Channel combining and splitting for cutoff rate improvement

TL;DR

This paper explores how channel combining and splitting techniques can enhance the cutoff rate of discrete memoryless channels, potentially surpassing the sum of subchannel cutoff rates, with implications for coding strategies.

Contribution

The paper introduces methods of channel combining and splitting to improve the cutoff rate of DMCs, extending Massey's findings to general channels and relating to multi-level coding.

Findings

Cutoff rate can be increased through channel splitting and combining.

The proposed methods can outperform the sum of individual subchannel cutoff rates.

Connections to Pinsker's work and multi-level coding are discussed.

Abstract

The cutoff rate $R_0(W)$ of a discrete memoryless channel (DMC) $W$ is often used as a figure of merit, alongside the channel capacity $C(W)$. Given a channel $W$ consisting of two possibly correlated subchannels $W_1$, $W_2$, the capacity function always satisfies $C(W_1)+C(W_2) \le C(W)$, while there are examples for which $R_0(W_1)+R_0(W_2) > R_0(W)$. This fact that cutoff rate can be ``created'' by channel splitting was noticed by Massey in his study of an optical modulation system modeled as a $M$'ary erasure channel. This paper demonstrates that similar gains in cutoff rate can be achieved for general DMC's by methods of channel combining and splitting. Relation of the proposed method to Pinsker's early work on cutoff rate improvement and to Imai-Hirakawa multi-level coding are also discussed.