192 research outputs found
On Maximum-Likelihood Decoding of Time-Varying Trellis Codes
Decoding complexity of convolutional and trellis codes by Viterbi decoder can be reduced by applying suggested merging algorithm to the Forney code trellis. The algorithm can be applied for every trellis section separately, which is convenient for time-varying codes, and it outputs the minimal trellis of the section. In case of convolutional codes, the same minimal trellis of every section can be obtained from the syndrome trellis of proposed split code
Quantum Approximation Optimization Algorithm for the trellis based Viterbi decoding of classical error correcting codes
We construct a quantum-classical Viterbi decoder for the classical
error-correcting codes. Viterbi decoding is a trellis-based procedure for
maximum likelihood decoding of classical error-correcting codes. In this
article, we show that any number of paths with the minimum Hamming distance
with respect to the received erroneous vector present in the trellis can be
found using the quantum approximate optimization algorithm. We construct a
generalized method to map the Viterbi decoding problem into a parameterized
quantum circuit for any classical linear block codes. We propose a uniform
parameter optimization strategy to optimize the parameterized quantum circuit.
We observe that the proposed method is efficient for generating low-depth
trainable parameterized quantum circuits. This renders the hybrid decoder more
efficient than previous attempts at making quantum Viterbi algorithm. We show
that using uniform parameter optimization, we obtain parameters more
efficiently for the parameterized quantum circuit than many previous attempts
made through random sampling and fixing the parameters.Comment: 28 pages, 18 figures, pre-prin
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