# US 12,003,436 B2 · Methods and systems for encoding and decoding based on partitioned complementary sequences > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,003,436 B2 - Document ID: US12003436B2 - Status: Granted - Kind: B2 - Application number: 17/562,265 - Filed: 2021-12-27 - Published: 2022-07-07 - Granted: 2024-06-04 - Earliest claimed: 2020-12-29 - Assignees: University of South Carolina - Applicants: University of South Carolina - Inventors: Alphan Sahin - Web page: https://patentgrep.com/patent/US12003436B2 ## CPC - H04L 1/0041: {Arrangements at the transmitter end} - H04L 5/0035: {Resource allocation in a cooperative multipoint environment} - H03M 13/033: {Theoretical methods to calculate these checking codes} - H03M 13/136: {Reed-Muller [RM] codes} - H03M 13/31: combining coding for error detection or correction and efficient use of the spectrum (without error detection or correction H03M5/14 {, H03M5/145}) - H03M 13/47: Error detection, forward error correction or error protection, not provided for in groups H03M13/01 - H03M13/37 - H04L 1/0054: {Maximum-likelihood or sequential decoding, e.g. Viterbi, Fano, ZJ algorithms} - H04L 1/0057: {Block codes (H04L1/0061, H04L1/0064 take precedence)} - H04L 5/0007: {the frequencies being orthogonal, e.g. OFDM(A) or DMT} - H04L 5/0098: {Signalling of the activation or deactivation of component carriers, subcarriers or frequency bands} - H04L 27/2615: {Reduction thereof using coding} - 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 A method includes generating, by processing circuitry of a communications device, a partitioned complementary sequence based on information bits for transmission. The partitioned complementary sequence may include zero-valued elements. The method may include encoding a plurality of symbols on a plurality of orthogonal subcarriers using the partitioned complementary sequence. The encoding may include mapping additional information bits on subcarriers associated with the zero-valued elements of the partitioned complementary sequence. Additionally, the method may include controlling a radio of the communications device to transmit the plurality of symbols on the plurality of orthogonal subcarriers via an antenna of the communications device. ## Claims ### Claim 1 An apparatus comprising: an antenna; a radio configured to transmit and receive wireless communications via the antenna; and processing circuity configured to control the radio to establish a wireless communications link with a receiving communications device; wherein the processing circuitry is further configured to: generate a partitioned complementary sequence based on information bits for transmission, the partitioned complementary sequence comprising zero-valued elements; encode a plurality of symbols on a plurality of orthogonal subcarriers using the partitioned complementary sequence, wherein the processing circuitry is configured to map additional information bits for encoding on subcarriers associated with the zero-valued elements of the partitioned complementary sequence; and control the radio to transmit the plurality of symbols on the plurality of orthogonal subcarriers via the antenna. ### Claim 2 (depends on 1) The apparatus of claim 1, wherein the processing circuitry configured to generate the partitioned complementary sequence is further configured to apply a minimum Euclidean distance constraint as a partitioning restriction criterion. ### Claim 3 (depends on 2) The apparatus of claim 2, wherein the minimum Euclidean distance constraint is based on a selected spectral efficiency range and a selected bandwidth. ### Claim 4 (depends on 1) The apparatus of claim 1, wherein the partitioned complementary sequence is defined for a selected bandwidth. ### Claim 5 (depends on 1) The apparatus of claim 1, wherein the plurality of symbols are orthogonal frequency division multiplexed (OFDM) symbols. ### Claim 6 (depends on 1) The apparatus of claim 1, wherein the processing circuitry is configured to encode the plurality of symbols on the plurality of orthogonal subcarriers using the partitioned complementary sequence to have a peak-to-average-power ratio (PAPR) that is below a predefined threshold level. ### Claim 7 (depends on 1) The apparatus of claim 1, wherein the processing circuitry is configured to encode the plurality of symbols using an alphabet for non-zero elements of the partitioned complementary sequence based on a phase shift keying alphabet. ### Claim 8 (depends on 1) The apparatus of claim 1, wherein the processing circuitry is further configured to activate and deactivate one or more of the subcarriers based on index modulation. ### Claim 9 (depends on 1) The apparatus of claim 1, wherein the processing circuitry is configured to implement an encoder and decoder based on the partitioned complementary sequence. ### Claim 10 (depends on 1) The apparatus of claim 1, wherein the processing circuitry is configured to generate the partitioned complementary sequence having non-squashing partitions. ### Claim 11 A method comprising: generating, by processing circuitry of a communications device, a partitioned complementary sequence based on information bits for transmission, the partitioned complementary sequence comprising zero-valued elements; encoding a plurality of symbols on a plurality of orthogonal subcarriers using the partitioned complementary sequence, wherein the encoding comprises mapping additional information bits on subcarriers associated with the zero-valued elements of the partitioned complementary sequence; and controlling a radio of the communications device to transmit the plurality of symbols on the plurality of orthogonal subcarriers via an antenna of the communications device. ### Claim 12 (depends on 11) The method of claim 11, wherein generating the partitioned complementary sequence further comprises applying a minimum Euclidean distance constraint as a partitioning restriction criterion. ### Claim 13 (depends on 12) The method of claim 12, wherein the minimum Euclidean distance constraint is based on a selected spectral efficiency range and a selected bandwidth. ### Claim 14 (depends on 11) The method of claim 11, wherein the partitioned complementary sequence is defined for a selected bandwidth. ### Claim 15 (depends on 11) The method of claim 11, wherein the plurality of symbols are orthogonal frequency division multiplexed (OFDM) symbols. ### Claim 16 (depends on 11) The method of claim 11, wherein encoding the plurality of symbols on the plurality of orthogonal subcarriers comprises using the partitioned complementary sequence to have a peak-to-average-power ratio (PAPR) that is below a predefined threshold level. ### Claim 17 (depends on 11) The method of claim 11, wherein the plurality of symbols are encoded using an alphabet for non-zero elements of the partitioned complementary sequence based on a phase shift keying alphabet. ### Claim 18 (depends on 11) The method of claim 11, further comprising activating and deactivating one or more of the subcarriers based on index modulation. ### Claim 19 (depends on 11) The method of claim 11, further comprising implementing an encoder and decoder based on the partitioned complementary sequence. ### Claim 20 (depends on 11) The method of claim 11, wherein the partitioned complementary sequence is generated with non-squashing partitions.