Channel combining and splitting for cutoff rate improvement

Abstract

The cutoff rate R0(W) of a discrete memoryless channel (DMC) W is often used as a figure of merit alongside the channel capacity C(W). If a channel W is split into two possibly correlated subchannels W1, W2, the capacity function always satisfies C(W1) + C(W2) ≤ C(W), while there are examples for which R0(W1) + R0(W2) > R0(W). The fact that cutoff rate can be "created" by channel splitting was noticed by Massey in his study of an optical modulation system. This paper gives a general framework for achieving similar gains in the cutoff rate of arbitrary DMCs by methods of channel combining and splitting. The emphasis is on simple schemes that can be implemented in practice. We give several examples that achieve significant gains in cutoff rate at little extra system complexity. Theoretically, as the complexity grows without bound, the proposed framework is capable of boosting the cutoff rate of a channel to arbitrarily close to its capacity in a sense made precise in the paper. Apart from Massey's work, the methods studied here have elements in common with Forney's concatenated coding idea, a method by Pinsker for cutoff rate improvement, and certain coded-modulation techniques, namely, Ungerboeck's set-partitioning idea and Imai-Hirakawa multilevel coding; these connections are discussed in the paper.