An “Umbrella” bound of the Lovász-Gallager type

We propose a novel approach for bounding the probability of error of discrete memoryless channels with a zero-error capacity based on a combination of Lovász´ and Gallager´s ideas. The obtained bounds are expressed in terms of a function v(ρ), introduced here, that varies from the cut-off rate of the channel to the Lovázs theta function as ρ varies from 1 to ∞ and which is intimately related to Gallager´s expurgated coefficient. The obtained bound to the reliability function, though loose in its present form, is finite for all rates larger than the Lovász theta function.