T HE LQ D IGITAL M ODE FAMILY
Luis Quesada (HB9IPH)
The LQ Digital Mode Family: Protocol Architecture and Reference Specification for Weak-Signal Communications Luis Quesada (HB9IPH) — Independent Researcher
arXiv:2609.06427v1 [cs.NI] 6 Sep 2026
l-u-i-s [at] l-q-8 [dot] o-r-g Abstract—This paper introduces LQ8, an open-source weak-signal digital mode for amateur radio that completes structured two-way contacts in 4 transmissions (60 s), achieving a 1.50× speedup over canonical 6-transmission exchanges (90 s) and 1.25× over 5-transmission RR73 exchanges (75 s) while preserving complete bidirectional exchange of Maidenhead grid locators, signal reports, and mutual acknowledgments. By replacing fixed-width message-type headers with variable-length prefix codes matched to physical-layer bit budgets, LQ8 packs the answering station’s grid locator and measured signal report into a single 77-bit reply. In multi-station pileup operations, LQ8 confirms up to two answering stations simultaneously within a single-carrier, constant-envelope 50.0 Hz transmission with a 0.0 dB RF power-splitting penalty, enabling a theoretical peak rate of up to 160 QSOs/h (scaling to 320 QSOs/h in dual-carrier operation) while retaining the −21.0 dB SNR sensitivity of continuous-phase 8-GFSK transport. The protocol family also defines three extended profiles (LQ16, LQ4, and LQ2) tailored for extreme sensitivity, VHF/UHF contesting, and fast-burst channels.
I. I NTRODUCTION The FT8 digital mode [1], designed by Steve Franke (K9AN) and Joe Taylor (K1JT), has transformed amateur radio since its introduction in 2017 in the WSJT-X software suite [2], enabling reliable contacts at signal-to-noise ratios as low as −21.0 dB in a 2500 Hz bandwidth. Its 77-bit message payload, combined with a low-density parity-check (LDPC) forward error correction code [5] and 8-tone Gaussian frequency-shift keying (8-GFSK), provides a robust physical layer that is now well-proven across millions of contacts worldwide. In conventional weak-signal protocols (e.g., FT8), a structured two-way contact canonically requires six sequential transmissions across 15-second time slots (90 seconds total), or five transmissions (75 seconds) when using shortened RR73 confirmations (CQ → CALL → REPORT → RREPORT → RR73). Under a 77-bit payload budget, encoding two 28-bit standard callsigns, a 15-bit Maidenhead grid locator, and a 5-bit signal report requires 76 information bits (28 + 28 + 15 + 5 = 76). Uniform fixed-width type headers (typically 3 or 4 bits) exceed the remaining 1-bit margin, preventing the simultaneous transmission of locator and report in a single transmission. LQ8 resolves this constraint by employing variablelength prefix codes [4] tailored to physical-layer bit budgets. By allocating a 1-bit prefix to the dominant response message format, LQ8 preserves 76 bits for payload data, packing both the answering station’s grid locator and measured signal report into a single frame. This completes confirmed contacts in 4 transmissions (60 seconds) with full mutual verification, while retaining the proven continuous-phase 8-GFSK and LDPC(174, 91) physical layer (−21.0 dB SNR sensitivity). Furthermore, for high-rate DXpedition Fox and Hound (F/H) pileups, LQ8 introduces the MULTI-REPORT+73 protocol to confirm two answering Hound stations simultaneously within a single-carrier transmission without RF power-splitting penalties. Cross-isolated Costas synchronization arrays (C7 = [2, 5, 6, 1, 3, 0, 4], exhibiting ≤ 1 coincidence hit) isolate traffic from legacy decoders. Physical layer,
CRC-14, and LDPC parameters are presented in Section V. Building upon LQ8, the protocol family defines three complementary profiles (LQ16, LQ4, and LQ2) tailored for ultraweak fading channels, rapid contesting, and fast burst links. A. Architectural Philosophy & Design Principles
The LQ family is engineered around four core design tenets: • Payload-Matched Prefix Allocation: Replacing uniform headers with variable-length prefix codes frees capacity for simultaneous locator and report transmission, shortening 1-on-1 contacts to 4 slots (60 s) and reducing vulnerability to ionospheric fading (QSB) and transient interference. • Coexistence and Spectrum Preservation: All modes maintain continuous-phase GFSK and LDPC(174, 91) channel coding while employing low-cross-coincidence Costas sync arrays to prevent cross-protocol false decodes. • Robust Special-Case Support: Non-standard callsigns (up to 13 characters), dedicated 1-bit portable suffixes (0=none, 1=/P), 24/20-bit collision-resistant callsign hashes, and a 104-character free-text Varicode provide seamless support for contesting, portable activations (POTA/SOTA), and DXpeditions. • Clear-Text Station Identification: Transmitting stations convey their callsigns in clear text across all 1-on-1 exchanges (including non-standard caller replies via 48-bit Base-38 encoding), reserving compact hashes strictly for target addressing and multi-station pileup frames. B. Implementations & Reference Software
The complete suite is implemented in the open-source C++ reference library (lq_lib) [11] (MIT License), featuring an automated verification harness and golden vector test suites across all four modulation profiles. Web demonstrations and interactive protocol resources are published on the official project portal [12]. Native portable operation is provided by qFT8 for Android [13], deploying LQ8 alongside live testbeds for LQ16, LQ4, and LQ2. 1
T HE LQ D IGITAL M ODE FAMILY
Luis Quesada (HB9IPH)
II. QSO P ROTOCOL
QSO Logging Semantics. Contacts are logged once callsigns, locators, reports, and acknowledgments are exchanged: Station A logs upon decoding the final 73 in T4 (or transmitting REPORT+73 in Fox pileup mode); Station B logs upon transmitting 73 in T4 (having decoded Station A’s report in T3). In ADIF logging (LoTW, QRZ.com, Club Log), contacts map to mode DATA with submode LQ8 (LQ4, LQ2, LQ16). A watchdog aborts after three unacknowledged attempts (45 s in LQ8, 22.5 s in LQ4), returning to idle monitoring.
The LQ protocol establishes deterministic state transitions, transmission slot timing, and multi-station arbitration to achieve confirmed bilateral contacts across low-SNR channels. A. Standard Four-Message Exchange
The LQ QSO protocol is built upon two core principles: bidirectional exchange of Maidenhead grid locators and signal reports (measured SNR in dB), coupled with mutual confirmation (Table 1). Following weak-signal convention, LQ establishes an operational termination criterion: each station must hear an explicit confirmation after delivering its own signal report before considering the contact complete. Station A considers the contact complete upon receiving Station B’s concluding 73 in T4, while Station B considers it complete upon decoding Station A’s report in T3 and transmitting its final 73.
C. DXpedition Fox and Hound Multi-Station Pileup Operation
During DXpedition pileups or contest operations in Fox and Hound (F/H) mode, Station A (Fox) activates the MULTIREPORT+73 protocol (Type 11) to confirm up to two answering Hound stations simultaneously on a single carrier: 1. Slot 1 (Fox): Fox broadcasts directed CQ on its primary run frequency (e.g., CQ DX <FOX>). 2. Slot 2 (Hounds): Remote Hounds call simultaneously on split audio frequencies via directed CALL (e.g., <FOX> <HOUND1> FN42 -08). 3. Slot 3 (Fox): Fox confirms both Hounds simultaneously on the run frequency via MULTI-REPORT+73 (<HOUND1> R+05 <HOUND2> R-02 <FOX>). 4. Slot 4 (Hounds): Both Hounds respond with concluding 73 acknowledgments on their split frequencies (<FOX> <HOUND1> 73). When confirming a single Hound in Fox mode, standard callers are confirmed using Type 8 (REPORT+73 STD + SUF). Single-target Type 11 (or Type 12 for final acknowledgments) is used when confirming non-standard callers or when operating under strict split-frequency F/H scheduling; in this case, Target 2 duplicates Target 1 (identical hash and SNR), which decoders process as a single-station transmission.
Table 1: QSO sequence comparison between conventional protocols (FT8) and the LQ8 4-slot protocol. Seq
Conventional Protocols (FT8)
Seq
LQ8 Protocol
1 2 3 4 5 6
CQ YO1YO JN47 YO1YO TU2TU KL22 TU2TU YO1YO +05 YO1YO TU2TU R-03 TU2TU YO1YO RR73 (or RRR) YO1YO TU2TU 73 (optional if RR73)
1 2 3 4 — —
CQ YO1YO JN47 YO1YO TU2TU KL22 -03 TU2TU YO1YO R+05 YO1YO TU2TU 73 [Confirmed] — —
As summarized in Table 1, LQ8 completes a contact in 4 time slots (60 s vs. 5–6 messages / 75–90 s in conventional exchanges ending in RR73 or RRR/73), delivering full bidirectional callsigns, Maidenhead locators, and signal reports with mutual verification: 1. T1 (Slot 1, Even): Station A transmits a CQ broadcast (catalogued in Section III, Types 1–4) containing its callsign, optional portable suffix, grid locator, or CQ modifier. 2. T2 (Slot 2, Odd): Station B transmits a directed CALL reply (Types 5–7) packing Station A’s target address, caller callsign, measured SNR report, and grid locator into a single frame. 3. T3 (Slot 3, Even): Station A acknowledges with REPORT+73 (Type 8 for standard callsigns, or multi-station Type 11), delivering its measured SNR report for Station B. 4. T4 (Slot 4, Odd): Station B transmits a final 73 acknowledgment (Types 9, 10, or 12), completing the confirmed bidirectional contact.
Throughput Multiplier Analysis. In continuous pileup operation, each QSO cycle completes in 3 slots (45 s vs. 60 s conventional). Confirming two answering Hounds simultaneously in Step 3 delivers a peak capacity of 160 QSOs/h on a single 50.0 Hz carrier with 0.0 dB power-splitting penalty, avoiding the −3.0 dB RF loss of multi-carrier FT8 F/H mode. Under dual-carrier LQ8 (100 Hz bandwidth), capacity reaches 320 QSOs/h while halving exposure to fading. D. Multi-Caller Contention and Pileup Queuing
When multiple stations answer the same CQ simultaneously in 1-on-1 mode, Station A selects one caller and transmits REPORT+73 addressed to that station; other callers retry in the next alternating time slot. Frames are disambiguated via uniform 24-bit callsign hashes (224 ≈ 16.78 × 106 bins, Section IV-D) and canonical precedence (Section III-C). To optimize pileup resolution, transceivers implement opportunistic candidate queuing (up to 16 stations). Priority aging balances throughput with fairness, preventing highSNR arrivals from starving marginal callers. Upon decoding 73 in T4, Station A immediately directs REPORT+73 to the highest-priority queued station without an intermediate CQ, accelerating turnover. If the queue is full, lowest-SNR entries below decode threshold are evicted first; entries expire after four unacknowledged cycles (60 s in LQ8, 30 s in LQ4).
B. Retransmission, Error Recovery and Logging Semantics
To ensure session progress over lossy channels, LQ formalizes timeout recovery and logging rules. Retransmission and Repeat Calls. If Station B misses REPORT+73 in T3 (due to QSB or interference), it repeats CALL in the next odd slot. Receiving this repeat informs Station A that its report was lost, prompting Station A to resend REPORT+73. Similarly, if Station A misses the final 73 in T4, it retransmits REPORT+73; Station B reacknowledges with 73 without duplicate logging. 2
T HE LQ D IGITAL M ODE FAMILY
Luis Quesada (HB9IPH)
III. M ESSAGE A RCHITECTURE To maximize channel efficiency within the 77-bit physical frame budget, LQ replaces fixed-width bit fields with an entropy-matched variable-length message architecture.
• Callsign Hashes: “Hash” is a 24-bit CRC-24/Q hash (224 ≈ 16.78 × 106 bins); “hash† ” is the 16-bit DX hash (Section IV-D). • Multi-Station Fields: Type 11 Fox pileup sequences [Prefix3 | DX16 | Tgt124 | SNR15 | Tgt224 | SNR25 ] (77 bits); Type 12 formats [Prefix8 | DX16 | Tgt124 | Tgt224 | 000002 ] (77 bits, 5 zero-padded bits). • Modifiers, Locators & SNR: “Mod” is a 20-bit modifier (Section IV-F); “loc” is a 15-bit locator (Section IV-E); “SNR” is a 5-bit report (Section IV-G).
A. Design Motivation & Prefix-Free Framing
Under a strict 77-bit physical payload budget, conventional fixed-width message headers impose an unnecessary penalty on high-entropy transmissions. In a standard CALL reply, encoding two 28-bit standard callsigns, a 15-bit Maidenhead grid locator, and a 5-bit measured SNR report requires 76 information bits: 1b + |{z} 28b + |{z} 28b + |{z} 15b + |{z} 5b = 77 bits. (1) |{z} Prefix
Target
Caller
Locator
C. Protocol Boundary Conditions & Canonical Precedence
To eliminate ambiguity across station profiles, LQ formalizes eight canonical precedence and boundary rules:
SNR
Uniform 3-bit or 4-bit type headers exceed the remaining 1-bit margin, preventing simultaneous transmission of locator and report in conventional protocols. LQ resolves this constraint by synthesizing variable-length prefix coding [4, 3] with physical-layer bit budgets. Assigning a 1-bit codeword (1) to the dominant CALL STD ( NO SUF ) format preserves 76 bits for payload data, combining station identification, locator delivery, and signal report measurement into a single frame. Simpler messages (such as standard CQ, requiring 43 payload bits) readily accommodate longer prefix codes. Formally, the prefix code C = {c1 , c2 , . . . , ck } is prefixfree: ∀ i ̸= j : ci is not a prefix of c j . (2) The receiver traverses a binary prefix tree bit-by-bit from the most-significant bit until reaching a terminal leaf node, identifying the message type without length fields or delimiters. Although the mathematical binary prefix tree across −leni = 1.0, the active operational all 16 slots satisfies ∑16 i=1 2 codebook is intentionally prefix-free without being Kraftcomplete because Types 14–16 are explicitly reserved for future backward-compatible protocol expansions rather than active operational message formats.
1. Strict Canonical Precedence: Transmitters must use the most compact format permitted by their callsign: Type 5 precedes Type 6, and Type 6 precedes Type 7 for CALL; Type 8 precedes Type 11 for REPORT+73; Type 9 precedes Types 10 and 12 for 73. Hashed formats are prohibited if standard representation fits, ensuring deterministic decode interpretation. 2. Deterministic Hash Disambiguation: In 1-on-1 exchanges, decoders strictly following canonical precedence ignore incoming hashed frames (Types 7, 10, 11) for local address matching, preventing spurious collisions against standard stations during active contacts. 3. Universal Locator and SNR in Type 6: Type 6 allocates 4 prefix bits and 24 target hash bits, leaving 49 bits for caller callsign, suffix, 15-bit locator, and 5-bit SNR (4 + 24 + 28 + 1 + 15 + 5 = 77b). Suffixed callers deliver locator and SNR on their initial call without extra steps. 4. Clear-Text Identity in Type 7: Type 7 encodes the target via 20-bit hash (H20 = H24 ≫ 4), the non-standard caller via clear-text 48-bit Base-38 representation (≤ 9 characters), 1-bit suffix (/P), and 5-bit SNR (3 + 20 + 48 + 1 + 5 = 77b), delivering unhashed identity directly in Step 2. 5. Single-Target Multi-Station Framing: When confirming a single station in Fox pileup mode (Types 11 and 12), Target 2 duplicates Target 1 (identical hash and SNR), which decoders process as a single-station transmission. In standard 1-on-1 contacts, Type 8 strictly supersedes Type 11; single-target Type 11 is reserved for non-standard callers or split-frequency F/H schedules. 6. Collision Resistance: Uniform 24-bit callsign hashes (224 ≈ 16.78 × 106 bins) yield Pcollision ≤ 0.75% across 500 stations, disambiguated via local callsign caches and canonical precedence. 7. Compound Callsigns: Stations with callsigns exceeding 9 characters (up to 13 characters, e.g., 3B9/HB9IPH/P, Category D) utilize the 69-bit Base-38 field in CQ frames (Type 4); directed replies use CQ or free text (Type 13). 8. Verification & Compatibility: Bit-exact codec traces and golden vectors across all 13 message formats are verified in the reference suite [11] across AWGN, Rayleigh fading, and clock-drift conditions. Compliant decoders treat unassigned opcodes (Types 14–16) as valid framing boundaries, safely ignoring them.
B. Operational Categories & Message Catalogue
Stations select transmission formats according to the operational categories defined in Table 2. Table 3 catalogues all 16 message slots with their prefix codewords, payload layouts, and bit budgets. Frame payloads ≤ 77 bits are zero-padded to the 77-bit link-layer boundary. Payloads are serialized in big-endian bit order (MSB first) into a 10-byte buffer: bit 0 corresponds to 0x80 of Byte 0, bit 7 to 0x01 of Byte 0, and bits 77–79 (the three least significant bits of Byte 9) are set to zero. Field Designations in Table 3: • Canonical Short Identifiers: Standardized mnemonics: CQ, CALL, RPT73 (for REPORT+73), 73, RPT73M (for MULTI-REPORT+73), and 73M (for MULTI-73). • Prefix & Standard Callsign: “Code” denotes prefix length; “call:std” is a 28-bit standard callsign (Section IVA). • Non-Standard Callsigns & Suffixes: “call:n” is an n-character non-standard callsign packed via Base-38 (Section IV-C); “Suf” encodes 1-bit portable modifiers (0=none, 1=/P). Type 5 omits suffixes to pack two standard callsigns, locator, and SNR into 77 bits (1 + 28 + 28 + 15 + 5 = 77b). 3
T HE LQ D IGITAL M ODE FAMILY
Luis Quesada (HB9IPH)
Table 2: Operational categories and corresponding 4-step message sequences. Cat. Callsign / Mode Configuration
Step 1: CQ
Step 2: CALL
Step 3: REPORT+73
Step 4: 73
A B C D
Standard (no suffixes) Standard + std suffix (/P) Non-standard (≤ 9 chars) + optional suffix Long compound (10–13 chars) + optional suffix
Type 1 Type 1 Type 2 / 3 Type 4
Type 5 Type 6 Type 7∗ / Type 6 —‡
Type 8 Type 8 Type 11 Type 11
E
Multi-station reply
—
—
Type 11 (Fox)
Type 9 Type 9 Type 10 / 12 Type 12 Type 12 (Fox) / Type 9, 10 (Hounds)
∗ In Step 2, Category C callers transmit Type 7 (clear-text callsign, suffix, SNR to target 20-bit hash); standard callers answering a Category C CQ transmit Type 6 (locator, SNR to target 24-bit hash). ‡ Category D compound stations (10–13 chars) initiate contact via CQ (Type 4) or free text (Type 13).
Table 3: Complete LQ message-type catalogue. Huffman Code ID Type
0000000000 0000000001 00000001 0000001 1 0100 001 0000000010 0000000011 0001 011 00000111 0101 00001 0000010 00000110
Bits (Payload)
1 CQ std+suf 2 CQ non-std 1 3 CQ non-std 2 4 CQ non-std 3 5 CALL std (nosuf) 6 CALL std+suf 7 CALL non-std 8 REPORT+73 std+suf (RPT73) 9 73 std+suf 10 73 non-std 11 MULTI-REPORT+73 (RPT73M) 12 MULTI-73 (73M) 13 FREE TEXT 14 (reserved A) 15 (reserved B) 16 (reserved C)
Suf
Caller
Total
Code
Target
10 10 8 7 1 4 3 10 10 4 3 8 4 5 7 8
— — 28 call:std 1 suf 20 mod 15 loc — — 48 call:9 1 suf — 15 loc — — 48 call:9 1 suf 20 mod — — — 69 call:13 1 suf — — 28 call:std —∗ 28 call:std —∗ — 15 loc 24 hash — 28 call:std 1 suf — 15 loc 20 hash — 48 call:9 1 suf — — 28 call:std 1 suf 28 call:std 1 suf — — 28 call:std 1 suf 28 call:std 1 suf — — 24 hash — 48 call:9 1 suf — — 16 hash† + 2 × (24 hash + 5 SNR) 16 hash† + 2 × 24 hash 73 text (Varicode) 72 payload 70 payload 69 payload
Suf Modifier Locator SNR — — — — 5 SNR 5 SNR 5 SNR 5 SNR — —
74 74 77 77 77 77 77 73 68 77 77 72 77 77 77 77
∗ Type 5 omits suffix fields to pack two standard callsigns, locator, and SNR into 77 bits (1 + 28 + 28 + 15 + 5 = 77b). † 16-bit DX hash (Section IV-D). The “Total” column indicates active information bits; formats with Total < 77 bits (Types 1, 2, 8, 9, 12) are right-padded with trailing zeros (77 − Total bits) to complete the 77-bit physical frame boundary prior to CRC-14 computation.
Table 4: LQ Varicode assignments for the 104-character free-text alphabet. Char Varicode E T A O N I S R H D L C U M F W P G Y B V K X J
Len
Freq Char Varicode
3 16.73% 001 3 10.23% 010 11 4 7.44% 0 0 111 4 6.59% 0 1000 4 6.24% 4 5.96% 1001 1010 4 5.90% 4 5.41% 1011 1100 4 5.00% 4 4.76% 1101 11100 5 3.48% 11101 5 3.21% 11110 5 2.34% 111110 6 2.24% 111111 6 2.05% 6 1.95% 000100 6 1.63% 000101 6 1.60% 000110 6 1.56% 000111 6 1.46% 000010 6 1.18% 000011 7 0.85% 0000010 8 0.53% 00000110 8 0.34% 00000111 1 9 0.16% 000000 00 0000001010 10 0.10%
1 Q ! ? Z , . 0 2 8 3 4 5 9 6 7 " ' _ ; : = ( ) #
Len Freq Char Varicode
Len
Freq
Char
Varicode
Len
Freq
10 0.09% * 0000000000110 13 0.01% Å 0000001011 00000000000010111 17 <0.01% 10 0.07% [ 00000000001110 14 0.01% Æ 0000001100 00000000000011000 17 <0.01% 11 1 10 0.07% ] 1111 14 0.01% Ç 000000 0 0000000000 00000000000011001 17 <0.01% 111 10 0.07% | 1 14 0.01% È 000000 0 00000000000 00 00000000000011010 17 <0.01% 10 0.06% / 000000000001010 15 <0.01% É 0000001111 00000000000011011 17 <0.01% 11 0.06% $ 0000000000010110 16 <0.01% Ê 00000001000 00000000000011100 17 <0.01% 11 0.05% + 0000000000010111 16 <0.01% Ë 00000001001 00000000000011101 17 <0.01% 11 0.05% \n 0000000000011000 16 <0.01% Ì 00000001010 00000000000011110 17 <0.01% 11 0.05% % 0000000000011001 16 <0.01% Í 00000001011 00000000000011111 17 <0.01% 11 0.04% & 0000000000011010 16 <0.01% Î 00000001100 00000000000001000 17 <0.01% 11 0.04% < 0000000000011011 16 <0.01% Ï 00000001101 00000000000001001 17 <0.01% 11 0.04% > 00000000000111000 17 <0.01% Ð 00000000000001010 17 <0.01% 00000001110 11 0.04% @ 00000000000111001 17 <0.01% Ñ 00000001111 00000000000001011 17 <0.01% 11 0.03% \ 00000000000111010 17 <0.01% Ò 00000000100 00000000000001100 17 <0.01% 11 0.03% ˆ 00000000000111011 17 <0.01% Ó 00000000101 00000000000001101 17 <0.01% Ô 000000001100 12 0.03% ‘ 00000000000111100 17 <0.01% 00000000000001110 17 <0.01% Õ 000000001101 12 0.03% { 00000000000111101 17 <0.01% 00000000000001111 17 <0.01% Ö 000000001110 12 0.03% } 00000000000111110 17 <0.01% 00000000000000100 17 <0.01% Ø 000000001111 12 0.02% ˜ 00000000000111111 17 <0.01% 00000000000000101 17 <0.01% Ù 000000000100 12 0.02% ¡ 00000000000010000 17 <0.01% 00000000000000110 17 <0.01% Ú 000000000101 12 0.02% ¿ 00000000000010001 17 <0.01% 00000000000000111 17 <0.01% Û 000000000110 12 0.02% À 00000000000010010 17 <0.01% 00000000000000010 17 <0.01% Ü 0000000001110 13 0.02% Á 00000000000010011 17 <0.01% 00000000000000011 17 <0.01% Ý 0000000001111 13 0.01% Â 00000000000010100 17 <0.01% 00000000000000001 17 <0.01% 1 13 0.01% Ã 1 1 1 17 <0.01% Þ 0000000000 00 000000000000 0 0 000000000000000001 18 <0.01% 0000000000101 13 0.01% Ä 00000000000010110 17 <0.01% [FILL] 000000000000000000 18 <0.01%
4
T HE LQ D IGITAL M ODE FAMILY
Luis Quesada (HB9IPH)
IV. F IELD E NCODINGS
16-Bit DX Callsign Hash (H16 ): Used in multi-station frames (Types 11 and 12), computed via the WSJT-X 16-bit multiplicative hash [2]. Callsigns right-pad to 11 characters over alphabet ( → 0, 0-9 → 1 . . . 10, A-Z → 11 . . . 36, / → 37): 10−i ·47055833459)/248 ⌋ mod 216 , H16 (call) = ⌊(∑10 i=0 vi ·38 (4) yielding 65,536 states (e.g., H16 (HB9IPH) = 0x7A8B). UI Resolution: Resolved hashes display bracketed by callsign (e.g., <HB9IPH>); unresolved hashes display in hex (e.g., <01A4F2>, <01A4F>, or <7A8B>).
To maintain compatibility, LQ adopts core field structures from FT8 [1, 2] (K9AN/K1JT)—28-bit callsigns, 15-bit grid locators, 20-bit CQ modifiers, and 5-bit signal reports— while introducing 1-bit portable suffixes, Base-38 nonstandard callsigns, CRC-24/Q hashes, and a 104-character free-text Varicode. A. Standard Callsign (28 bits)
Adopted from FT8 [1, 2], standard ITU amateur callsigns canonicalize to 6 characters anchored around decimal digit d at position 3: c1 c2 ds1 s2 s3 . Prefix (c1 , c2 ) right-aligns with space padding in c1 if 1 character; suffix (s1 , s2 , s3 ) left-aligns with spaces. Callsigns matching c1 c2 ds1 s2 s3 without slashes are standard; all others are non-standard (Section IV-C). Symbol index mappings: c1 ∈ { , 0–9, A–Z} (radix 37: space → 0, 0-9 → 1 . . . 10, A-Z → 11 . . . 36); c2 ∈ {0–9, A–Z} (radix 36: 0-9 → 0 . . . 9, A-Z → 10 . . . 35); d ∈ {0–9} (radix 10); and s1 , s2 , s3 ∈ { , A–Z} (radix 27: space → 0, A-Z → 1 . . . 26). With indices (n1 , . . . , n6 ), mixed-radix serialization packs into 28-bit integer N28 : N28 = (n1 · 36 · 10 + n2 · 10 + n3 ) · 273 + n4 · 272 + n5 · 27 + n6 . (3) Standard callsigns occupy 0 ≤ N28 ≤ Nmax = 262,177,559 < 228 ; subsequent states encode tokens DE = 262,177,560, QRZ = 262,177,561, and CQ = 262,177,562. Decoders validate radix ranges to reject corrupted values.
E. Maidenhead Grid Locator (15 bits)
Following the FT8 standard [1, 2, 8], four-character Maidenhead grid locators (F1 F2 D1 D2 , with fields F1 , F2 ∈ [A–R] and squares D1 , D2 ∈ [0–9]) divide the globe into 18 × 18 = 324 fields of 10 × 10 = 100 squares (32,400 total squares). Packed into 15 bits (Ngrid < 32,400 < 215 = 32,768): Ngrid = (F1 − ’A’) · 1800 + (F2 − ’A’) · 100 (5) + (D1 − ’0’) · 10 + (D2 − ’0’). Values 0 ≤ Ngrid ≤ 32,399 represent valid Maidenhead squares; Ngrid = 32,400 is the blank locator sentinel; values 32,401 ≤ Ngrid ≤ 32,767 are rejected. F. CQ Modifiers (20 bits)
Directed CQ frames (Types 1 and 3) adopt the 20-bit modifier structure from WSJT-X / FT8 [1, 2] (220 = 1,048,576 states): 1) Unmodified CQ: Nmod = 0 designates general CQ calls. 2) 3-Digit Numeric (000–999): 1 ≤ Nmod ≤ 1000 conveys numeric designators (e.g., net/channel IDs CQ 040), mapped as Nmod = val + 1. 3) Alphanumeric Tokens (≤ 4 chars): 1001 ≤ Nmod ≤ 1,048,575 encodes tokens up to 4 characters (e.g., DX, NA, POTA, SOTA, QRP, CQWW; values > 220 − 1 rejected). Tokens < 4 characters right-pad with spaces over a 32-symbol alphabet ( → 0, A-Z → 1 . . . 26, 0-4 → 27 . . . 31):
B. Standard Dedicated Suffixes (1 bit)
To support field activations (POTA/SOTA) without hashing, frames reserve an explicit 1-bit suffix: 0=none (e.g., HB9IPH), 1=/P (portable). C. Non-Standard Callsigns (Base-38 Big-Integer Packing)
Non-standard or slashed callsigns pack as Base-38 strings over alphabet (0), A–Z (1–26), / (27), and 0–9 (28–37), right-padded with spaces to length L and evaluated bigL−1−i . 9-Char Callsigns (48 endian as Nb38 = ∑L−1 i=0 vi · 38 9 48 bits): 38 < 2 (Types 2, 3, 7, 10), supporting up to 9 characters plus 1-bit portable suffix (/P, e.g., EA6/HB9IP/P) or slashed calls (HB9IPH/Q). 13-Char Callsigns (69 bits): 3813 < 269 (Type 4), supporting compound callsigns up to 13 characters plus suffix in CQ (3B9/HB9IPH/P). Unnormalized whitespace is rejected. Alphabet Disambiguation: This Base-38 alphabet (space → 0, A-Z → 1 . . . 26, / → 27, 0-9 → 28 . . . 37) places letters before digits, unlike the legacy WSJT-X order (0-9 → 1 . . . 10, A-Z → 11 . . . 36) used in the 16-bit hash (Section IV-D).
3
Nmod = 1000 + ∑ vi · 323−i .
(6)
i=0 Omitting digits 5–9 ensures 324 = 220 fits without overflow;
longer modifiers use 4-character abbreviations (WPX) or free text. G. Signal Reports (5 bits)
Following FT8 [1], signal reports convey measured SNR from −26 dB to +5 dB via integer Nsnr = clamp(SNRdB + 26, 0, 31) ∈ [0, 31]. In directed CALL replies (Types 5–7), reports display without prefix (e.g., -03); in acknowledgments (REPORT+73, Types 8 and 11), R is prepended (e.g., R-03).
D. Callsign Hashes (24-bit, 20-bit, and 16-bit) & Dehashing
H. Free-Text Varicode Encoding (73 bits)
Non-standard stations addressed in directed frames are identified via collision-resistant hashes: 24-Bit Callsign Hash (H24 ): Computed over trimmed ASCII callsigns via CRC24/Q [9] (G(x) = 0x1864CFB, init/final 0x000000, nonreflected): H24 (call) = CRC-24/Q(call), yielding 224 = 16,777,216 states (Pcollision ≤ 0.75% across 500 stations). 20-Bit Target Hash (H20 ): Used in Type 7 directed replies as 20 MSBs: H20 (call) = ⌊H24 (call)/24 ⌋ = H24 (call) ≫ 4, yielding 220 = 1,048,576 states (e.g., H20 = 0x01A4F for H24 = 0x01A4F2), conserving 4 payload bits for reports while maintaining high collision resistance.
Unstructured text in Type 13 (FREE TEXT, 73 payload bits) uses a 104-character prefix code (Table 4) [7] optimized from character frequencies [10]. The alphabet spans uppercase A-Z, digits 0-9, space, 32 punctuation symbols, 32 Latin-1 characters (¡–Þ), newline \n, , and [FILL]. Codewords range from 3 to 18 bits (mean 4.25 bits/char), conveying ≈17.2 characters on average (+32.3% over conventional 13character payloads). Unused bits are zero-padded; decoders terminate extraction at the first zero bit without emitting fill tokens. 5
Frequency Shift (Hz)
T HE LQ D IGITAL M ODE FAMILY
Luis Quesada (HB9IPH)
Sync 1 Sync 2 Sync 3 (7 sym) LDPC Data Block 1 (29 sym, 87 bits) (7 sym) LDPC Data Block 2 (29 sym, 87 bits) (7 sym)
T7 (43.8) T6 (37.5) T5 (31.2) T4 (25.0) T3 (18.8) T2 (12.5) T1 (6.2) T0 (0.0) 0
1
2
3
4
5
6
7
8
9
10
Transmission Time (seconds elapsed)
Costas Synchronization Arrays (3 × 7 symbols)
11
12
13
LDPC(174,91) Data Payloads (2 × 29 symbols)
Figure 1: LQ8 physical frame structure (8-GFSK, 50.0 Hz bandwidth, 12.64 s duration).
V. P HYSICAL L AYER To ensure equal weak-signal sensitivity (−21.0 dB SNR in 2500 Hz bandwidth) and transceiver compatibility, LQ8 deliberately adopts the core physical-layer modulation and error-correction coding of the FT8 protocol [1], engineered by Steve Franke (K9AN) and Joe Taylor (K1JT).
C. Modulation Mapping & Continuous-Phase Synthesis
The 3-bit Gray code maps channel bit triplets to tones: 000→0, 001→1, 011→2, 010→3, 110→4, 100→5, 101→6, and 111→7. Continuous-phase audio synthesis s(t) = A(t) cos(φ (t)) at fs = 12,000 Hz employs half-symbol raised-cosine envelope shaping (Tramp = Ts /2 = 80.0 ms in LQ8, 160.0 ms in LQ16) and Gaussian frequency trajectories (BT = 2.0): ! Z N −1
A. Channel Coding: CRC-14 and Systematic LDPC(174,91)
Link-layer encapsulation preserves FT8’s channel-coding structure [1]: (1) 77-Bit Payload from the application layer; (2) 14-Bit CRC Checksum (GCRC14 (x), Table 5) evaluated by shifting the 77-bit payload MSB-first into a 14-bit LFSR using FT8’s generator polynomial 0x2757 followed by 14 trailing zeros, appending remainder (d77 . . . d90 ) to form a 91-bit systematic block (Pfalse ≤ 2−14 ≈ 6.1 × 10−5 ); 5 zero bits pad to a 12-byte boundary; and (3) Systematic LDPC(174,91) FEC utilizing the identical Gallager generator matrix G83×91 (Table 6) [1, 5] producing 83 parity bits (R ≈ 0.523, 174 codeword bits). Systematic codeword c ∈ F174 2 sets c j = d j for 0 ≤ j < 91. Parity bits are: c91+i =
90 M
sym
t
φ (t) = φ0 + 2π
0
f0 +
∑ ak · ∆ f · g(τ − kTs ) dτ,
k=0
(8) where tone index ak ∈ {0, 1, . . . , M − 1} is uncentered with tone 0 at base subcarrier f0 (∆ f = 6.25 Hz in LQ8). Frequency pulse g(t) is truncated to duration L = 3Ts (t ∈ [−1.5Ts , +1.5Ts ]): 1 t − Ts /2 t + Ts /2 g(t) = − erf 2πB √ . erf 2πB √ 2Ts 2 ln 2 2 ln 2 (9) D. Costas Synchronization & DSP Pipeline
Gi, j · d j ,
0 ≤ i < 83,
(7)
While LQ8 shares FT8’s modulation, CRC-14, and LDPC codes, it deliberately departs in its synchronization structure to achieve physical cross-protocol isolation. Rather than FT8’s sync sequence ([3, 1, 4, 0, 6, 5, 2]), 8-GFSK modes (LQ8 and LQ16) synchronize via three 7-symbol Costas arrays [6] (C7 = [2, 5, 6, 1, 3, 0, 4]) at symbols 0–6, 36–42, and 72–78. The 174-bit systematic LDPC codeword is partitioned without bit interleaving into two 87-bit data blocks: Data Block 1 (symbols 7–35, 29 × 3 = 87 bits) carries codeword bits c0 . . . c86 , while Data Block 2 (symbols 43–71) carries c87 . . . c173 . Each symbol maps 3 consecutive bits MSB-first via the 3-bit Gray code. Preambles exhibit ideal autocorrelation with peak sidelobe ≤ 1 and ≤ 1 coincidence hit against FT8, preventing false decodes. Receiver DSP executes the multi-pass decoding paradigm from WSJT-X [1, 2]: sliding STFT (Hann window, 4hop oversampling) generating spectral density S[ti , f j ], 2D matched filter detection across ±0.5 s timing windows, 3point parabolic frequency refinement (|∆ ferr | < 0.1 Hz), soft LLR extraction, log-domain LDPC belief-propagation decoding (up to 25 passes, terminating early upon H · ĉT = 0 and CRC-14 verification), and time-frequency candidate subtraction to decode weaker signals.
j=0
where G83×91 is the Gallager matrix in Table 6 (23 hex digits/row, 91 MSB-aligned bits; bit 0 of digit 23 is zero pad). CRC-14 parameters are listed in Table 5. Table 5: CRC-14 channel coding parameter specification. Parameter
Value / Specification
Generator Polynomial GCRC14 (x) Hex / LFSR Representation Initial State / Final XOR Input / Output Reflection Bit Framing & Padding Undetected Error Probability Invalid Checksum Sentinel Target FEC Input Block
x14 + x13 + x10 + x9 + x8 + x6 + x4 + x2 + x + 1 0x2757 (14-bit: 100111010101112 ; 15-bit monic: 0x6757) 0x0000 (14 zeros) / 0x0000 (uninverted) False / False (MSB-first evaluation & output) 77 payload bits + 14 CRC bits = 91 systematic bits (+5 pad → 96) Pfalse ≤ 2−14 ≈ 6.10 × 10−5 Remainder 0x0000 rejected as corrupt Feeds LDPC(174, 91) generator G83×91
B. LQ8 Physical Transport & UTC Slot Framing
LQ8 adopts FT8’s continuous-phase 8-GFSK transport parameters [1]: 79 symbols in 12.64 s within 15.0 s UTC slots (Rs = 6.25 Bd, ∆ f = 6.25 Hz, 50.0 Hz footprint, −21.0 dB SNR sensitivity, Figure 1). Transmissions occupy 3.0 kHz USB segments with multiple concurrent subcarrier offsets. For timestamp tUTC , slot index and parity s ∈ {0, 1} evaluate as k = ⌊tUTC /Tslot ⌋ and s = k mod 2 (Even :00/:30 vs. Odd :15/:45). Guard interval Tguard = Tslot − Ttx (2.36 s in LQ8, 2.46 s in LQ4) provides propagation and T/R turnaround margin; stations alternate parity across cycles. 6
T HE LQ D IGITAL M ODE FAMILY
Luis Quesada (HB9IPH)
Table 6: The complete Gallager LDPC(174, 91) generator matrix G83×91 (83 rows × 23 hex digits). Each row represents 92 bits MSBaligned; bit 0 of the 23rd hex digit is an unused zero padding bit. Row
Generator Vector (23 Hex Digits)
Row
Generator Vector (23 Hex Digits)
Row
Generator Vector (23 Hex Digits)
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
8329ce11bf31eaf509f27fc 761c264e25c259335493132 dc265902fb277c6410a1bdc 1b3f417858cd2dd33ec7f62 09fda4fee04195fd034783a 077cccc11b8873ed5c3d48a 29b62afe3ca036f4fe1a9da 6054faf5f35d96d3b0c8c3e e20798e4310eed27884ae90 775c9c08e80e26ddae56318 b0b811028c2bf997213487c 18a0c9231fc60adf5c5ea32 76471e8302a0721e01b12b8 ffbccb80ca8341fafb47b2e 66a72a158f9325a2bf67170 c4243689fe85b1c51363a18 0dff739414d1a1b34b1c270 15b48830636c8b99894972e 29a89c0d3de81d665489b0e 4f126f37fa51cbe61bd6b94 99c47239d0d97d3c84e0940 1919b75119765621bb4f1e8 09db12d731faee0b86df6b8 488fc33df43fbdeea4eafb4 827423ee40b675f756eb5fe abe197c484cb74757144a9a 2b500e4bc0ec5a6d2bdbdd0 c474aa53d70218761669360
28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
8eba1a13db3390bd6718cec 753844673a27782cc42012e 06ff83a145c37035a5c1268 3b37417858cc2dd33ec3f62 9a4a5a28ee17ca9c324842c bc29f465309c977e89610a4 2663ae6ddf8b5ce2bb29488 46f231efe457034c1814418 3fb2ce85abe9b0c72e06fbe de87481f282c153971a0a2e fcd7ccf23c69fa99bba1412 f0261447e9490ca8e474cec 4410115818196f95cdd7012 088fc31df4bfbde2a4eafb4 b8fef1b6307729fb0a078c0 5afea7acccb77bbc9d99a90 49a7016ac653f65ecdc9076 1944d085be4e7da8d6cc7d0 251f62adc4032f0ee714002 56471f8702a0721e00b12b8 2b8e4923f2dd51e2d537fa0 6b550a40a66f4755de95c26 a18ad28d4e27fe92a4f6c84 10c2e586388cb82a3d80758 ef34a41817ee02133db2eb0 7e9c0c54325a9c15836e000 3693e572d1fde4cdf079e86 bfb2cec5abe1b0c72e07fbe
56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
7ee18230c583cccc57d4b08 a066cb2fedafc9f52664126 bb23725abc47cc5f4cc4cd2 ded9dba3bee40c59b5609b4 d9a7016ac653e6decdc9036 9ad46aed5f707f280ab5fc4 e5921c77822587316d7d3c2 4f14da8242a8b86dca73352 8b8b507ad467d4441df770e 22831c9cf1169467ad04b68 213b838fe2ae54c38ee7180 5d926b6dd71f085181a4e12 66ab79d4b29ee6e69509e56 958148682d748a38dd68baa b8ce020cf069c32a723ab14 f4331d6d461607e95752746 6da23ba424b9596133cf9c8 a636bcbc7b30c5fbeae67fe 5cb0d86a07df654a9089a20 f11f106848780fc9ecdd80a 1fbb5364fb8d2c9d730d5ba fcb86bc70a50c9d02a5d034 a534433029eac15f322e34c c989d9c7c3d3b8c55d75130 7bb38b2f0186d46643ae962 2644ebadeb44b9467d1f42c 608cc857594bfbb55d69600
Data Block 3 (syms 71–99, 29 symbols, bits 116 . . . 173); Costas S4 = [3, 1, 0, 2] (syms 100–103); and tone-0 rampdown (sym 104, Tramp = Ts /2). • Scrambling & Whitening: Prior to CRC-14/LDPC channel encoding, the 77-bit payload is bitwise XORed with the 10-byte whitening sequence (4A 5E 89 B4 B0 8A 79 55 BE 2816 ) to suppress discrete spectral lines. Bits 77–79 (byte 9, 0x28) are zeros prior to CRC-14 calculation. • Data Framing & Gray Coding: Codeword bits are mapped sequentially without bit interleaving. The three 29-symbol data blocks map consecutive pairs (b2k , b2k+1 ) of the 174-bit codeword to 4-GFSK tones via Gray coding (00→0, 01→1, 11→2, 10→3). • Ramping & Guard Margins: Tone-0 symbols at indices 0 and 104 frame the sequence (5.04 s for LQ4, 2.52 s for LQ2). Guard intervals (2.46 s in LQ4, 1.23 s in LQ2) absorb propagation delay and T/R turnaround.
VI. E XTENDED M ODES : LQ16, LQ4, AND LQ2 While LQ8 is the primary mode for 15-second scheduled weak-signal communications, the 77-bit variable-length architecture scales across three complementary physical profiles (Table 7): • LQ16 (Slow / Ultra Weak): 8-GFSK mode for severe weak-signal conditions (−24.0 dB SNR threshold in 2500 Hz) with 320 ms symbol period (25.0 Hz bandwidth, BT = 2.0, 25.28 s duration) for extreme weak-signal and EME paths. • LQ4 (Fast / Contest): 4-GFSK mode for rapid contesting and pileups (30.0 s contact, 120 QSOs/h standard, 320 QSOs/h Fox/Hound) with 48 ms symbol period, 83.3 Hz bandwidth, and 5.04 s transmission in 7.5 s UTC slots. • LQ2 (Turbo Burst): 4-GFSK high-throughput profile for dynamic burst channels (15.0 s full contact, 240 QSOs/h standard, 640 QSOs/h Fox/Hound) with 24 ms symbol period, 166.7 Hz bandwidth, and 2.52 s transmission in 3.75 s slots for meteor scatter.
B. Profile Selection and Channel Matching
Transceivers dynamically select operational profiles according to ionospheric channel coherence time Tc and link signalto-noise ratio: • When SNR < −21.0 dB and Doppler spread σ f ≤ 0.5 Hz, LQ16 provides a +3.0 dB gain over LQ8, sustaining readability down to −24.0 dB for extreme paths. • In rapid-fading channels (Tc < 10 s), LQ4’s 48 ms symbols and 7.5 s slots ensure robust sync, completing verified contacts in 30.0 s before phase degrades. • For dynamic burst channels (e.g., meteor scatter), LQ2’s 2.52 s bursts capture transient trails, completing 4-slot exchanges in 15.0 s.
A. 4-GFSK Frame Structure & Modulation
LQ4 and LQ2 transmit 105 symbols/frame using continuousphase 4-GFSK (BT = 1.0, tone spacing ∆ f = 1/Ts , modulation index h = 1.0): • Consolidated Framing Sequence: The 105-symbol frame is partitioned into: tone-0 ramp-up (sym 0, Tramp = Ts /2, 24 ms in LQ4, 12 ms in LQ2); Costas sync S1 = [0, 2, 3, 1] (syms 1–4); Data Block 1 (syms 5–33, 29 symbols, codeword bits 0 . . . 57); Costas S2 = [1, 3, 2, 0] (syms 34–37); Data Block 2 (syms 38–66, 29 symbols, bits 58 . . . 115); Costas S3 = [2, 0, 1, 3] (syms 67–70); 7
T HE LQ D IGITAL M ODE FAMILY
Luis Quesada (HB9IPH)
Table 7: Multi-mode parameter and performance comparison across standard reference modes and the LQ family. Parameter
FT8 (Ref)
FT4 (Ref)
LQ8
LQ16
LQ4
LQ2
Modulation Bandwidth Time slot Transmission time Sensitivity (SNR) Relative RF power req.
8-GFSK 50.0 Hz 15.0 s 12.64 s −21.0 dB 0 dB (ref)
4-GFSK 83.3 Hz 7.5 s 5.04 s −17.5 dB +3.5 dB (2.2×)
8-GFSK 50.0 Hz 15.0 s 12.64 s −21.0 dB 0 dB (ident.)
8-GFSK 25.0 Hz 30.0 s 25.28 s −24.0 dB −3.0 dB (0.5×)
4-GFSK 83.3 Hz 7.5 s 5.04 s −17.5 dB +3.5 dB (2.2×)
4-GFSK 166.7 Hz 3.75 s 2.52 s −14.0 dB +7.0 dB (5.0×)
Type coding QSO messages QSO duration Standard QSO Rate∗ Pileup Rate (1-carrier)∗ Pileup Rate (2-carrier)∗
Fixed 5–6 75.0–90.0 s 40–48/h 60/h 120/h
Fixed 5–6 37.5–45.0 s 80–96/h 120/h 240/h
Huffman 4 60.0 s 60/h 160/h 320/h
Huffman 4 120.0 s 30/h 80/h 160/h
Huffman 4 30.0 s 120/h 320/h 640/h
Huffman 4 15.0 s 240/h 640/h 1280/h
Standard Suffixes Max non-std callsign Callsign hash length Free-text alphabet Free-text capacity
/P, /R 11 chars 10/12/22-b 42 chars 71 bits (∼13 c)
/P, /R 11 chars 10/12/22-b 42 chars 71 bits (∼13 c)
/P 13 + std suffix 24/20/16-b 104 chars 73 bits (∼17 c)
/P 13 + std suffix 24/20/16-b 104 chars 73 bits (∼17 c)
/P 13 + std suffix 24/20/16-b 104 chars 73 bits (∼17 c)
/P 13 + std suffix 24/20/16-b 104 chars 73 bits (∼17 c)
∗ FT8/FT4 contacts require 5–6 messages (75–90 s / 37.5–45 s) using RR73 or RRR/73; LQ completes full contacts in 4 messages (60 s in LQ8). Peak rates
assume continuous zero-loss operation. Pileup rates reflect Fox and Hound mode confirming 1 station/slot in FT8/FT4 vs. 2 stations/slot in LQ (Type 11).
R EFERENCES
VII. C ONCLUSION LQ8 demonstrates that continuous-phase 8-GFSK and systematic LDPC(174, 91) transport deliver higher throughput through variable-length prefix framing while maintaining full backward physical compatibility and −21.0 dB SNR sensitivity in a 2500 Hz reference bandwidth. By optimizing message prefix allocations to match operational entropy, LQ8 packs callsigns, locators, and reports into a 77-bit budget, finalizing confirmed two-way contacts in 4 transmission slots (60 s). For high-density pileups, LQ8 introduces the single-carrier MULTI-REPORT+73 protocol, confirming two answering stations simultaneously without RF power-splitting penalties and achieving throughputs up to 160 QSOs/h (320 QSOs/h in dual-carrier operation). The unified protocol family extends this architecture across three complementary physical profiles. LQ16 scales symbol duration to 320 ms, delivering a +3.0 dB sensitivity advantage (−24.0 dB SNR threshold) across ultra-weak fading and EME paths. For rapid contesting and dynamic propagation, LQ4 (7.5 s slots) and LQ2 (3.75 s slots) utilize 4-GFSK modulation and Costas sync arrays to complete contacts in 30.0 s and 15.0 s, supporting burst rates up to 640 QSOs/h on VHF/UHF meteor scatter and sporadic-E openings. The complete software suite is implemented in the opensource C++ reference library (lq_lib) under the MIT License, featuring an automated verification harness achieving > 90% line coverage alongside comprehensive golden vector test suites across all operational profiles. End-to-end field verification has been demonstrated in real-world portable activations via qFT8 for Android across HF bands. Future protocol evolution will explore multi-carrier wideband chat aggregation, dedicated 60-meter channel sub-allocations, and low-complexity satellite telemetry framing.
[1] S. Franke, K9AN, B. Somerville, G4WJS, and J. Taylor, K1JT, “The FT4 and FT8 Communication Protocols,” QEX, pp. 7–17, Jul./Aug. 2020. [2] J. Taylor, K1JT, S. Franke, K9AN, and B. Somerville, G4WJS, “WSJT-X: Weak-Signal Communication by K1JT,” https://wsjtx.github.io/wsjtx/, 2024. [3] C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, Jul. 1948. [4] D. A. Huffman, “A Method for the Construction of Minimum-Redundancy Codes,” Proceedings of the IRE, vol. 40, no. 9, pp. 1098–1101, Sep. 1952. [5] R. G. Gallager, “Low-density parity-check codes,” IRE Transactions on Information Theory, vol. 8, no. 1, pp. 21–28, Jan. 1962. [6] J. P. Costas, “A study of a class of detection waveforms having nearly ideal range-Doppler ambiguity properties,” Proceedings of the IEEE, vol. 72, no. 8, pp. 996–1009, Aug. 1984. [7] P. Martinez, G3PLX, “PSK31: A new digital mode for HF and VHF amateur radio communications,” RadCom, vol. 75, no. 1, pp. 42–46, Jan. 1999. [8] IARU Region 1 (J. Morris, GM4ANB, ed.), “Maidenhead Locator System,” https://www.iaru-r1.org/, 1999. [9] RTCA, Inc., “Minimum Operational Performance Standards for 1090 MHz Extended Squitter Automatic Dependent Surveillance-Broadcast (ADS-B),” RTCA DO-260B / ICAO Doc 9871, Dec. 2009. [10] R. E. Lewand, Cryptological Mathematics, Mathematical Association of America, 2000. [11] L. Quesada, HB9IPH, “LQ Digital Mode Family — C++ Reference Library (lq_lib),” https://github.com/lquesada/lq_lib, 2026. [12] L. Quesada, HB9IPH, “The LQ Digital Mode Family Portal,” https://lq8.org, 2026. [13] L. Quesada, HB9IPH, “qFT8: Portable Amateur Radio for Android,” https://qft8.com, 2026.
ACKNOWLEDGMENT The original concept, protocol architecture, and reference implementations were developed by the author. Generative AI was used to assist with background research, code testing, and manuscript drafting. The author thanks the global amateur radio community for valuable feedback during early on-air testing. 8