A method comprising: receiving a collection of message bits having a first sequence in a source data stream; generating a sequence of parity bits, wherein each parity bit “x<sub>j</sub>” in the sequence is in accordance with the formula <maths 010" num="00010">$x_j=x_{j-1}+\sum _{i=1}^{\lambda }{v}_{\left(j-1\right)\lambda +i},$ where “x_j−1” is the value of a parity bit “j−1,” and $\mathrm{``}\sum _{i=1}^a{v}_{\left(j-1\right)a+1}″$ is the value of a sum of “a” randomly chosen irregular repeats of the message bits; and making the sequence of parity bits available for transmission in a transmission data stream. view more

A device comprising: a message passing decoder configured to decode a received data stream that includes a collection of parity bits, the message passing decoder comprising two or more check/variable nodes operating in parallel to receive messages from neighboring check/variable nodes and send updated messages to the neighboring variable/check nodes, wherein the message passing decoder is configured to decode the received data stream that has been encoded in accordance with the following Tanner graph: view more

An apparatus for performing encoding operations, the apparatus comprising: a first set of memory locations to store information bits; a second set of memory locations to store parity bits; a permutation module to read a bit from the first set of memory locations and combine the read bit to a bit in the second set of memory locations based on a corresponding index of the first set of memory locations and a corresponding index of the second set of memory locations; and an accumulator to perform accumulation operations on the bits stored in the second set of memory locations, wherein two or more memory locations of the first set of memory locations are read by the permutation module different times from one another. view more

A method of performing encoding operations, the method comprising: receiving a sequence of information bits from a first set of memory locations; performing an encoding operation using the received sequence of information bits as an input, said encoding operation comprising: reading a bit from the received sequence of information bits, and combining the read bit to a bit in a second set of memory locations based on a corresponding index of the first set of memory locations for the received sequence of information bits and a corresponding index of the second set of memory locations; and accumulating the bits in the second set of memory locations, wherein two or more memory locations of the first set of memory locations are read by the permutation module different times from one another. view more