[Paper Review] Strong Converse Exponent for State Dependent Channels with Full State Information at the Sender and Partial State Information at the Receiver

Yasutada Oohama|arXiv (Cornell University)|Mar 21, 2016

Wireless Communication Security Techniques3 citations

TL;DR

This paper establishes an exponential decay rate for the probability of correct decoding when transmitting at rates above the capacity of a state-dependent channel with full state information at the transmitter and partial state information at the receiver. It derives an explicit lower bound on the strong converse exponent, proving that error probability vanishes exponentially fast above capacity, thus quantifying the sharpness of the capacity limit.

ABSTRACT

We consider the state dependent channels with full state information with at the sender and partial state information at the receiver. For this state dependent channel, the channel capacity under rate constraint on the state information at the decoder was determined by Steinberg. In this paper, we study the correct probability of decoding at rates above the capacity. We prove that when the transmission rate is above the capacity this probability goes to zero exponentially and derive an explicit lower bound of this exponent function.

Motivation & Objective

• To analyze the reliability of communication over state-dependent channels where the sender has full state information and the receiver has partial state information.
• To investigate the behavior of the decoding error probability when transmission rates exceed the channel capacity.
• To establish a strong converse theorem by quantifying the exponential decay rate of the correct decoding probability above capacity.
• To derive an explicit lower bound for the strong converse exponent, providing a quantitative measure of the sharpness of the capacity limit.

Proposed method

• Formalizing the state-dependent channel model with full state information at the encoder and partial state information at the decoder.
• Using information-theoretic tools to analyze the error probability of decoding at rates above the channel capacity.
• Applying large deviations techniques to characterize the exponential decay rate of the correct decoding probability.
• Deriving a lower bound on the strong converse exponent through optimization over auxiliary distributions and channel parameters.
• Leveraging the structure of the channel and state information to bound the error exponent using conditional mutual information and divergence terms.
• Establishing the strong converse by showing that the probability of correct decoding decays exponentially fast when rate exceeds capacity.

Experimental results

Research questions

• RQ1 What is the exponential decay rate of the correct decoding probability when transmission rates exceed the capacity of a state-dependent channel with full state information at the transmitter and partial at the receiver?
• RQ2 How does the availability of partial state information at the receiver affect the strong converse exponent compared to full state information?
• RQ3 Can an explicit lower bound be derived for the strong converse exponent in this channel model?
• RQ4 Is the decay of the decoding error probability above capacity exponentially fast, and if so, what is the rate of this decay?

Key findings

• The probability of correct decoding decays exponentially fast when the transmission rate exceeds the channel capacity.
• An explicit lower bound is derived for the strong converse exponent, quantifying the rate of exponential decay.
• The strong converse exponent is strictly positive above capacity, confirming the sharpness of the capacity limit.
• The derived lower bound depends on the channel transition probabilities and the available state information at both terminals.
• The result extends the strong converse to state-dependent channels with asymmetric state information availability.
• The analysis confirms that reliable communication is impossible above capacity, with error probability vanishing exponentially fast.