Also known as: Fire code
A Fire code is a cyclic block code designed specifically to handle burst errors — runs of corrupted bits packed close together — rather than the scattered, independent errors that random-error codes target.1 Devised by Philip Fire in 1959, it is built from a carefully chosen generator polynomial so that a single contiguous burst up to a guaranteed length can be located and corrected (or, when configured for detection, flagged), using nothing more than a shift register and a small amount of logic.
How it works
The Fire code’s power comes from the shape of its generator polynomial:
g(x) = (x^c − 1) · p(x)
where p(x) is an irreducible polynomial of degree m whose period does not divide
c. This factored form is what buys burst performance rather than random-error
performance. The p(x) factor acts like a cyclic-hash fingerprint that fixes the
pattern of a burst, while the (x^c − 1) factor pins down the burst’s position
within the block. Together they guarantee correction of any single burst up to length
b = min(m, c − m + 1) (and typically longer detection). Because the code is cyclic,
both encoding and syndrome computation are just clocking the received bits through an
LFSR built from g(x); decoding is error trapping — cycle the syndrome register
until the nonzero part collapses into a window of at most b bits, revealing exactly
where the burst sits and what to flip.
The trade-off is deliberate and narrow: a Fire code is superb against one clustered burst and makes no promise about several independent scattered errors, which is why it is paired with the assumption that fading and impulse noise arrive in bursts on a radio link.
In practice
The canonical deployment is GSM signalling. GSM’s control channels — the FACCH and SACCH that carry handover commands, measurement reports and paging — protect their 184-bit message blocks with a shortened binary Fire code whose generator is
g(x) = (x^23 + 1)(x^17 + x^3 + 1) = x^40 + x^26 + x^23 + x^17 + x^3 + 1,
adding 40 parity bits to make a 224-bit block. GSM uses this code chiefly for burst detection (a failed check marks the block as erased before the convolutional decoder runs), exploiting the same cyclic, LFSR-friendly structure. Fire codes also appeared in early magnetic-disk and tape controllers, where head defects and media dropouts produce exactly the clustered errors they were built for.
Relevance to SDR
Fire codes belong to the cellular and storage lineage rather than the land-mobile trunking stack, so GopherTrunk does not implement a Fire decoder — the P25, DMR, NXDN and TETRA control channels it reads use BCH, Golay and Reed–Solomon codes, combined with interleaving to convert channel bursts into the scattered errors those codes prefer. That contrast is the useful lesson: a Fire code embraces bursts and repairs them in place, whereas the trunking world spreads bursts out with an interleaver and then leans on a random-error code — two opposite answers to the same fading channel. Anyone reverse-engineering a GSM signalling capture in a software radio, however, will meet the Fire code directly as the first integrity gate on every control block.
Sources
-
Burst error-correcting code — Wikipedia, for the Fire code generator polynomial
(x^c − 1)·p(x), its guaranteed burst-correction length, error-trapping decoding, and the GSM signalling application. ↩