A method for generating an LDPC (low-density parity check) code with a required error floor, comprising: using a parity generation circuit to generate an LDPC code; using a detection circuit to detect the LDPC code according to a plurality of trapping set cores in a database and to generate at least one piece of trapping-set-core information; using a verification circuit to perform an important sampling simulation according to the LDPC code and each trapping-set-core information separately to obtain an estimated error floor for each trapping-set-core information; using the verification circuit to separately compare each of the estimated error floors with an expected error floor; and when all of the estimated error floors are lower than or equal to the expected error floor, using the verification circuit to output the LDPC code.

A method for generating an LDPC (low-density parity check) code with a required error floor, comprising: using a parity generation circuit to generate an LDPC code; using a detection circuit to detect the LDPC code according to a plurality of trapping set cores in a database and to generate at least one piece of trapping-set-core information; using a verification circuit to perform an important sampling simulation according to the LDPC code and each trapping-set-core information separately to obtain an estimated error floor for each trapping-set-core information; using the verification circuit to separately compare each of the estimated error floors with an expected error floor; and when all of the estimated error floors are lower than or equal to the expected error floor, using the verification circuit to output the LDPC code.

A method of near-lossless universal data compression using correlated data sequences includes detecting first target surroundings via a first sensor, encoding a first data sequence indicative of the detected target surroundings, and communicating to an electronic controller, the encoded first data sequence. The method additionally includes detecting the first target surroundings via a second sensor, and encoding a second data sequence indicative of the target surroundings detected by the second sensor. The method also includes communicating the encoded second data sequence to the controller. The method additionally includes decoding, via the controller, the encoded first and second data sequences. The method also includes, via the controller, determining a statistical correlation between the decoded first and second data sequences and formulating a mapping function having reduced cardinality and indicative of the determined statistical correlation. Furthermore, the method includes feeding back the mapping function by the controller to the first processor.

A method of near-lossless universal data compression using correlated data sequences includes detecting first target surroundings via a first sensor, encoding a first data sequence indicative of the detected target surroundings, and communicating to an electronic controller, the encoded first data sequence. The method additionally includes detecting the first target surroundings via a second sensor, and encoding a second data sequence indicative of the target surroundings detected by the second sensor. The method also includes communicating the encoded second data sequence to the controller. The method additionally includes decoding, via the controller, the encoded first and second data sequences. The method also includes, via the controller, determining a statistical correlation between the decoded first and second data sequences and formulating a mapping function having reduced cardinality and indicative of the determined statistical correlation. Furthermore, the method includes feeding back the mapping function by the controller to the first processor.

An encoding circuit includes an allocator configured to allocate symbols among a plurality of symbols within a constellation of multilevel modulation and correspond to values of a plurality of bit strings, a converter configured to convert values of each of bit strings excluding a first bit string so that, as a region within the constellation is closer to the center of the constellation, the number of symbols allocated in the region is larger, a switch configured to switch between a first time period in which a first error correction code is inserted and a second time period in which the first error correction code is not inserted, and an insertor configured to generate the first error correction code from a second bit string in the second time period and inserts the first error correction code in two or more bit strings in the first time period according to the switching.

An encoding circuit includes an allocator configured to allocate symbols among a plurality of symbols within a constellation of multilevel modulation and correspond to values of a plurality of bit strings, a converter configured to convert values of each of bit strings excluding a first bit string so that, as a region within the constellation is closer to the center of the constellation, the number of symbols allocated in the region is larger, a switch configured to switch between a first time period in which a first error correction code is inserted and a second time period in which the first error correction code is not inserted, and an insertor configured to generate the first error correction code from a second bit string in the second time period and inserts the first error correction code in two or more bit strings in the first time period according to the switching.

A spectrum coding method includes quantizing spectral data of a current band based on a first quantization scheme, generating a lower bit of the current band using the spectral data and the quantized spectral data, quantizing a sequence of lower bits including the lower bit of the current band based on a second quantization scheme, and generating a bitstream based on a upper bit excluding N bits, where N is 1 or greater, from the quantized spectral data and the quantized sequence of lower bits.

A spectrum coding method includes quantizing spectral data of a current band based on a first quantization scheme, generating a lower bit of the current band using the spectral data and the quantized spectral data, quantizing a sequence of lower bits including the lower bit of the current band based on a second quantization scheme, and generating a bitstream based on a upper bit excluding N bits, where N is 1 or greater, from the quantized spectral data and the quantized sequence of lower bits.

The disclosure discloses an algebraic decoding method and a decoder for a (n, n(n1), n1) permutation group code in a communication modulation system. The basic principle of the decoding method is: assuming that two code elements p(r.sub.1)=s.sub.1 and p(r.sub.2)=s.sub.2 can be correctly detected in a received real vector with a length of n, including their element values s.sub.1, s.sub.2 and position indices r.sub.1, r.sub.2 in the vector, an intermediate parameter w is determined by solving an equation (r.sub.1r.sub.2)w=(s.sub.1s.sub.2)(mod n); and each code element is calculated by w according to p(i)=(s.sub.1+(nr.sub.1+i)w)(mod n), i=1, 2, . . . , n. The decoder is mainly composed of multiple n-dimensional registers, a w calculator, n code element calculators, and a code element buffer. In the disclosure, in a case where a receiver only correctly detects two code elements in a transmitted codeword with a length of n, the codeword can be correctly decoded by using the received information of the two code elements.

Disclosed herein are techniques to provide forward error correction for a high-speed interconnect symbol stream, such as, DisplayPort. The symbol stream may be split into FEC blocks and parity bits generated for each of the FEC blocks. The parity bits may be interleaved, encoded, and transmitted over an interconnect along with the symbol stream to provide forward error correction for the symbol stream.