A bound on the unequal error protection capabilities of rate k/n convolutional codes

In a previous paper by Mills and Costello (see ibid., p.114, 1993) the effective free distance vector of a convolutional encoder was defined. This paper presents a new bound relating two individual effective free distances. Evaluating the bound is a useful tool in determining the possible unequal error protection capabilities of encoders of specified rate and memory distribution. In addition, the bound allows a comparison between the effective free distance vector of a specific encoder and the theoretically optimal effective free distance vector. First, a bound on the Hamming weight of the sum of two vectors with known Hamming weights is presented. Then this bound is applied to effective free distances of encoders with both balanced and unbalanced memory distributions.< >