PCM Frame Structure

The PCM (Pulse Code Modulation) telemetry system converts analog sensor readings and digital status words from the spacecraft into a serial bit stream. This stream is organized into fixed-length frames, each beginning with a sync word that lets the ground station find the frame boundaries in the raw data. Understanding the frame structure is essential for interpreting anything the spacecraft sends.

Frame formats, sync word structure, and A/D converter specifications are from the NAA Telecommunication Systems Study Guide (Course A-624). AGC channel assignments are from the Virtual AGC project.

Frame layout

Each high-rate frame contains exactly 128 eight-bit words, for a total of 1024 bits. The first four words (32 bits) are the sync word. The remaining 124 words carry telemetry data.

block-beta
    columns 8

    block:sync:4
        s1["Word 1"] s2["Word 2"] s3["Word 3"] s4["Word 4"]
    end
    block:data:4
        d1["Word 5"] d2["..."] d3["..."] d4["Word 128"]
    end

    style sync fill:#5c3a1a,stroke:#bd7a3a
    style data fill:#1a3a5c,stroke:#3a7abd

At the high bit rate of 51,200 bps, each 1024-bit frame takes exactly 20 milliseconds to transmit. Fifty of these frames make up one subframe, which spans exactly one second.

The sync word

The 32-bit sync word is not a simple fixed pattern. It encodes four distinct fields:

block-beta
    columns 32
    block:a:5
        a1["A field<br/>5 bits"]
    end
    block:core:15
        c1["Fixed Core<br/>15 bits"]
    end
    block:b:6
        b1["B field<br/>6 bits"]
    end
    block:fid:6
        f1["Frame ID<br/>6 bits"]
    end

    style a fill:#2d5016,stroke:#4a8c2a
    style core fill:#5c3a1a,stroke:#bd7a3a
    style b fill:#2d5016,stroke:#4a8c2a
    style fid fill:#1a3a5c,stroke:#3a7abd

Field	Bits	Default Value	Purpose
A	5	10101	Patchboard-selectable identifier
Core	15	111001101011100	Fixed correlator pattern (complemented on odd frames)
B	6	110100	Patchboard-selectable identifier
Frame ID	6	1-50	Frame number within subframe

The A and B fields were configurable via patchboard on the actual spacecraft hardware — they served as a mission identifier, letting the ground station distinguish between multiple spacecraft transmitting on similar frequencies. gr-apollo uses the default values from the study guide.

The Frame ID counts from 1 to 50 within each subframe. This is how the ground station knows which frame it is looking at within the one-second subframe cycle.

Complement-on-odd

The 15-bit fixed core is bitwise complemented on odd-numbered frames. On even frames (2, 4, 6, …, 50), the core bits are 111001101011100. On odd frames (1, 3, 5, …, 49), they become 000110010100011.

This alternation serves two purposes:

1. DC balance. If the core never changed, the sync word would have a persistent DC bias that could cause baseline wander in the NRZ bit stream. Alternating between the pattern and its complement ensures the long-term average is near zero.

2. Frame counting verification. The ground station can confirm it has not gained or lost a frame by checking whether the core matches the expected polarity for the current frame ID. If the polarity disagrees with the frame count, something has slipped.

Tip

The correlator in pcm_frame_sync checks against both the normal and complemented core simultaneously. Whichever matches tells the engine whether the current frame is odd or even, which it reports in the odd_frame metadata field of each output PDU.

Frame sync state machine

Finding frame boundaries in a continuous bit stream is a three-phase process. The FrameSyncEngine implements a state machine:

stateDiagram-v2
    [*] --> SEARCH
    SEARCH --> VERIFY : Sync match found<br/>(Hamming distance <= 3)
    VERIFY --> LOCKED : N consecutive hits<br/>at frame boundaries
    VERIFY --> SEARCH : Miss at expected boundary
    LOCKED --> LOCKED : Hit at frame boundary
    LOCKED --> SEARCH : M consecutive misses

    note right of SEARCH
        Sliding 32-bit window
        checks every bit position
    end note

    note right of VERIFY
        Candidate found,
        waiting to confirm
        at next frame boundary
    end note

    note right of LOCKED
        Stable lock,
        emitting frames
    end note

SEARCH — The engine slides a 32-bit window across the incoming bits one bit at a time. At each position, it correlates the window contents against both the even and odd reference patterns (the 26 static bits — A + core + B). When the Hamming distance falls within the threshold, the engine has a candidate.

VERIFY — One match is not enough. Noise could produce a false trigger. The engine waits for the next frame boundary (1024 bits later at high rate) and checks whether another valid sync word appears there. After the configured number of consecutive hits at expected boundaries (default: 2), it transitions to LOCKED.

LOCKED — The engine is confident it has found the correct frame alignment. It emits complete frames as PDUs. If noise corrupts a sync word, the engine tolerates it and keeps going. Only after multiple consecutive misses at frame boundaries (default: 3) does it give up and return to SEARCH.

Why a 3-bit Hamming distance threshold?

The sync word has 26 static bits (the A, core, and B fields). The frame ID changes every frame, so the correlator ignores it. A random 26-bit sequence has an expected Hamming distance of 13 from any reference pattern. Allowing up to 3 bit errors gives a comfortable margin:

• Probability of false trigger (random data matching within distance 3 of a 26-bit pattern): approximately 1 in 4,000. At 51,200 bits per second, this means a false trigger roughly every 80 milliseconds — which is why the VERIFY state exists. Two false triggers landing exactly 1024 bits apart is astronomically unlikely.

• Probability of missed detection (a real sync word with more than 3 errors): at typical operating SNR, the bit error rate is well below 10^-3, making 4 or more errors in the 26 static bits extremely rare.

Data words

The 124 data words (positions 5-128) carry three types of measurements:

High-Level Analog

Most data words are high-level analog measurements. The spacecraft’s A/D converter (the “coder”) samples 0-5V sensor outputs with 8-bit resolution.

The mapping is not quite what you would expect from a standard ADC:

Code	Voltage	Meaning
0	—	Below range (error)
1	0.00 V	Zero reference
2	0.0197 V	First real step
127	2.48 V	Midscale
254	4.98 V	Full scale
255	> 5.0 V	Overflow

The step size is 19.7 mV per LSB, calculated as 4.98V / 253 steps. Code 0 and code 255 are reserved as boundary indicators, leaving 253 actual measurement levels from code 1 to code 254.

Note

The adc_to_voltage() function in protocol.py implements this exact mapping: voltage = (code - 1) * 4.98 / 253.

Low-Level Analog

Some spacecraft sensors produce signals in the 0-40 mV range (thermocouples, strain gauges). These are amplified by a factor of 125 before reaching the A/D converter, so a 40 mV input produces a full-scale 5V signal at the coder input.

The telemetry system does not mark which words are low-level — that is determined by the patchboard configuration and known a priori from the telemetry assignment list. When processing low-level channels, divide the recovered voltage by 125 to get the actual sensor voltage.

Digital Words

Several word positions carry digital status bits rather than analog measurements. These come from two sources:

• Parallel digital inputs — 8-bit status registers read directly into frame positions
• Serial digital inputs — shift-register data clocked in by the PCM system

The most important digital words for gr-apollo are at positions 34, 35, and 57, which carry AGC downlink telemetry data. These three positions are the pipeline through which the Apollo Guidance Computer’s internal state reaches the ground.

AGC telemetry channels

Three word positions within each frame have special significance for computer telemetry:

Word Position	AGC Channel	Octal	Role
34	DNTM1	034	Telemetry word high byte (bits 14-8)
35	DNTM2	035	Telemetry word low byte (bits 7-0)
57	OUTLINK	057	Additional digital downlink data

The Apollo Guidance Computer uses 15-bit words internally. Since the PCM system works in 8-bit bytes, each AGC word is split across two consecutive frame positions. Word 34 carries the upper 7 bits (bits 14 through 8) in its lower 7 bits. Word 35 carries the lower 8 bits (bits 7 through 0) directly.

Reassembly is straightforward:

agc_word = ((dntm1_byte & 0x7F) << 8) | dntm2_byte

At 50 frames per second, this means 50 AGC words per second arrive through the telemetry channel. The AGC buffers 400 words into each downlink list snapshot (taking about 8 seconds at high rate), then transmits the buffer contents as a coherent block of navigation state, autopilot settings, or other mission-phase-specific data.

High rate vs. low rate

The PCM system supports two bit rates, selectable by ground command. The choice affects frame size, frame rate, and the amount of data per second:

Parameter	High Rate	Low Rate
Bit rate	51,200 bps	1,600 bps
Clock divider	512 kHz / 10	512 kHz / 320
Words per frame	128	200
Frames per second	50	1
Words per second	6,400	200
Subframe period	1 second (50 frames)	N/A
Bits per frame	1,024	1,600
Frame period	20 ms	1 second

Low rate was used during translunar coast and other quiet phases where the Deep Space Network antenna time was shared between missions. High rate was used during critical mission phases — launch, lunar orbit insertion, powered descent, EVA — where dense telemetry coverage was essential.

Caution

Low-rate mode uses 200 words per frame instead of 128. The frame sync word is still 32 bits (4 words), but the frame boundary is now 1,600 bits apart instead of 1,024. The FrameSyncEngine automatically adjusts its frame-boundary prediction based on the configured bit rate.

Subframe structure

At high rate, 50 consecutive frames form one subframe spanning exactly one second. The subframe concept matters because some telemetry measurements are commutated — they appear in different word positions across different frames within the subframe.

For example, a temperature sensor might be assigned to word position 72 in frame 3 of each subframe, while a pressure sensor occupies word 72 in frame 4. The same word position carries different physical measurements depending on which frame within the subframe you are looking at.

The frame ID field in the sync word (values 1 through 50) tells you which frame you are in, enabling the ground station software to route each word to the correct telemetry parameter.

graph LR
    subgraph Subframe ["Subframe (1 second)"]
        F1["Frame 1<br/>ID=1, odd"] --> F2["Frame 2<br/>ID=2, even"]
        F2 --> F3["Frame 3<br/>ID=3, odd"]
        F3 --> F4["..."]
        F4 --> F50["Frame 50<br/>ID=50, even"]
    end

    style Subframe fill:#1a1a2e,stroke:#3a7abd
    style F1 fill:#5c3a1a,stroke:#bd7a3a
    style F2 fill:#1a3a5c,stroke:#3a7abd
    style F3 fill:#5c3a1a,stroke:#bd7a3a
    style F50 fill:#1a3a5c,stroke:#3a7abd

The alternating colors reflect the complement-on-odd behavior of the sync core: odd frames (1, 3, 5, …) use the complemented pattern, even frames (2, 4, 6, …) use the normal pattern.