Frame Format

v0.3 Frame Structure

Bit offset:  0         13        37        53        85
             |---------|---------|---------|---------|
             | Barker  | Position| CRC-16  | RS(4)   |
             | 13 bits | 24 bits | 16 bits | 32 bits |

Total: 85 bits per frame = 4250 carrier cycles = 1.417 seconds

Sync Word: Barker-13

1 1 1 1 1 0 0 1 1 0 1 0 1

The Barker-13 code has the best known autocorrelation properties for its length. Peak autocorrelation is 13, and all sidelobes are exactly 0 or 1.

Position Field

24-bit unsigned integer encoding position in centiseconds:

Bits	Range	Resolution
24	0 -- 167,772 seconds	0.01 seconds

This provides 46+ hours of unique position encoding.

CRC-16

CRC-16/ARC polynomial (0x8005) with initial value 0xFFFF. Computed over the 3 position bytes only.

Purpose: O(1) fast-reject of corrupted frames before running the more expensive Reed-Solomon syndrome computation.

Reed-Solomon RS(4)

4 parity symbols in GF(2^8) with primitive polynomial 0x11D. The RS codeword covers the position bytes plus CRC bytes (5 data bytes + 4 parity bytes = 9 total).

Can detect up to 4 symbol errors and correct up to 2 symbol errors.

Modulation: Missing Cycle

Each bit is modulated onto the carrier using amplitude dips:

Bit	Amplitude	Description
0	1.0 (full)	No change
1	0.25 (dip)	Raised-cosine envelope

Bits are spaced at 50 carrier cycles (~16.7 ms) apart.

Multi-Rate Encoding

Position	Frame interval	Frame rate
0 -- 300 s	4250 cycles	0.706 frames/s
Over 300 s	2125 cycles	1.412 frames/s