A hybrid decoding method and a gigabit Ethernet receiver using the same are provided. The hybrid decoding method and the gigabit Ethernet receiver detect and determine error propagation due to burst interference in a currently used main P-tap parallel decision feedback decoder, decode an Ethernet data stream using a trellis coded modulation (TCM) decoder, and determine a follow-up main decoding algorithm according to the decoded results of the two decoders in the same time interval to effectively prevent error propagation due to burst interference.

Methods and systems adapted for providing forward error correction for data packets containing a relationship between the data in each data packet. Data packets encoded in one error correction coding scheme are received and a second error correction coding scheme is identified based on the relationship between the data in each data packet. The data packets are then decoded using the second error correction coding scheme.

Disclosed is a three-dimensional TPC decoding apparatus. A three-dimensional TPC decoding apparatus includes an X decoder which decodes an X axis of an m-th upper half layer based on decoding results of a Y axis and a Z axis of an m1-th upper half layer; a Y decoder which decodes a Y axis of an m-th lower half layer based on decoding results of an X axis and a Z axis of an m1-th lower half layer; and a Z decoder which decodes a Z axis based on a decoding result of the Y axis of an m-th upper half layer and a decoding result of the X axis of an m-th lower half layer.

Devices, systems and methods for list decoding of polarization-adjusted convolutional (PAC) codes are described. One example method for improving error correction in a decoder for data in a communication channel includes receiving a noisy codeword, the codeword having been generated using a polarization-adjusted convolutional (PAC) code and provided to the communication channel prior to reception by the decoder, and performing PAC list decoding on the noisy codeword, wherein an encoding operation of the PAC code comprises a convolutional precoding operation that generates one or more dynamically frozen bits, and wherein the PAC list decoding comprises extending, based on the one or more dynamically frozen bits, at least two paths of a plurality of paths in the PAC list decoding differently and independently.

A hybrid decoding method and a gigabit Ethernet receiver using the same are provided. The hybrid decoding method and the gigabit Ethernet receiver detect and determine error propagation due to burst interference in a currently used main P-tap parallel decision feedback decoder, decode an Ethernet data stream using a trellis coded modulation (TCM) decoder, and determine a follow-up main decoding algorithm according to the decoded results of the two decoders in the same time interval to effectively prevent error propagation due to burst interference.

Technologies for providing efficient error correction with half product codes include an apparatus having a memory to store data and a controller to manage read and write operations of the memory. The controller is to obtain, in response to a write request, data to write to the memory. The controller is further to encode the data with a half product code to define a matrix that includes at least one matrix element based on a soft decision error correction encoder algorithm and at least one other matrix element based on a hard decision error correction encoder algorithm. Additionally, the controller is to write the half product code to the memory.

Technologies for providing efficient error correction with half product codes include an apparatus having a memory to store data and a controller to manage read and write operations of the memory. The controller is to obtain, in response to a write request, data to write to the memory. The controller is further to encode the data with a half product code to define a matrix that includes at least one matrix element based on a soft decision error correction encoder algorithm and at least one other matrix element based on a hard decision error correction encoder algorithm. Additionally, the controller is to write the half product code to the memory.

A method for transmitting data using a convolutional turbo code (CTC) encoder. Specifically, the method comprises: encoding input data bits, which have been input through two input ports of the CTC encoder; interleaving the input data bits using four CTC interleaver parameters P.sub.0, P.sub.1, P.sub.2 and P.sub.3 corresponding to sizes of the input data bits; encoding the interleaved data bits; and selectively transmitting the input data bits, the first encoded bits and the second encoded bits, in accordance with a predetermined coding rate. Here, P.sub.0 is a relative prime number to N, which is of the size of each of the input data bits, P.sub.2 has a value of N1, and an absolute value of a difference between P.sub.1 and P.sub.3 is 1.

This disclosure describes systems and methods for detecting multiple insertion and deletion errors in the presence of substitution errors in a signal (such as a sequenced DNA string). A convolutional code that includes two or more component convolutional codes is used for encoding. Each of the two or more component convolutional codes generates only a subset of all possible outputs of the convolutional code. The subsets of the two or more component convolutional codes are disjoint from each other. Only one of the two or more convolutional codes is active at any given time. The two or more convolutional codes together define a super code. The two or more convolutional codes are time interlaced within the super code, and the super code defines the convolutional code. A trellis that includes two or more component trellises designed based on the two or more component convolutional codes is used for decoding.

Devices, systems and methods for list decoding of polarization-adjusted convolutional (PAC) codes are described. One example method for improving error correction in a decoder for data in a communication channel includes receiving a noisy codeword, the codeword having been generated using a polarization-adjusted convolutional (PAC) code and provided to the communication channel prior to reception by the decoder, and performing PAC list decoding on the noisy codeword, wherein an encoding operation of the PAC code comprises a convolutional precoding operation that generates one or more dynamically frozen bits, and wherein the PAC list decoding comprises extending, based on the one or more dynamically frozen bits, at least two paths of a plurality of paths in the PAC list decoding differently and independently.