Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The State-Dependent Channel with a Rate-Limited Cribbing Helper

Amos Lapidoth, Yossef Steinberg

TL;DR

The paper analyzes a memoryless state-dependent channel with a rate-limited cribbing helper that observes the state causally and the encoder’s past inputs. It derives a single-letter capacity characterization $C^{(I)}=\max\min\{ I(UV;Y), I(U;X|VT)\}$ over joint laws with $T$ describing the cribbing and an auxiliary Markov structure, proving that $C=C^{(I)}$ and that optimal $P_{T|SV}$ and $P_{X|UVT}$ can be taken as $0$-$1$ laws with explicit alphabet bounds. Achievability uses a block-Markov coding scheme with backward decoding, where the helper’s cribbing of state and past inputs drives the cloud-center/satellite codebook structure and the $T$-assisted encoding. A binary example demonstrates that cribbing can outperform a purely causal- or oblivious-helper, yet remains strictly inferior to a message-cognizant helper, highlighting a nuanced hierarchy among helper models. The results advance understanding of rate-limited state information sharing and provide concrete coding strategies for optimizing capacity in presence of cribbing.

Abstract

The capacity of a memoryless state-dependent channel is derived for a setting in which the encoder is provided with rate-limited assistance from a cribbing helper that observes the state sequence causally and the past channel inputs strictly-causally. Said cribbing may increase capacity but not to the level achievable by a message-cognizant helper.

The State-Dependent Channel with a Rate-Limited Cribbing Helper

TL;DR

The paper analyzes a memoryless state-dependent channel with a rate-limited cribbing helper that observes the state causally and the encoder’s past inputs. It derives a single-letter capacity characterization over joint laws with describing the cribbing and an auxiliary Markov structure, proving that and that optimal and can be taken as - laws with explicit alphabet bounds. Achievability uses a block-Markov coding scheme with backward decoding, where the helper’s cribbing of state and past inputs drives the cloud-center/satellite codebook structure and the -assisted encoding. A binary example demonstrates that cribbing can outperform a purely causal- or oblivious-helper, yet remains strictly inferior to a message-cognizant helper, highlighting a nuanced hierarchy among helper models. The results advance understanding of rate-limited state information sharing and provide concrete coding strategies for optimizing capacity in presence of cribbing.

Abstract

The capacity of a memoryless state-dependent channel is derived for a setting in which the encoder is provided with rate-limited assistance from a cribbing helper that observes the state sequence causally and the past channel inputs strictly-causally. Said cribbing may increase capacity but not to the level achievable by a message-cognizant helper.
Paper Structure (9 sections, 1 theorem, 55 equations)

This paper contains 9 sections, 1 theorem, 55 equations.

Table of Contents

  1. Introduction
  2. Problem Statement and Main Result
  3. Example
  4. Proof of Theorem \ref{['theo:main']}
  5. Direct Part
  6. Code Construction
  7. Operation of the code
  8. Decoding
  9. Converse Part

Key Result

Theorem 1

The capacity $C$ of the memoryless state dependent channel with a rate-limited cribbing helper equals $C^{(I)}$: Moreover, the maximum in eq:def_ci can be achieved when:

Theorems & Definitions (1)

  • Theorem 1