[Paper Review] Technical Report: Achievable Rates for the MAC with Correlated Channel-State Information

Tal Philosof, Ram Zamir+1 more|ArXiv.org|Dec 28, 2008

Advanced MIMO Systems Optimization3 references18 citations

TL;DR

This paper establishes an achievable rate region for the discrete memoryless multiple access channel (MAC) with correlated channel-state information (CSI) non-causally known at both encoders, using a generalized random binning technique inspired by Gel'fand-Pinsker coding. The key contribution is a capacity inner bound that accounts for asymmetric CSI correlation through auxiliary random variables U and V, enabling interference mitigation and achieving higher sum rates than without CSI knowledge.

ABSTRACT

In this paper we provide an achievable rate region for the discrete memoryless multiple access channel with correlated state information known non-causally at the encoders using a random binning technique. This result is a generalization of the random binning technique used by Gel'fand and Pinsker for the problem with non-causal channel state information at the encoder in point to point communication.

Motivation & Objective

• To extend the Gel'fand-Pinsker random binning technique to the multiple access channel (MAC) with correlated, non-causally known channel states.
• To characterize an achievable rate region for the MAC where each encoder observes a different but correlated state sequence.
• To derive an inner bound on the capacity region that accounts for the correlation between the two state sequences and their impact on reliable communication.
• To generalize dirty paper coding principles to the two-user MAC with correlated CSI, improving spectral efficiency.

Proposed method

• Introduce auxiliary random variables U and V to model the state-dependent encoding strategy, with (U,X1) dependent on S1 and (V,X2) on S2.
• Use random binning: generate codebooks with M1 and M2 bins for messages, each bin containing 2^{nJ1} and 2^{nJ2} codewords, respectively.
• Encode by selecting a U-sequence jointly typical with S1 and X1 in bin m1, and a V-sequence jointly typical with S2 and X2 in bin m2.
• Decode by finding unique (U,V) sequences jointly typical with the received Y, leveraging typicality decoding and Markov chains.
• Apply the asymptotic equipartition property (AEP) and typical set enumeration to bound error probabilities for each encoding and decoding event.
• Derive the achievable rate region by analyzing error events and ensuring vanishing error probability as blocklength n → ∞.

Experimental results

Research questions

• RQ1 What is the achievable rate region for a two-user MAC when each encoder has non-causal knowledge of a correlated state sequence?
• RQ2 How does the correlation between the two state sequences affect the achievable sum rate and individual rates?
• RQ3 Can the random binning technique from point-to-point channels be generalized to the MAC with correlated CSI to achieve a larger rate region?
• RQ4 What is the role of auxiliary random variables U and V in mitigating interference caused by correlated channel states?
• RQ5 How does the proposed scheme compare to the clean MAC (no CSI) and single-encoder CSI cases in terms of capacity?

Key findings

• The paper establishes an inner bound on the capacity region of the MAC with correlated CSI, parameterized by auxiliary random variables U and V.
• The achievable rate region is given by R1 ≤ I(U;Y|V) - I(U;S1|V), R2 ≤ I(V;Y|U) - I(V;S2|U), and R1+R2 ≤ I(U,V;Y) - I(U,V;S1,S2), for admissible (U,V) satisfying specific Markov chains.
• For the special case of a single common state S=S1=S2, the region reduces to R1 ≤ I(U;Y|V) - I(U;S|V), R2 ≤ I(V;Y|U) - I(V;S|U), and R1+R2 ≤ I(U,V;Y) - I(U,V;S).
• In the independent states case, the region simplifies to R1 ≤ I(U;Y|V) - I(U;S1), R2 ≤ I(V;Y|U) - I(V;S2), and R1+R2 ≤ I(U,V;Y) - I(U;S1) - I(V;S2), matching prior results.
• The Gaussian special case shows that with non-causal CSI, the capacity region equals that of the clean MAC, implying full mitigation of interference.
• The error probability vanishes as n → ∞ under the derived rate conditions, proving the achievability of the region.