Illustration of C4-sequences

Related publications

- E. Boutillon "Constellations Cross Circular auto-Correlation C4-sequences", IEEE Transactions On Communications, in press, june 2024.
- E. Boutillon "C4-Sequences: Rate Adaptive Coded Modulation for Few Bits Message", 12th International Symposium on Topics in Coding (ISTC 2023), IEEE, Sep 2023, Brest, France
- C. Marchand, A. Olteanu, E. Boutillon, "Rate-Adaptive Cyclic Complex Spreading Sequence for Non-Binary Decoders", 12th International Symposium on Topics in Coding (ISTC 2023), IEEE, Sep 2023, Brest, France

Matlab codes: The following files contain some Matlab codes to generate and optimize C4 sequences. Specifically, it contains:

1) x = build_C4(s, c), return C4-sequence x from seed s and clockwise direction c.

2) x = measure(x, l), Return the first l terms of the Normalized Minimum Square distance of sequence x.

3) mi = mi_2d_awgn(signal, SNRdB, N), return the Mutual Information of the constellation signal at SNRdB (function written by Prof. Raphaël Le Bidan).

4) x = optimize_sequence(x, mode, param), Optimization of the C4 sequence from the seed sequence s according to a given objective. There are 3 possible optimization objectives

- mode = 'PAPR': try to return a unitary C4-sequence, "param" not use.
- mode = 'SNR': optimize the mutual information for the snr given by "param".
- mode = 'WS' : optimize the Weighted Sum of normalized minimum square distance of x. "param" is then a vector of length(x) that gives the ponderation weight of the minimum normalized square distance of x.

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