Codebook Mismatch Can Be Fully Compensated by Mismatched Decoding

TL;DR

This paper demonstrates that codebook mismatch in communication systems can be fully mitigated using mismatched decoding metrics, achieving optimal error exponents and capacity under certain conditions.

Contribution

It introduces a mismatched additive decoding metric that compensates for codebook mismatch in linear codes, achieving the same error exponent as ideal decoding.

Findings

Mismatched decoding can fully compensate for codebook mismatch.

The optimal mismatched metric approaches MAP as rate approaches mutual information.

Codebook mismatch with mismatched MAP is capacity-achieving.

Abstract

We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of simultaneously benefiting both from the probabilistic shaping of the channel input and from the linear structure of the code. We prove that the codebook mismatch can be fully compensated by using a mismatched additive decoding metric that achieves the random coding error exponent of (non-linear) constant composition codes. As the coding rate tends to the mutual information, the optimal mismatched metric approaches the maximum a posteriori probability (MAP) metric, showing that codebook mismatch with mismatched MAP metric is capacity-achieving for the optimal input assignment.