Encoding method using a low density parity check code with a column weight of two
AssigneeCarnegie Mellon University
InventorsHongwei Song, Vijayakumar Bhagavatula, Jingfeng Liu
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Abstract
A method for communicating binary data and a digital communication system are presented. According to one embodiment, the method includes encoding a message word by multiplying the message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two. Additionally disclosed is an encoding scheme based on a three-tier Tanner graph having a girth of twelve.
Claims26
A method for encoding binary data, comprising multiplying a message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve.
A coded data system, comprising an encoder for encoding a message word by multiplying the message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve.
A coded data system, comprising:
- an encoder for encoding a message word by multiplying the message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a quasi-cyclic parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve;
- a decoder in communication with the encoder via a channel.
A coded data system, comprising:
- means for encoding a message word by multiplying the message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve;
- and
- means for decoding the message word in communication with the means for encoding via a channel.
A coded data system, comprising:
- a first encoder for encoding a message word according to an error correction code to thereby generate a first codeword;
- and
- a second encoder for encoding the first codeword by multiplying the first codeword with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve.
A method of encoding binary data, comprising:
- receiving a first message word;
- and
- adding a first plurality of redundancy bits to the first message word to thereby generate a first codeword, wherein adding the first plurality of redundancy bits includes adding a first plurality of redundancy bits based on a three-tier Tanner graph having a girth of twelve, wherein adding the first plurality of redundancy bits based on the three-tier Tanner graph includes:
- operating on the first message word at a first tier of the three-tier Tanner graph during a first time period;
- operating on an output from the first tier at a second tier of the Tanner graph during a second time period;
- and
- operating on an output from the second tier at a third tier of the Tanner graph during a third time period.
Dependencies are inferred from the claim text.