A method, apparatus, and non-transitory computer-readable recording medium for generating an algebraic Spatially-Coupled Low-Density Parity-Check (SC LDPC) code are provided. The method includes selecting an LDPC block code over a finite field GF(q) with a girth of at least 6; constructing a parity-check matrix H from the selected LDPC block code; replicating H a user-definable number of times to form a two-dimensional array H.sub.rep; constructing a masking matrix W with a user-definable spatially-coupled pattern; and masking a sub-matrix of H.sub.rep using W to obtain a spatially-coupled parity-check matrix H.sub.SC, wherein a null space of H.sub.SC is the algebraic SC LDPC code.

A decoder having an input configured to receive a sequence of softbits presumed to correspond to a convolutionally-encoded codeword; and a decoding circuit configured to: determine, as part of a decoding process, a Maximum Likelihood (ML) survivor path in a trellis representation of the codeword; determine whether the presumed convolutionally-encoded codeword meets an early-termination criteria; and abort the decoding process if the presumed convolutionally-encoded codeword meets the early-termination criteria, continue the decoding process if the presumed convolutionally-encoded codeword fails to meet the early-termination criteria.

A transmission apparatus includes an encoder that codes a data sequence with a parity check matrix, wherein the data sequence includes a final information bit sequence and virtual information bits, and outputs the final information bit sequence and a parity sequence, as LDPC codes, and a transmitter that transmits the LDPC codes as a transmission data. A column length of the parity check matrix is longer than a total length of the final information bit sequence and the parity sequence, by a length of the virtual information bits that are set to 0 and are not transmitted. The total length of the final information bit sequence and the parity sequence has a sequence length corresponding to a length from a first column to a determined column of the parity check matrix. The encoder generates the LDPC codes by using the first column to the determined column among one or more column(s) of the parity check matrix.

An encoding method changes an encoding rate of an erasure correcting code. One cycle is defined as 12k bits (wherein k represents a natural number) which is an encoding output using LDPC-CC with an encoding rate of 1/2, and includes information and parity. From the one cycle, only the information is arranged in the output order of the encoding output to obtain 6k bit information X6i, X6i+1, X6i+2, X6i+3, X6i+4, X6i+5, . . . , X6(i+k?1) X6(i+k?1)+1, X6(i+k?1)+2, X6(i+k?1)+3, X6(i+k?1)+4, and X6(i+k?1)+5. Known information is inserted in 3k pieces of information (Xj) among the 6k bit information, so that when 3k pieces of mutually different j is divided by 3, there is a remainder of 0 regarding k pieces, there is a remainder of 1 regarding k pieces, and there is a remainder of 2 regarding k pieces, to thereby obtain the parity from the information containing the known information.

A method for encoding bits according to a convolutional code. Bits to be encoded with the convolutional code are obtained for transmission over a communication channel. The bits are encoded according to the convolutional code with an encoder having an M-bit memory and a plurality of logic gates so as to separate trellis segments of the convolutional code into trellis sub-segments having a reduced number of branches per state than that of the trellis segments.

A transmission apparatus includes an encoder that codes a data sequence with a parity check matrix, wherein the data sequence includes a final information bit sequence and virtual information bits, and outputs the final information bit sequence and a parity sequence, as LDPC codes, and a transmitter that transmits the LDPC codes as a transmission data. A column length of the parity check matrix is longer than a total length of the final information bit sequence and the parity sequence, by a length of the virtual information bits that are set to 0 and are not transmitted. The total length of the final information bit sequence and the parity sequence has a sequence length corresponding to a length from a first column to a determined column of the parity check matrix. The encoder generates the LDPC codes by using the first column to the determined column among one or more column(s) of the parity check matrix.

An embodiment encoder device for encoding an information word c=[c.sub.0, c.sub.1, . . . , c.sub.K1] having K information bits, c.sub.i, includes an encoder for a tail biting convolutional code having a constraint length, L, where K<L1; the encoder being configured to receive the K information bits; and encode the K information bits so as to provide an encoded code word. An embodiment decoder device for determining an information word c=[c.sub.0, c.sub.1, . . . , c.sub.K1], having K information bits, c.sub.i, includes a decoder for a tail biting convolutional code having a constraint length, L, where K<L1; the decoder being configured to: receive an input sequence; compute at least one reliability parameter based on the received input sequence; and determine an information word c based on the at least one reliability parameter.

In an aspect, an apparatus may receive content to be transmitted and generate a first turbo encoded codeword from the content through use of a first turbo encoder. The apparatus maybe further configured to generate an interleaved codeword based on the first turbo encoded codeword through use of an interleaver, generate a second turbo encoded codeword from the interleaved codeword through use of a second turbo encoder, and transmit at least a portion of the second turbo encoded codeword. In an aspect, an apparatus may receive data including outer turbo encoded, interleaved, inner turbo encoded content. The apparatus may generate a first decoded instance of the data, generate a de-interleaved instance of the data based on the first decoded instance of the data, generate a second decoded instance of the data from the de-interleaved instance of the data, and perform a CRC on the second decoded instance of the data.

A transmission apparatus includes a signal processing circuit configured to obtain information data bits to be transmitted; add known information data bits to the information data bits to generate first data blocks; perform error-correction coding on the first data blocks to generate first coded data blocks including parity data blocks such that the first coded data blocks satisfy a first code rate; remove the known information data bits from the first coded data blocks to generate second coded data blocks, the second coded data blocks satisfying a second code rate different from the first code rate; and modulate the second coded data blocks using a modulation scheme to generate a modulated signal, which is then transmitted. A number of the known information data bits depends on a number of the information data bits such that the first code rate is fixed regardless of the number of the information data bits.

A low-density parity check convolution code (LDPC-CC) is made, and a signal sequence is sent after being subjected to an error-correcting encodement using the low-density parity check convolution code. In this case, a low-density parity check code of a time-variant period (3g) is created by linear operations of first to 3g-th (letter g designates a positive integer) parity check polynomials and input data.