Channel Coding meets Sequence Design via Machine Learning for Integrated Sensing and Communications

TL;DR

The paper addresses ISAC by seeking codes that serve both communication and sensing roles, focusing on short block lengths where traditional dual-use approaches fail. It proposes training autoencoder-based encoders/decoders with a loss that jointly optimizes error-correcting performance and autocorrelation properties, enabling a large codebook of complex-valued codewords with low sidelobes. Empirical results show substantial ACSL reductions and competitive BER performance at short lengths, particularly for K = 16, while block-length gains at high SNR remain elusive for larger K; ZC sequences offer ideal autocorrelation but severely limit codebook size. The work highlights ML as a viable bridge between channel coding and sequence design for ISAC, enabling scalable dual-use signals and motivating further research into architectures and curricula to achieve block-length gains.

Abstract

For integrated sensing and communications, an intriguing question is whether information-bearing channel-coded signals can be reused for sensing - specifically ranging. This question forces the hitherto non-overlapping fields of channel coding (communications) and sequence design (sensing) to intersect by motivating the design of error-correcting codes that have good autocorrelation properties. In this letter, we demonstrate how machine learning (ML) is well-suited for designing such codes, especially for short block lengths. As an example, for rate 1/2 and block length 32, we show that even an unsophisticated ML code has a bit-error rate performance similar to a Polar code with the same parameters, but with autocorrelation sidelobes 24dB lower. While a length-32 Zadoff-Chu (ZC) sequence has zero autocorrelation sidelobes, there are only 16 such sequences and hence, a 1/2 code rate cannot be realized by using ZC sequences as codewords. Hence, ML bridges channel coding and sequence design by trading off an ideal autocorrelation function for a large (i.e., rate-dependent) codebook size.

Figures (5)

• Figure 1: $g_{\rm enc}(\cdot)$ and $g_{\rm dec}(\cdot)$ form an autoencoder. We consider $K = 16,~ 32$ and $r = K/N = 1/2$.
• Figure 2: (Top): The ACSL (first term in (\ref{['eq:loss']})) for each of the $2^{16} = 65536$ codewords of length 32. The median ACSL equals: $-40.08{\rm dB}$ (ML code, $\lambda = 0.9$), $-15.23{\rm dB}$ (ML code, $\lambda = 0$) and $-15.49{\rm dB}$ (Polar code + BPSK). (Bottom): The ACSL of each ZC sequence of length 32. By design, this should be equal to $-\infty {\rm dB}$, the values here are due to limited numerical precision.
• Figure 3: For $K = 16$, the boxplots capture the ACSL distribution of Fig. \ref{['fig:per_cw_acsl']}a. For $K = 32$, the boxplots capture the empirical ACSL distribution of codewords corresponding to a common test set of $10^6$ message vectors. The additional reduction in the ACSL for $\lambda = 0.9$ is due to prioritizing sensing in (\ref{['eq:loss']}).
• Figure 4: For the ML codes, there is no communications-sensing trade-off -- the BER performance is identical for $\lambda = 0$ and $\lambda = 0.9$. The ML codes outperform Polar codes at low SNR, but do not exhibit block length gain at high SNR.
• Figure 5: The evolution of the training loss with concatenated code initialization for $K = 32$.

Theorems & Definitions (2)

• Definition 1: Autocorrelation function
• Definition 2: Concatenated Code