A Simultaneous Decoding Approach to Joint State and Message Communications

TL;DR

The paper studies capacity-distortion trade-offs for joint state and message communications over state-dependent channels with generalized state information and feedback. It introduces a backward simultaneous decoding framework that decodes messages and compressed state descriptions jointly, avoiding Wyner-Ziv binning and achieving the optimal CD function in the point-to-point setting, while providing improved achievable regions for degraded broadcast and multiple-access channels through successive refinement and Willems-style encoder cooperation. The results are illustrated with radar-like ISAC scenarios and in both discrete and quadratic-Gaussian models, highlighting that state descriptions can enhance both communication performance and state estimation. The work offers practical benchmarks for ISAC system design and opens avenues for extending the framework to channels with memory and further multi-user scenarios.

Abstract

The capacity-distortion (C-D) trade-offs for joint state and message communications (JSMC) over single- and multi-user channels are investigated, where the transmitters have access to generalized state information and feedback while the receivers jointly decode the messages and estimate the channel state. A coding scheme is proposed based on backward simultaneous decoding of messages and compressed state descriptions without the need for the Wyner-Ziv random binning technique. For the point-to-point channel, the proposed scheme results in the optimal C-D function. For the state-dependent discrete memoryless degraded broadcast channel (SD-DMDBC), the successive refinement method is adopted for designing multi-stage state descriptions. With the simultaneous decoding approach, the derived achievable region is shown to be larger than the region obtained by the sequential decoding approach that is utilized in existing works. As for the state-dependent discrete memoryless multiple access channel (SD-DMMAC), in addition to the proposed method, Willem's coding strategy is applied to enable partial collaboration between transmitters through the feedback links. Moreover, the state descriptions are shown to enhance both communication and state estimation performance. Examples are provided for the derived results to verify the analysis, either numerically or analytically. With particular focus, simple but representative integrated sensing and communications (ISAC) systems are also considered, and their fundamental performance limits are studied.

Figures (7)

• Figure 1: Channel model for point-to-point jsmc system.
• Figure 2: cd function for the quadratic-Gaussian case with different correlation levels between $S$ and $S_T$.
• Figure 3: The degraded broadcast jsmc model.
• Figure 4: Comparison of $(R_1, R_2, D_1)$ achieved by simultaneous and sequential decoding methods while fixing $D_2$. The black region corresponds to $R_1=0$, and lighter areas indicate higher $R_1$.
• Figure 5: Achieved rate regions of the degraded binary broadcast channel with different choices of $V_2$.

Theorems & Definitions (39)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Remark 1
• Definition 1
• Remark 2
• Theorem 1