Methods and systems are described for obtaining a plurality of information bits, and responsively partitioning the obtained plurality of information bits into a plurality of subsets of information bits, generating a plurality of streams of forward error correction (FEC)-encoded bits using a plurality of FEC encoders receiving respective subsets of the plurality of subsets of information bits, providing the plurality of streams of FEC-encoded bits to a plurality of sub-channel encoders, each sub-channel encoder receiving a respective stream of FEC-encoded bits from a different FEC encoder of the plurality of FEC encoders for generating a set of codewords of a vector signaling code, and wherein sequential streams of FEC-encoded bits from a given FEC encoder are provided to different sub-channel encoders for each successively generated set of codewords, and transmitting the successively generated sets of codewords of the vector signaling code over a multi-wire bus.

The present invention is directed to communication systems and methods. In a specific embodiment, the present invention provides a receiver that includes an error correction module. A syndrome value, calculated based on received signals, may be used to enable the error correction module. The error correction module includes an error generator, a Nyquist error estimator, and a decoder. The decoder uses error estimation generated by the Nyquist error estimator to correct the decoded data. There are other embodiments as well.

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 method includes receiving a first data frame and a second data frame from a communication channel; decoding the first data frame using a first portion of an extended parity-check matrix (PCM); and decoding the second data frame using a second portion of the extended PCM. The first portion is a subset of the second portion.

A method includes authenticating, by a computing device, a first connection between one or more storage units and at least one of the computing device and a first user computing device. The method further includes determining, by the computing device, to add a second connection between the one or more storage units and at least one of the computing device and a second user computing device. The method further includes generating, by the computing device, a secret code and sending the secret code to the one or more storage units via the first connection. The method further includes sending, by the one or more storage units, responses to the secret code to the computing device via the second connection. The method further includes authenticating, by the computing device, the second connection based on the authentication of the first connection and the responses from the one or more storage units.

As system is provided for performing a method of receiving a superposition state defined by a sum of a plurality of addends, wherein each addend of the plurality of addends is a product between a corresponding coefficient of a plurality of coefficients and a corresponding state of a plurality of states encoded with block unary encoding. The system may identify at least one error state, of the plurality of states, having a string value that is not a block unary code string of a set of block unary code strings. The system may compute an updated superposition state based on the plurality of states without the error state.

A node receives transmissions associated with a given set of information bits, wherein each of the transmissions use a different polar code and share one or more information bits of the given set of information bits. The node determines, at each of a plurality of polar decoders of the node, soft information for each information bit included in an associated one of the transmissions, wherein each of the plurality of polar decoders is associated with a different transmission of the transmissions. The node provides, from each polar decoder of the plurality to one or more other polar decoders of the plurality, the determined soft information for any information bits shared by their respective associated transmissions, and uses the provided soft information in an iterative decoding process to decode one or more of the received transmissions.

A receiver is provided. The receiver includes: a first decoder configured to decode a superposition-coded signal by using a parity check matrix to generate Low Density Parity Check (LDPC) information word bits and first parity bits corresponding to a first layer signal; an encoder configured to encode the LDPC information word bits and the first parity bits to generate second parity bits, or encode the LDPC information word bits to generate the first parity bits and the second parity bits, by using the parity check matrix; and a second decoder configured to decode a signal which is generated by removing the first layer signal, corresponding to the LDPC information word bits, the first parity bits, and the second parity bits, from the superposition-coded signal, to reconstruct bits transmitted through the second layer signal.

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.