IP Library › Granted Patent US 12671441

Granted Patent B2

US 12671441 · App. 18/647,780 · Granted Jun 30, 2026

Systems and methods for block-kronecker based low density parity check (LDPC) code with 5/6 code rate

Inventors: Rethnakaran Pulikkoonattu (San Diego, CA); Andrew Blanksby (Irvine, CA); Vinko Erceg (San Diego, CA)

Assignee: Avago Technologies International Sales Pte. Limited

H03M13/116 H03M13/616

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Patent No.: US 12671441
App. No.: 18/647,780
Granted: Jun 30, 2026
Kind: B2

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Abstract

An apparatus may include a transmitter and one or more processors. The one or more processors may identify, based on a first parity check matrix of a first quasi-cyclic-low-density parity-check (QC-LDPC) code according to a code rate of 5/6, a second parity check matrix corresponding to a first exponent matrix comprising 384 values for a second QC-LDPC code. The second QC-LDPC code may have a code block size that is twice a code block size of the first QC-LDPC code. The one or more processors may encode data using the second parity check matrix. The transmitter may be configured to transmit the encoded data.

Claims (71)

1 . A method, comprising:

identifying, by baseband circuitry of a first device, a first parity check matrix of a first quasi-cyclic-low-density parity-check (QC-LDPC) code having a code rate of 5/6;

determining, by the baseband circuitry, based at least on a result of a Khatri-Rao product of the first parity check matrix and a first binary matrix having the same dimensions as dimensions of an exponent matrix of the first parity check matrix, a second parity check matrix corresponding to a first exponent matrix comprising 384 values for a second QC-LDPC having a code block size that is twice a code block size of the first QC-LDPC code;

encoding, by an encoder of the baseband circuitry of the first device while concurrently encoding other data, data using the second parity check matrix to increase a gain in signal-to-noise ratio (SNR) across multiple modulation schemes over wireless channels; and

transmitting, by a transmitter of the first device, the encoded data.

2 . The method of claim 1 , wherein

determining the first binary matrix comprises:

determining a second binary matrix having the same dimensions as dimensions of the first binary matrix; and

determining the first binary matrix comprising at least (1) one or more rows of a second binary matrix or (2) one or more columns of the second binary matrix, and

determining the second parity check matrix comprises:

determining, based at least on a result of the Khatri-Rao product, a second exponent matrix having the same dimensions as dimensions of the first exponent matrix,

determining, based at least on the second exponent matrix, the first exponent matrix; and

determining, based at least on the first exponent matrix, the second parity check matrix.

3 . The method of claim 2 , wherein

the second binary matrix comprises the following set of values: [1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0], and

the second exponent matrix comprises the following set of values: [−1 13 48 −1 80 −1 −1 66 −1 4 74 −1 −1 7 30 −1 76 −1 −1 52 −1 37 60 −1 −1 −1 49 −1 73 −1 −1 31 −1 74 −1 73 23 −1 −1 −1 1 −1 0 −1 −1 −1 −1 −1 13 −1 −1 48 −1 80 66 −14 −1 −1 74 7 −1 −1 30 −1 76 52 −1 37 −1 −1 60 −1 −1 −1 49 −1 73 31 −1 74 −1 73 −1 −1 23 −1 −1 −1 1 −1 0 −1 −1 −1 −1 69 −1 63 −1 74 −1 −1 56 64 −1 −1 77 57 −1 65 −1 −1 6 −1 16 −1 51 −1 −1 64 −1 −1 −1 68 −19 −1 48 −1 62 −1 −1 54 −1 27 −1 −1 0 −1 0 −1 −1 −1 −1 69 −1 63 −1 74 56 −1 −1 64 77 −1 −1 57 −1 65 6 −1 16 −1 51 −1 −1 −1 −1 64 −1 −1 −1 68 −1 9 −1 48 −1 62 54 −1 27 −1 −1 −1 −1 0 −1 0 −1 −1 −1 51 −1 15 −1 0 80 −1 24 −1 −1 25 42 −1 54 −1 −1 44 −1 71 −1 71 9 −1 67 −1 35 −1 −1 −1 −1 58 −1 −1 −1 29 −1 −1 −1 53 0 −1 −1 −1 0 −1 0 −1 51 −1 15 −1 0 −1 −1 80 −1 24 25 −1 −1 42 −1 54 44 −1 71 −1 71 −1 −1 9 −1 67 35 −1 −1 58 −1 −1 −1 29 −1 −1 −1 53 −1 −1 0 −1 −1 −1 0 −1 0 51 −1 16 29 −1 −1 36 −1 41 −1 44 −1 56 −1 59 −1 37 50 −1 −1 24 −1 −1 −1 65 4 −1 −1 65 −1 52 −1 −1 −14 −1 −1 73 −1 −1 52 1 −1 −1 −1 −1 −1 0 −1 16 −1 −1 29 36 −1 41 −1 44 −1 44 −1 56 −1 59 −1 37 −1 −1 50 24 −1 −1 −1 65 −1 −14 65 −1 52 −1 −1 −14 −1 −1 −1 −1 73 52 −1 −1 1 −1 −1 −1 −1].

4 . The method of claim 2 , wherein

the second binary matrix comprises the following set of values: [0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0], and

the second exponent matrix comprises the following set of values: [13 −1 48 −1 −1 80 66 −1 −1 4 −1 74 −1 7 −1 30 −1 76 −1 52 −1 37 60 −1 −1 −1 49 −1 73 −1 −1 31 −1 74 −1 73 23 −1 −1 −1 1 −1 0 −1 −1 −1 −1 −1 −1 13 −1 48 80 −1 −1 66 4 −1 74 −1 7 −1 30 −1 76 −1 52 −1 37 −1 −1 60 −1 −1 −1 49 −1 73 31 −1 74 −1 73 −1 −1 23 −1 −1 −1 1 −1 0 −1 −1 −1 −1 69 −1 −1 63 74 −1 56 −1 64 −1 77 −1 57 −1 65 −1 6 −1 −1 16 −1 51 −1 −1 64 −1 −1 −1 68 −1 9 −1 48 −1 62 −1 −1 54 −1 27 −1 −1 0 −1 0 −1 −1 −1 −1 69 63 −1 −1 74 −1 56 −1 64 −1 77 −1 57 −1 65 −1 6 16 −1 51 −1 −1 −1 −1 64 −1 −1 −1 68 −1 9 −1 48 −1 62 54 −1 27 −1 −1 −1 −1 0 −1 0 −1 −1 51 −1 15 −1 −1 0 80 −1 −1 24 25 −1 −1 42 54 −1 44 −1 71 −1 −1 71 9 −1 67 −1 35 −1 −1 −1 −1 58 −1 −1 −1 29 −1 −1 −1 53 0 −1 −1 −1 0 −1 0 −1 −1 51 −1 15 0 −1 −1 80 24 −1 −1 25 42 −1 −1 54 −1 44 −1 71 71 −1 −1 9 −1 67 −1 35 −1 −1 58 −1 −1 −1 29 −1 −1 −1 53 −1 −1 0 −1 −1 −1 0 −1 0 −1 16 29 −1 −1 36 −1 41 −1 44 56 −1 −1 59 −1 37 −1 50 −1 24 −1 −1 −1 65 4 −1 −1 65 −1 52 −1 −1 −14 −1 −1 73 −1 −1 52 1 −1 −1 −1 −1 −1 0 −1 16 −1 −1 29 36 −1 41 −1 44 −1 −1 56 59 −1 37 −1 50 −1 24 −1 −1 −1 65 −1 −14 65 −1 52 −1 −1 −14 −1 −1 −1 −1 73 52 −1 −1 1 −1 −1 −1 −1 −1 0].

5 . The method of claim 2 , wherein

the second binary matrix comprises the following set of values: [0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0], and

the second exponent matrix comprises the following set of values: [13 −1 −1 48 −1 80 −1 66 −1 4 74 −1 7 −1 −1 30 76 −1 −1 52 37 −1 −1 60 −1 −1 −1 49 73 −1 31 −1 −1 74 73 −1 −1 23 −1 −1 1 −1 0 −1 −1 −1 −1 −1 −1 13 48 −1 80 −1 66 −14 −1 −1 74 −17 30 −1 −1 76 52 −1 −1 37 60 −1 −1 −1 49 −1 −1 73 −1 31 74 −1 −1 73 23 −1 −1 −1 −1 1 −1 0 −1 −1 −1 −1 −1 69 −1 63 −1 74 56 −1 64 −1 −1 77 57 −1 −1 65 6 −1 −1 16 −1 51 −1 −1 64 −1 −1 −1 68 −1 −1 9 48 −1 −1 62 54 −1 27 −1 −1 −1 0 −1 0 −1 −1 −1 69 −1 63 −1 74 −1 −1 56 −1 64 77 −1 −1 57 65 −1 −16 16 −1 51 −1 −1 −1 −1 64 −1 −1 −1 68 9 −1 −1 48 62 −1 −1 54 −1 27 −1 −1 −1 0 −1 0 −1 −1 51 −1 15 −1 −1 0 −1 80 −1 24 −1 25 −1 42 54 −1 −1 44 71 −1 71 −1 7 19 67 −1 −1 35 −1 −1 −1 58 −1 −1 −1 29 −1 −1 53 −1 0 −1 −1 −1 0 −1 0 −1 −1 51 −1 15 0 −1 80 −1 24 −1 25 −1 42 −1 −1 54 44 −1 −1 71 −1 71 9 −1 −1 67 35 −1 −1 −1 58 −1 −1 −1 29 −1 −1 −1 −1 53 −1 0 −1 −1 −1 0 −1 0 −1 16 29 −1 36 −1 −1 41 −1 44 56 −1 −1 59 −1 37 −1 50 24 −1 −1 −1 −1 65 4 −1 65 −1 52 −1 −1 −14 −1 −1 −1 −1 73 −1 52 1 −1 −1 −1 −1 −1 0 −1 16 −1 −1 29 −1 36 41 −1 44 −1 −1 56 59 −1 37 −1 50 −1 −1 24 −1 −1 65 −1 −14 −1 65 −1 52 −1 −1 −1 4 −1 −1 73 −1 52 −1 −1 1 −1 −1 −1 −1 −1 0].

6 . The method of claim 2 , wherein determining the first exponent matrix comprises:

selecting, from values of the second exponent matrix, at least 382 values as values of the first exponent matrix;

shifting one or two values of the first exponent matrix from one or more corresponding positive values of the second exponent matrix by −1 or +1 wherein the one or more corresponding positive values of the second exponent matrix are not selected as the at least 382 values; and

determining a resulting matrix of the shifting as the first exponent matrix.

7 . The method of claim 1 , further comprising:

identifying, by a second device, the second parity check matrix;

receiving, by the second device from the first device, the encoded data; and

decoding, by the second device, the encoded data using the second parity check matrix.

8 . An apparatus comprising:

a transmitter and baseband circuitry including an encoder, wherein

the baseband circuitry is configured to:

identify a first parity check matrix of a first quasi-cyclic-low-density parity-check (QC-LDPC) code having a code rate of 5/6; and

determine, based at least on a result of a Khatri-Rao product of the first parity check matrix and a first binary matrix having the same dimensions as dimensions of an exponent matrix of the first parity check matrix, a second parity check matrix corresponding to a first exponent matrix comprising 384 values for a second QC-LDPC having a code block size that is twice a code block size of the first QC-LDPC code,

the encoder is configured to encode, while concurrently encoding other data, data using the second parity check matrix to increase a gain in signal-to-noise ratio (SNR) across multiple modulation schemes over wireless channels, and

the transmitter is configured to transmit the encoded data.

9 . The apparatus of claim 8 , wherein

in determining the first binary matrix, the one or more processors are configured to:

determine a second binary matrix having the same dimensions as dimensions of the first binary matrix; and

determine the first binary matrix comprising at least (1) one or more rows of a second binary matrix or (2) one or more columns of the second binary matrix, and

in determining the second parity check matrix, the one or more processors are configured to:

determine, based at least on the result of the Khatri-Rao product, a second exponent matrix having the same dimensions as dimensions of the first exponent matrix,

determine, based at least on the second exponent matrix, the first exponent matrix; and

determine, based at least on the first exponent matrix, the second parity check matrix.

10 . The apparatus of claim 9 , wherein

11 . The apparatus of claim 9 , wherein

12 . The apparatus of claim 9 , wherein

13 . The apparatus of claim 9 , wherein in determining the first exponent matrix, the one or more processors are configured to:

select, from values of the second exponent matrix, at least 382 values as values of the first exponent matrix;

shift one or two values of the first exponent matrix from one or more corresponding positive values of the second exponent matrix by −1 or +1 wherein the one or more corresponding positive values of the second exponent matrix are not selected as the at least 382 values; and

determine a resulting matrix of the shifting as the first exponent matrix.

14 . An apparatus comprising:

a receiver configured to receive encoded data to increase a gain in signal-to-noise ratio (SNR) across multiple modulation schemes over wireless channels, wherein the encoded data is encoded using a second quasi-cyclic-low-density parity-check (QC-LDPC) code according to a code rate of 5/6, wherein the second QC-LDPC code has a code block size that is twice a code block size of a first QC-LDPC code; and

baseband circuitry configured to:

identify a first parity check matrix of the first QC-LDPC code having a code rate of 5/6;

decode, while concurrently decoding other data, the received encoded data using the second parity check matrix.

15 . The apparatus of claim 14 , wherein

the first exponent matrix comprises at least 382 values selected from a second exponent matrix having the same dimensions as dimensions of the first exponent matrix,

the first exponent matrix comprises one or two values shifted from one or more corresponding positive values of the second exponent matrix by −1 or +1, and

the one or more corresponding positive values of the second exponent matrix are not selected as the at least 382 values.

16 . The apparatus of claim 14 , wherein the second exponent matrix comprises the following set of values: [−1 13 48 −1 80 −1 −1 66 −1 4 74 −1 −1 7 30 −1 76 −1 −1 52 −1 37 60 −1 −1 −1 49 −1 73 −1 −1 31 −1 74 −1 73 23 −1 −1 −1 1 −1 0 −1 −1 −1 −1 −1 13 −1 −1 48 −1 80 66 −1 4 −1 −1 74 7 −1 −1 30 −1 76 52 −1 37 −1 −1 60 −1 −1 −1 49 −1 73 31 −1 74 −1 73 −1 −1 23 −1 −1 −1 1 −1 0 −1 −1 −1 −1 69 −1 63 −1 74 −1 −1 56 64 −1 −1 77 57 −1 65 −1 −1 6 −1 16 −1 51 −1 −1 64 −1 −1 −1 68 −19 −1 48 −1 62 −1 −1 54 −1 27 −1 −1 0 −1 0 −1 −1 −1 −1 69 −1 63 −1 74 56 −1 −1 64 77 −1 −1 57 −1 65 6 −1 16 −1 51 −1 −1 −1 −1 64 −1 −1 −1 68 −1 9 −1 48 −1 62 54 −1 27 −1 −1 −1 −1 0 −1 0 −1 −1 −1 51 −1 15 −1 0 80 −1 24 −1 −1 25 42 −1 54 −1 −1 44 −1 71 −1 71 9 −1 67 −1 35 −1 −1 −1 −1 58 −1 −1 −1 29 −1 −1 −1 53 0 −1 −1 −1 0 −1 0 −1 51 −1 15 −1 0 −1 −1 80 −1 24 25 −1 −1 42 −1 54 44 −1 71 −1 71 −1 −1 9 −1 67 35 −1 −1 58 −1 −1 −1 29 −1 −1 −1 53 −1 −1 0 −1 −1 −1 0 −1 0 51 −1 16 29 −1 −1 36 −1 41 −1 44 −1 56 −1 59 −1 37 50 −1 −1 24 −1 −1 −1 65 4 −1 −1 65 −1 52 −1 −1 −14 −1 −1 73 −1 −1 52 1 −1 −1 −1 −1 −1 0 −1 16 −1 −1 29 36 −1 41 −1 44 −1 44 −1 56 −1 59 −1 37 −1 −1 50 24 −1 −1 −1 65 −1 −14 65 −1 52 −1 −1 −14 −1 −1 −1 −1 73 52 −1 −1 1 −1 −1 −1 −1].

17 . The apparatus of claim 14 , wherein the second exponent matrix comprises the following set of values: [13 −1 48 −1 −1 80 66 −1 −1 4 −1 74 −1 7 −1 30 −1 76 −1 52 −1 37 60 −1 −1 −1 49 −1 73 −1 −1 31 −1 74 −1 73 23 −1 −1 −1 1 −1 0 −1 −1 −1 −1 −1 −1 13 −1 48 80 −1 −1 66 4 −1 74 −1 7 −1 30 −1 76 −1 52 −1 37 −1 −1 60 −1 −1 −1 49 −1 73 31 −1 74 −1 73 −1 −1 23 −1 −1 −1 1 −1 0 −1 −1 −1 −1 69 −1 −1 63 74 −1 56 −1 64 −1 77 −1 57 −1 65 −1 6 −1 −1 16 −1 51 −1 −1 64 −1 −1 −1 68 −1 9 −1 48 −1 62 −1 −1 54 −1 27 −1 −1 0 −1 0 −1 −1 −1 −1 69 63 −1 −1 74 −1 56 −1 64 −1 77 −1 57 −1 65 −1 6 16 −1 51 −1 −1 −1 −1 64 −1 −1 −1 68 −1 9 −1 48 −1 62 54 −1 27 −1 −1 −1 −1 0 −1 0 −1 −1 51 −1 15 −1 −1 0 80 −1 −1 24 25 −1 −1 42 54 −1 44 −1 71 −1 −1 71 9 −1 67 −1 35 −1 −1 −1 −1 58 −1 −1 −1 29 −1 −1 −1 53 0 −1 −1 −1 0 −1 0 −1 −1 51 −1 15 0 −1 −1 80 24 −1 −1 25 42 −1 −1 54 −1 44 −1 71 71 −1 −1 9 67 −1 35 −1 −1 58 −1 −1 −1 29 −1 −1 −1 53 −1 −1 0 −1 −1 −1 0 −1 0 −1 16 29 −1 −1 36 −1 41 −1 44 56 −1 −1 59 −1 37 −1 50 −1 24 −1 −1 −1 65 4 −1 −1 65 −1 52 −1 −1 −14 −1 −1 73 −1 −1 52 1 −1 −1 −1 −1 −1 0 −1 16 −1 −1 29 36 −1 41 −1 44 −1 −1 56 59 −1 37 −1 50 −1 24 −1 −1 −1 65 −1 −1 4 65 −1 52 −1 −1 −14 −1 −1 −1 −1 73 52 −1 −1 1 −1 −1 −1 −1 −1 0].

18 . The apparatus of claim 14 , wherein the second exponent matrix comprises the following set of values: [13 −1 −1 48 −1 80 −1 66 −1 4 74 −1 7 −1 −1 30 76 −1 −1 52 37 −1 −1 60 −1 −1 −1 49 73 −1 31 −1 −1 74 73 −1 −1 23 −1 −1 1 −1 0 −1 −1 −1 −1 −1 −1 13 48 −1 80 −1 66 −1 4 −1 −1 74 −17 30 −1 −1 76 52 −1 −1 37 60 −1 −1 −1 49 −1 −1 73 −1 31 74 −1 −1 73 23 −1 −1 −1 −1 1 −1 0 −1 −1 −1 −1 −1 69 −1 63 −1 74 56 −1 64 −1 −1 77 57 −1 −1 65 6 −1 −1 16 −1 51 −1 −1 64 −1 −1 −1 68 −1 −1 9 48 −1 −1 62 54 −1 27 −1 −1 −1 0 −1 0 −1 −1 −1 69 −1 63 −1 74 −1 −1 56 −1 64 77 −1 −1 57 65 −1 −1 6 16 −1 51 −1 −1 −1 −1 64 −1 −1 −1 68 9 −1 −1 48 62 −1 −1 54 −1 27 −1 −1 −1 0 −1 0 −1 −1 51 −1 15 −1 −1 0 −1 80 −1 24 −1 25 −1 42 54 −1 −1 44 71 −1 71 −1 7 19 67 −1 −1 35 −1 −1 −1 58 −1 −1 −1 29 −1 −1 53 −1 0 −1 −1 −1 0 −1 0 −1 −1 51 −1 15 0 −1 80 −1 24 −1 25 −1 42 −1 −1 54 44 −1 −1 71 −1 71 9 −1 −1 67 35 −1 −1 −1 58 −1 −1 −1 29 −1 −1 −1 −1 53 −1 0 −1 −1 −1 0 −1 0 −1 16 29 −1 36 −1 −1 41 −1 44 56 −1 −1 59 −1 37 −1 50 24 −1 −1 −1 −1 65 4 −1 65 −1 52 −1 −1 −14 −1 −1 −1 −1 73 −1 52 1 −1 −1 −1 −1 −1 0 −1 16 −1 −1 29 −1 36 41 −1 44 −1 −1 56 59 −1 37 −1 50 −1 −1 24 −1 −1 65 −1 −1 4 −1 65 −1 52 −1 −1 −1 4 −1 −1 73 −1 52 −1 −1 1 −1 −1 −1 −1 −1 0].