems frequently use a centralized metadata repository that stores metadata in an eventually consistent distributed database. However, a metadata repository cannot be relied upon for determining which erasure coded fragments are lost because of a storage node(s) failures. Instead, when recovering a failed storage node, a list of missing fragments is generated based on fragments stored in storage devices of available storage nodes. A storage node performing the recovery sends a request to one or more of the available storage nodes for a fragment list. The fragment list is generated, not based on a metadata database, but on scanning storage devices for fragments related to the failed storage node. The storage node performing the recovery merges retrieved lists to create a master list indicating fragments that should be regenerated for recovery of the failed storage node(s).

A packet processing method includes generating, by a processor of a network device, a first encoding task based on M original packets in a to-be-processed first data stream, where M is a positive integer, and where the first encoding task instructs to encode the M original packets; and performing, by a target hardware engine of the network device and based on the first encoding task, forward error correction (FEC) encoding on the M original packets to obtain R redundant packets, where R is a positive integer.

An accelerated erasure coding system includes a processing core for executing computer instructions and accessing data from a main memory, and a non-volatile storage medium for storing the computer instructions. The processing core, storage medium, and computer instructions are configured to implement an erasure coding system, which includes: a data matrix for holding original data in the main memory; a check matrix for holding check data in the main memory; an encoding matrix for holding first factors in the main memory, the first factors being for encoding the original data into the check data; and a thread for executing on the processing core. The thread includes: a parallel multiplier for concurrently multiplying multiple entries of the data matrix by a single entry of the encoding matrix; and a first sequencer for ordering operations through the data matrix and the encoding matrix using the parallel multiplier to generate the check data.

A reliable data transmission method and system based on a predicted amount of data in a vehicle-to-infrastructure (V2I) network is disclosed. A data transmission method of a base station includes determining a maximum amount of data to be transmitted from the base station disposed around a road to a vehicle traveling on the road, determining an encoding number for systematic network coding (SNC) based on the determined amount of data, performing the SNC on original data based on the encoding number and the amount of data, and transmitting encoded data obtained by performing the SNC to the vehicle.

Multistep recovery of chunk fragments of a peer group employing hierarchical erasure coding for geographically diverse data storage protection is disclosed. A peer group of chunks can employ zone-level erasure coding of chunks that can each employ chunk-level erasure coding. In a first iteration, fragment recovery can be performed across peer group chunks based on the zone-level erasure coding. Subsequently, the first iteration can perform recovery of other fragments within a chunk based on the chunk-level erasure coding. Where additional fragments are to be recovered, subsequent iterations can be performed. The disclosed multistep recovery can enable recovery of fragments that would typically have been considered unrecoverable via conventional techniques. Additionally, multistep recovery can enable recovery of fragments across a peer group of chunks that can be more computing resource efficient than recovery of chunks across the peer group of chunks.

A method for data communication between a first node and a second node includes forming one or more redundancy messages from data messages at the first node using an error correcting code and transmitting first messages from the first node to the second node over a data path, the transmitted first messages including the data messages and the one or more redundancy messages. Second messages are received at the first node from the second node, which are indicative of: (i) a rate of arrival at the second node of the first messages, and (ii) successful and unsuccessful delivery of the first messages. A transmission rate limit and a window size are maintained according to the received second messages. Transmission of additional messages from the first node to the second node is limited according to the maintained transmission rate limit and window size.