# US 12,119,932 B2 · Systems and methods for communicating using nested low density parity check codes

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- Number: US 12,119,932 B2
- Document ID: US12119932B2
- Status: Granted
- Kind: B2
- Application number: 17/146,343
- Filed: 2021-01-11
- Published: 2021-07-15
- Granted: 2024-10-15
- Earliest claimed: 2020-01-10
- Assignees: California Institute of Technology
- Applicants: California Institute of Technology
- Inventors: Michelle Effros; Yuxin Liu
- Web page: https://patentgrep.com/patent/US12119932B2

## CPC

- H04L 1/0057: {Block codes (H04L1/0061, H04L1/0064 take precedence)}
- H03M 13/1105: {Decoding}
- H03M 13/1148: {Structural properties of the code parity-check or generator matrix}
- H03M 13/63: {Joint error correction and other techniques (H03M13/31 and H03M13/33 take precedence)}
- H03M 13/6362: {by puncturing}
- H04L 1/0041: {Arrangements at the transmitter end}
- H04L 1/0045: {Arrangements at the receiver end}
- H04L 1/16: in which the return channel carries supervisory signals, e.g. repetition request signals
- H03M 13/3761: {using code combining, i.e. using combining of codeword portions which may have been transmitted separately, e.g. Digital Fountain codes, Raptor codes or Luby Transform [LT] codes}
- H04L 1/0009: {by adapting the channel coding (H04L1/1812 takes precedence)}
- H04L 1/0036: {arrangements specific to the receiver}
- H04L 2001/0092: {Error control systems characterised by the topology of the transmission link}
- H04L 2001/0093: {Point-to-multipoint}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)
- H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C)

## Abstract

Systems and methods in accordance with various embodiments of the invention enable communicating using nested Low Density Parity Check (LDPC) codes. A nested LDPC code is an LDPC code having a full blocklength, where shorter blocklengths of the nested LDPC code can be utilized as shorter blocklength LDPC codes. In certain embodiments, a transmitter utilizes a nested LDPC code to communicate via a point-to-point connection. In several embodiments, multiple transmitters utilize nested LDPC codes to communicate simultaneously via a Random Access Channel. One embodiment includes a transmitter capable of encoding a message as symbols using a nested LDPC code until a feedback message indicating an end of epoch message is received. A receiver can determine whether a decoding rule is satisfied at predetermined decode times and transmit an end of epoch message when the decoder can decode a message based upon the nested LDPC code.

## Claims

### Claim 1

A communication system, comprising:
at least one encoder configured to:
receive a start of epoch message;
encode message data as symbols using a rateless code determined using a nested Low Density Parity Check (LDPC) code by mapping a codeword to a symbol, wherein the nested LDPC code:
is an LDPC code with a full blocklength; and
comprises one or more shorter blocklength LDPC codes; and
receive feedback messages at a predetermined set of potential decoding times, wherein the at least one encoder is configured to transmit symbols until a received feedback message is an end of epoch message; and
a decoder, where the decoder is configured to:
cause a broadcast transmitter to transmit at least one start of epoch message;
receive observed symbols;
at each of a set of predetermined decode times, determine whether a decoding rule is satisfied; and
when the decoding rule is satisfied:
decode at least one message based upon the received observed symbols based upon the nested LDPC code; and
cause the broadcast transmitter to transmit an end of epoch message.

### Claim 2 (depends on 1)

The communication system of claim 1, wherein:
the full blocklength corresponds to a longest decode time from the set of predetermined decode times; and
each of the one or more shorter blocklength LDPC codes corresponds to a decode time from the set of predetermined decode times that is shorter than the longest decode time from the set of predetermined decode times.

### Claim 3 (depends on 1)

The communication system of claim 1, wherein:
the one or more shorter blocklength LDPC codes comprise a first shorter blocklength LDPC code and a second shorter blocklength LDPC code;
the first shorter blocklength LDPC code comprises a first set of variable nodes, and a first set of check nodes; and
the second shorter blocklength LDPC code comprises:
a second set of variable nodes comprising: the first set of variable nodes and an incremental set of variable nodes; and
a second set of check nodes comprising: the first set of check nodes, and an incremental set of check nodes.

### Claim 4 (depends on 3)

The communication system of claim 3, wherein:
the first set of check nodes are connected to one or more variable nodes from the first set of variable nodes; and
the incremental set of check nodes are connected to one or more variable nodes from the second set of variable nodes.

### Claim 5 (depends on 3)

The communication system of claim 3, wherein a ratio of the first set of variable nodes to the first set of check nodes is different from a ratio of the second set of variable nodes to the second set of check nodes.

### Claim 6 (depends on 1)

The communication system of claim 1, wherein determining whether a decoding rule is satisfied is based upon the received observed symbols.

### Claim 7 (depends on 1)

The communication system of claim 1, wherein the at least one encoder is configured to select a specific nested LDPC code based upon the start of epoch message.

### Claim 8 (depends on 1)

The communication system of claim 1, wherein:
the at least one encoder is a plurality of encoders; and
multiple encoders in the plurality of encoders are configured to select the same nested LDPC code to use when encoding the message data as symbols using the rateless code.

### Claim 9 (depends on 1)

The communication system of claim 1, wherein:
the at least one encoder is a plurality of encoders; and
at least two of the plurality of encoders are configured to select different nested LDPC codes to use when encoding the message data as symbols using the rateless code.

### Claim 10 (depends on 9)

The communication system of claim 9, wherein at least two of the different nested LDPC codes have different code rates.