Control-Field and Quasi-Cyclic Code Recovery in Starlink Downlink Signals

Public descriptions of the Starlink downlink specify synchronization sequences, edge pilots, and predictable symbol templates, but leave the coded control fields and explicit payload-code representations largely unresolved. We examine one continuous complex-baseband capture spanning approximately 24 ms and recover control and coding structure beyond those predictable elements. Reference-phase removal exposes terminated rate-1/3 convolutional control blocks with constraint length seven and a group-level cyclic redundancy check. A conditional descriptor layout predicts sequential allocations through per-codeword symbol rounding, agreeing exactly with independently estimated endpoints in 16 of 18 frame records and within two symbols in the remaining records. Quasi-cyclic closure, binary elimination, and sparse dual checks yield explicit systematic code representations at rates 1/2 and 5/8. Frozen encoders predict 78,848, 9,984, and 811,008 reserved parity bits for three formats without disagreement. A rank-deficient long-code fit is completed within a declared finite structural family, and shared encoders are tested across modulation formats. The recovered representations explain observed coded symbols; they do not authenticate transmitter-standard identities or plaintext semantics. Two high-order formats have only one target field each, while codes 28 and 37 admit verified shortened cores with unexplained extra bits and code 4 remains unresolved.