Introduction to Ham Radio Digital Modes
The Digital Revolution in Amateur Radio: A Comprehensive Guide to Digital Modes
Introduction
Ham radio digital modes have become increasingly popular among amateur radio operators, fundamentally transforming how we communicate across the airwaves. These modes allow for efficient and error-free communication, even under challenging conditions that would make voice contacts impossible. From the earliest days of radioteletype to the latest weak-signal protocols, digital modes have opened new frontiers in amateur radio, enabling global communication with minimal power and modest antennas.
The beauty of digital modes lies in their diversity—there’s a mode optimized for nearly every operating scenario, from high-speed data transfer to ultra-weak signal DX contacts, from real-time keyboard conversations to store-and-forward messaging systems.
Understanding Digital Modes
What Are Digital Modes?
Digital modes transmit information by modulating a radio carrier wave with digital data. Unlike analog voice transmission, where the audio directly modulates the carrier, digital modes encode information into discrete states (typically represented as binary data) that can be decoded by receiving equipment. This digital encoding provides several key advantages:
Error Detection and Correction: Many digital modes include sophisticated error-checking algorithms that can detect and correct transmission errors, ensuring accurate message delivery even when signals are weak or distorted.
Spectral Efficiency: Digital modes often occupy less bandwidth than voice transmissions, allowing more operators to share the same frequency space.
Weak Signal Performance: Digital signal processing can extract coherent signals from noise levels that would render voice communication impossible.
Automated Operation: Digital modes can operate with minimal human intervention, making them ideal for automated stations, remote operation, and specialized applications like propagation beacons.
The Computer Interface
Modern digital mode operation requires a computer running specialized software and an interface between the computer and the radio. The most common interfaces are:
Sound Card Interfaces: These connect the radio’s audio output to the computer’s sound card input, and vice versa. Popular interfaces include SignaLink USB, RigBlaster, and homebrew solutions using simple audio transformers.
USB CAT Control: Most modern radios feature Computer Aided Transceiver (CAT) control via USB, allowing software to control frequency, mode, and other radio settings automatically.
Software: Programs like WSJT-X, Fldigi, MMTTY, DM780, and JTDX provide the encoding, decoding, and control functions necessary for digital mode operation.
The Digital Modes Spectrum
PSK31 and the PSK Family
History and Development
PSK31 (Phase Shift Keying, 31 baud) was developed in 1998 by Peter Martinez, G3PLX, as an ultra-narrow bandwidth mode optimized for keyboard-to-keyboard communication. The mode was revolutionary for its time, requiring only 31 Hz of bandwidth—about 1/80th of an SSB voice signal.
Technical Characteristics
PSK31 uses binary phase shift keying, where the carrier phase shifts 180 degrees to represent data bits. The mode operates at a fixed 31.25 baud rate, which corresponds to approximately 50 words per minute typing speed—perfect for real-time conversation.
Variants in the PSK Family:
- PSK31: The original, using BPSK (Binary PSK)
- QPSK31: Quadrature PSK with forward error correction
- PSK63: Double the speed of PSK31, using 63 baud
- PSK125: Four times PSK31’s speed, requiring stronger signals
- PSK250, PSK500, PSK1000: High-speed variants for excellent conditions
Operating Characteristics
PSK31 excels in crowded band conditions. Its narrow bandwidth means dozens of simultaneous contacts can occur within the space of a single SSB voice channel. The mode typically requires signal-to-noise ratios of about 10 dB for reliable copy, making it effective for moderate DX work with modest power.
The waterfall display in PSK31 software shows signals as narrow vertical lines, with text decoding in real-time. Operators can click on signals in the waterfall to tune to them instantly, making band cruising efficient and intuitive.
Practical Applications
- Ragchewing: Real-time conversations with operators worldwide
- DXing: Working distant stations with low power (QRP operation)
- Contest Use: Some contests include PSK31 categories
- Emergency Communications: Low bandwidth makes it useful when spectrum is limited
Getting Started with PSK31
New operators can get on the air quickly with free software like Fldigi. Set your radio to USB mode on the PSK31 calling frequencies (14.070 MHz on 20 meters, 7.070 MHz on 40 meters, etc.), connect your sound card interface, and start decoding. Begin by monitoring conversations to understand the protocol, which typically includes:
- Initial call: “CQ CQ CQ de [callsign] [callsign] [callsign] K”
- Signal reports using RSQ (Readability, Strength, Quality) system
- Exchange of names, QTH (location), and rig information
- Closing with “73” (best regards)
RTTY: The Classic Digital Mode
Historical Significance
Radioteletype (RTTY) represents one of the earliest digital modes, with roots extending back to the 1930s. Originally developed for commercial and military communications, RTTY was adopted by radio amateurs in the late 1940s and became the dominant digital mode for decades.
Technical Foundation
RTTY uses Frequency Shift Keying (FSK), where the carrier frequency shifts between two states (mark and space) to represent binary data. The standard amateur configuration uses:
- Shift: 170 Hz (the frequency separation between mark and space)
- Baud Rate: Typically 45.45 baud (corresponds to 60 words per minute)
- Code: Baudot code (also called ITA2 or Murray code), a 5-bit character encoding
Unlike modern character encodings like ASCII (7-bit) or UTF-8, Baudot uses only 5 bits per character, limiting it to 32 possible characters. This limitation is overcome by using two shift characters (LTRS and FIGS) to switch between letters and numbers/symbols.
The RTTY Renaissance
While newer modes have gained popularity, RTTY remains the dominant mode for digital contesting. Major contests like the ARRL RTTY Roundup and CQ WW RTTY Contest attract thousands of operators. The mode’s reliability, ease of decoding (even by ear for experienced operators), and high-speed capability make it ideal for competitive operation.
Modern RTTY Variations:
- 45.45 Baud / 170 Hz shift: Standard amateur configuration
- 50 Baud: Slightly faster, used in some regions
- 75 Baud: High-speed variant for good conditions
- RTTY-R: Includes rudimentary error correction
Operating Characteristics
RTTY signals appear as two parallel lines in the waterfall display, separated by the shift frequency (typically 170 Hz). The mode requires about 250 Hz of bandwidth and performs well with signal-to-noise ratios of 6-10 dB.
Experienced RTTY operators develop an “ear” for RTTY, able to identify signals by their characteristic “diddle” sound and even decode simple messages by ear—a skill from the era when mechanical teleprinters were standard equipment.
Contesting with RTTY
RTTY contests are fast-paced events where operators strive to make as many contacts as possible. Common exchange formats include signal reports (599), serial numbers, and location information. Software like MMTTY, 2Tone, and Fldigi includes contest logging integration, automatic message sending, and advanced filtering to maximize contact rates.
Top contesters can achieve 150-200 contacts per hour during peak conditions, with signals rapidly appearing and disappearing in the waterfall as operators complete exchanges and move on.
FT8/FT4: The Weak Signal Revolution
The WSJT-X Family
The WSJT-X suite of modes, developed by Nobel Prize-winning physicist Joe Taylor, K1JT, and a team of collaborators, has revolutionized amateur radio weak-signal communication. Originally developed for moonbounce (EME) and meteor scatter, these modes have found applications far beyond their original purpose.
FT8: Franke-Taylor 8-FSK
Introduced in 2017, FT8 (Franke-Taylor design, 8-frequency shift keying) has become the most popular digital mode on the HF bands, fundamentally changing how amateur radio operators pursue DX and rare contacts.
Technical Specifications:
- Transmission Time: 15 seconds (12.64 seconds of transmission, 2.36 seconds gap)
- Bandwidth: Approximately 50 Hz
- Signal-to-Noise Threshold: Can decode signals as weak as -24 dB (SNR)
- Message Format: Highly structured, limited to callsigns, grid squares, and signal reports
- Timing: Requires computer clock synchronization (within ±1 second)
How FT8 Works:
FT8 divides each minute into four 15-second time slots. Stations transmit during odd or even periods, ensuring no overlap with stations you’re working. The protocol uses 77-bit messages encoded with strong forward error correction, allowing reception far below the noise floor.
A typical FT8 QSO sequence:
- CQ call: “CQ DX W1ABC FN42” (calling CQ DX, callsign, grid square)
- Answer: “W1ABC K2XYZ FN31” (answering station, their grid)
- Report: “K2XYZ W1ABC -07” (signal report in dB)
- Acknowledgment: “W1ABC K2XYZ R-12” (“R” means roger/received)
- Final: “K2XYZ W1ABC RR73” (RR=roger roger, 73=best regards)
The entire exchange takes just over one minute, and the software handles most of the process automatically.
FT4: Optimized for Contesting
FT4, introduced in 2019, uses a similar modulation scheme but with 7.5-second transmission periods, making it twice as fast as FT8. While slightly less sensitive (requiring about -17 dB SNR), FT4’s speed makes it ideal for contesting and high-rate operating.
FT4 Advantages:
- Double the contact rate of FT8
- Better suited for crowded contest conditions
- Reduced bandwidth requirements minimize interference
- Still provides weak-signal capability far exceeding voice or conventional digital modes
The FT8 Phenomenon
FT8’s popularity has been both celebrated and controversial. Supporters point to its accessibility—new operators can work DX with modest equipment and antennas—and its scientific applications for propagation research. Critics argue that the automated nature removes the “human element” from amateur radio and that the mode’s popularity has crowded traditional voice and CW operators.
Regardless of perspective, FT8’s impact is undeniable:
- DXpedition Efficiency: Rare DXpeditions can work thousands of stations per day
- Propagation Studies: FT8 provides unprecedented data on propagation paths
- Entry Point: New operators achieve success quickly, building confidence
- Digital First: Many new licensees begin with FT8 before exploring other modes
Operating FT8 Effectively
Success in FT8 requires understanding the protocol and band etiquette:
Frequency Management:
- Standard calling frequencies (e.g., 14.074 MHz on 20 meters)
- Operate ±3 kHz from the center frequency
- Fox and Hound mode for DXpeditions (one station working multiple callers)
Technical Requirements:
- Computer clock synchronized via internet time or GPS
- Calibrated soundcard for accurate frequency
- Antenna system resonant on the operating band
- Quiet electrical environment (minimize noise sources)
Advanced Techniques:
- Alert functions for wanted DXCC entities
- Selective calling of rare stations
- Band monitoring for propagation openings
- Integration with logging software and award tracking
Other WSJT-X Modes
JT65: The predecessor to FT8, still popular for EME (moonbounce) and extreme weak-signal work. Uses 1-minute transmission periods and can decode signals at -28 dB.
JT9: A faster variant of JT65, occupying less bandwidth. Less popular since FT8’s introduction but still used for VHF/UHF weak-signal work.
MSK144: Optimized for meteor scatter communication, with transmission periods as short as 0.5 seconds to catch brief meteor trails.
Q65: The latest addition, optimized for extreme conditions with variable transmission times. Designed for tropospheric scatter, EME, and extreme DX.
WSPR (Weak Signal Propagation Reporter): Not for making contacts, but for propagation beacons. Stations transmit their callsign, grid square, and power level, allowing worldwide monitoring of propagation conditions. WSPR can decode signals at -34 dB, revealing propagation paths invisible to other modes.
Digital Voice Modes
Digital voice represents the cutting edge of amateur radio technology, bringing digital encoding, error correction, and network linking to voice communications.
D-STAR (Digital Smart Technology for Amateur Radio)
Developed by the Japan Amateur Radio League (JARL) in the late 1990s, D-STAR was the first widely adopted digital voice mode for amateur radio.
Technical Characteristics:
- Voice Codec: AMBE (Advanced Multi-Band Excitation) at 3,600 bps
- Data Rate: 128 kbps (VHF/UHF) or 4.8 kbps (HF)
- Data Channel: 1,200 bps for simultaneous data
- Call Routing: Automatic routing via callsign
- Frequency Bands: Primarily VHF/UHF, with HF capability
D-STAR Features:
- Crystal-clear audio in good signal conditions
- Sudden degradation at signal threshold (no graceful degradation)
- GPS position reporting
- Slow-speed data transmission alongside voice
- Internet linking between repeaters worldwide
- Reflector system for multi-user conferences
Operating D-STAR:
D-STAR radios allow you to enter the destination callsign directly. The system automatically routes your call through the network to reach the station, regardless of physical location. This call routing makes D-STAR feel more like a phone system than traditional radio.
The UR (your) field can contain:
- A specific callsign to direct-call a station
- “CQCQCQ” for general calling
- A reflector designation for conference rooms
DMR (Digital Mobile Radio)
Originally a commercial land mobile radio standard (ETSI TS 102 361), DMR has been adapted for amateur radio use and has become extremely popular due to affordable equipment and extensive network coverage.
Technical Characteristics:
- Voice Codec: AMBE+2 at 3,600 bps
- TDMA: Time Division Multiple Access (two simultaneous conversations per 12.5 kHz channel)
- Talkgroups: Numbered groups for different topics/regions
- Color Code: Like CTCSS for digital, prevents interference
- Frequency Bands: VHF, UHF, and experimental HF
DMR Network Structure:
DMR uses a talkgroup system. Talkgroups are numbered channels that can represent:
- Worldwide: TG 91 (Global)
- Regional: TG 93 (North America)
- National: TG 3100 (USA)
- State/Province: TG 3147 (California)
- Local: TG 9 (Local repeater)
- Special Interest: Various TG numbers for topics, modes, languages
Major DMR Networks:
- Brandmeister: The largest open DMR network with thousands of repeaters
- DMR-MARC: Another extensive network, coordinating talkgroup usage
- TGIF: Smaller network with unique features
- FreeDMR: Open-source network infrastructure
Advantages of DMR:
- Inexpensive radios (Chinese models under $100)
- Dual time slots double repeater capacity
- Extensive global coverage via internet-linked repeaters
- Good battery life due to efficient codec
- Rich ecosystem of hotspots for home station linking
Programming DMR:
DMR radios require codeplug programming—creating contact lists, talkgroups, channels, and zones. This programming can be complex for beginners, but online databases and tools like EditCP make the process manageable. Many regional groups provide ready-made codeplugs.
System Fusion (C4FM)
Developed by Yaesu, System Fusion uses C4FM (4-level FSK) modulation, distinguishing it from D-STAR and DMR’s TDMA approach.
Technical Characteristics:
- Voice Codec: AMBE+2 (same as DMR)
- Modulation: C4FM (4-level FSK) - more spectrum-efficient than traditional FSK
- Data Rate: 9.6 kbps
- Modes: Voice/Data Full Rate (VW), Voice/Data Half Rate (V/D), Data Full Rate
- Frequency Bands: VHF and UHF
Unique Features:
- Automatic Mode Select (AMS): Radios automatically detect and decode C4FM or analog FM
- WIRES-X: Yaesu’s internet linking system with touch-screen node room access
- Dual Mode: Seamless operation between digital and analog repeaters
- GPS and Image Transmission: Built into many System Fusion radios
Operating System Fusion:
System Fusion’s strength lies in its backward compatibility. Repeaters can operate in “AMS” mode, automatically switching between analog FM and C4FM digital based on the incoming signal. This makes transition periods easier for clubs upgrading from analog.
WIRES-X rooms function similarly to D-STAR reflectors or DMR talkgroups but with an intuitive graphic interface accessible from compatible mobile radios.
Comparing Digital Voice Modes
| Feature | D-STAR | DMR | System Fusion |
|---|---|---|---|
| Modulation | GMSK | TDMA | C4FM |
| Voice Codec | AMBE | AMBE+2 | AMBE+2 |
| Development | JARL (Open) | Commercial (Open) | Yaesu (Proprietary) |
| Radio Cost | $$$ | $ to $$ | $$ to $$$ |
| Network | Reflectors | Talkgroups | WIRES-X Rooms |
| Mixed Mode | Digital only | Digital only | Analog compatible |
| Capacity | 1 per channel | 2 per channel (TDMA) | 1 per channel |
| Learning Curve | Moderate | Steep (codeplug) | Easy |
| Global Adoption | Moderate | High | Growing |
Which Mode to Choose?
The choice often depends on local adoption. Check which modes are active in your area:
- If you have active D-STAR repeaters and want call routing, choose D-STAR
- If cost is primary concern and you want maximum network access, choose DMR
- If you want seamless analog/digital operation and modern Yaesu features, choose System Fusion
Many serious VHF/UHF operators own radios for multiple modes to maximize access to different networks and user communities.
Other Notable Digital Modes
MFSK Modes
Olivia: Developed by Pawel Jalocha, SP9VRC, Olivia is an extremely robust MFSK (Multiple Frequency Shift Keying) mode designed for reliable communication under very poor conditions. It uses forward error correction and interleaving to combat fading and interference. Available in various bandwidth/tone configurations (e.g., Olivia 16/500, Olivia 32/1000).
Contestia: Similar to Olivia but optimized for slightly better conditions, offering higher throughput. Popular for keyboard chatting when conditions are marginal.
Throb and Thor: Variations on MFSK themes, each optimized for different propagation conditions and user preferences.
PACTOR
PACTOR (and its evolutions PACTOR-II, III, and IV) is a high-performance ARQ (Automatic Repeat Request) mode popular for email via radio (Winlink system) and maritime communications. PACTOR controllers are expensive but offer excellent performance:
- PACTOR-I: 200 baud, similar to packet radio
- PACTOR-II: Up to 800 bps with compression
- PACTOR-III: Up to 2,722 bps in ideal conditions
- PACTOR-IV: Up to 10,800 bps in exceptional conditions
Used primarily by cruising sailors, emergency communicators, and those in remote areas needing reliable email service without internet.
VARA
VARA (VAriety of MFSK modes Automatic Repeat request) is a newer HF mode offering high speeds similar to PACTOR but with free software. VARA HF can achieve speeds up to 7,800 bps and has become popular in the Winlink system as an alternative to PACTOR.
VARA Variants:
- VARA HF: For HF bands, high-speed data
- VARA FM: VHF/UHF packet replacement, up to 19,200 bps
- VARA SAT: Optimized for satellite operations
Packet Radio and APRS
Packet Radio: One of the earliest amateur digital modes, using AX.25 protocol at 1,200 or 9,600 baud. While less popular for ragchewing than in the 1980s-90s, packet remains important for:
- APRS (Automatic Packet Reporting System)
- Emergency digital communications
- Network experimentation
APRS: Developed by Bob Bruninga, WB4APR, APRS uses packet radio to transmit:
- GPS position and tracking
- Weather station data
- Status messages and bulletins
- Local information databases
APRS creates a real-time tactical picture of amateur radio activity, vehicle tracking, and weather conditions, viewable on maps via APRS.fi and other websites.
SSTV (Slow Scan Television)
While technically an image mode rather than a data mode, SSTV deserves mention. It transmits still images over SSB voice channels in various formats:
- Robot: Various speeds and resolutions (36, 72 color modes)
- Martin: M1, M2, M3, M4 with different timing
- Scottie: S1, S2, S3, S4 variants
- PD: PD90, PD120, PD180, PD240 (high resolution)
SSTV is popular for:
- Casual image exchange
- ISS (International Space Station) SSTV events
- DX confirmation via picture exchange
- Greeting card transmission during holidays
JS8Call
JS8Call, developed by Jordan Sherer, KN4CRD, bridges the gap between FT8’s automation and traditional keyboard-to-keyboard modes. Based on FT8’s modulation, JS8Call adds:
- Real-time typing: Send messages as you type
- Variable speed: Adjust between ultra-slow (weak signal) and normal speeds
- Store and forward: Messages can relay through intermediate stations
- Directed messages: Send to specific callsigns
- Groups: Multi-station conversations
JS8Call appeals to operators who want weak-signal capability with more traditional communication flow than FT8’s rigid protocol.
Practical Considerations
Getting Started with Digital Modes
Basic Equipment Requirements:
- HF Transceiver with SSB capability (most modes) or digital voice-capable VHF/UHF radio
- Computer: Modern multicore processor recommended for WSJT-X modes; older machines work fine for PSK31/RTTY
- Sound Card Interface: SignaLink USB, Tigertronics, MFJ, or homebrew options
- Software:
- WSJT-X (FT8, FT4, JT65, JT9, and more)
- Fldigi (PSK31, RTTY, Olivia, Contestia, MT63, and many more)
- MMTTY or 2Tone (RTTY)
- APRS software (various options)
- CAT Control Cable (optional but recommended): USB or serial cable for computer control of radio
- Quality Audio Cables: Shielded cables to minimize RF feedback and noise
Station Configuration
Audio Levels: Proper audio levels are critical. Too low, and signals won’t decode; too high, and you’ll create splatter (excessive bandwidth) and distortion. Most digital modes use the ALC (Automatic Level Control) meter as a guide—keep it just barely moving or completely inactive.
RF Grounding: Digital modes often reveal grounding issues that don’t affect voice operation. Proper station grounding prevents RF feedback, computer crashes, and interference to household electronics.
Filtering: Many digital modes benefit from narrow IF filters to reduce adjacent channel interference. Most modern radios include adjustable DSP filters that can optimize reception.
Best Practices and Etiquette
General Operating:
- Monitor before transmitting to avoid interference
- Keep transmissions concise
- Use appropriate power (QRP when possible)
- Follow band plans and mode-specific frequency allocations
- Identify properly (CW identification every 10 minutes required in many jurisdictions)
Mode-Specific:
- PSK31: Don’t call CQ on top of existing QSOs visible in waterfall
- RTTY: Use standard contest exchange formats during contests
- FT8: Respect the ±3 kHz window, don’t transmit outside it
- Digital Voice: Monitor before keying to avoid breaking into ongoing conversations
Frequency Allocations
Different digital modes have established “calling frequencies” where activity concentrates:
20 Meters (14 MHz):
- 14.070-14.095 MHz: PSK, RTTY (data modes)
- 14.074 MHz: FT8/FT4 center frequency
- 14.095-14.099.5 MHz: Packet
- 14.230 MHz: SSTV
40 Meters (7 MHz):
- 7.070-7.100 MHz: RTTY, PSK (Region 2)
- 7.074 MHz: FT8/FT4
Digital voice modes have separate band plans on VHF/UHF, coordinated by frequency coordinators in each region.
Contests and Awards
Digital modes support numerous contests and awards:
Contests:
- ARRL RTTY Roundup
- CQ WW RTTY Contest
- CQ WPX RTTY Contest
- ARRL FT Roundup (FT4/FT8)
- Various PSK31 contests
Awards:
- WAS (Worked All States) available for most digital modes
- DXCC (DX Century Club) available for most modes
- Digital-specific awards from various organizations
- VUCC (VHF/UHF Century Club) for digital voice modes
The Future of Digital Modes
Emerging Technologies
SDR Revolution: Software Defined Radio has made digital mode operation more accessible and powerful. Modern SDRs can simultaneously decode multiple modes, provide exceptional filtering, and integrate seamlessly with digital mode software.
AI and Machine Learning: Experimental modes are exploring AI-based encoding and decoding, potentially offering even better weak-signal performance and noise rejection.
Mesh Networks: Amateur radio mesh networks using Part 15 Wi-Fi equipment on amateur frequencies are creating high-speed data networks for emergency communications and experimentation.
Codec Development: As AMBE patents expire and open-source codec projects like Codec2 mature, expect new digital voice modes with improved quality and efficiency.
Philosophy and Community
The rise of digital modes has sparked philosophical discussions in the amateur radio community:
The Automation Debate: How much automation is too much? While FT8 requires minimal operator intervention, modes like PSK31 offer real-time conversation. The community continues exploring the balance between efficiency and the “human element.”
Accessibility: Digital modes have made amateur radio more accessible to those with physical limitations (typing easier than voice for some), those in noise-restricted environments (apartments, HOAs), and those with minimal antenna systems.
Learning Pathway: Digital modes provide multiple entry points to amateur radio, from highly automated FT8 to complex PACTOR stations, allowing operators to match modes to their interests and technical abilities.
Conclusion
Digital modes represent the cutting edge of amateur radio innovation while honoring the service’s tradition of experimentation and advancement. From the narrow chirps of PSK31 to the robotic precision of FT8, from the mechanical chatter of RTTY to the crystal clarity of digital voice, these modes demonstrate amateur radio’s continuing evolution.
The diversity of digital modes ensures there’s something for everyone—whether you’re chasing DX with minimal power, having relaxed keyboard conversations, pushing the limits of weak-signal communication, or exploring the latest digital voice technologies. Each mode brings unique capabilities and challenges, encouraging experimentation and skill development.
As software-defined radios become ubiquitous and processing power continues to increase, expect digital modes to evolve further. New modulation schemes, improved error correction, and innovative applications will emerge from the amateur radio community’s tradition of experimentation.
The invitation stands: explore these digital modes, experiment with their capabilities, and contribute to the ongoing digital revolution in amateur radio. Your next contact might come through a mode that didn’t exist a year ago, and tomorrow you might invent the next breakthrough in radio communication.
73 de K8OIP
“In the digital domain, we’ve discovered that radio waves can carry not just voice and code, but entire new languages of communication—each optimized for its purpose, each revealing new possibilities in the electromagnetic spectrum.”