Minimal Trellises for Degenerate Decoding of Quantum Stabilizer Codes

This paper introduces several techniques for minimal trellis construction for degenerate decoding of quantum stabilizer codes, specifically the minimal multi-goal trellis for the cosets of the stabilizer group S in the normalizer group N. The methods include a merging algorithm, a Shannon-product approach, and the BCJR-Wolf method. The study establishes the necessary properties of multi-goal trellises and bounds on the decoding complexity of the minimal multi-goal trellis using the sum-product Viterbi algorithm. The proposed multi-goal trellises decrease the decoding complexity by a factor O(n), where n is the code length.