Binary Convolutional Codes Revisited

Abstract

No general algebraic method is known for the construction of convolutional codes with optimum distance properties. Good binary rate-k/n convolutional codes have been found for small values of k and n by various computer search methods, where good means that the free Hamming distances of these codes closely approach or are equal to established upper bounds. In this paper, we report on another attempt to find convolutional codes by computer search. The considered codes are produced by encoders that resemble closely those employed for trellis-coded modulation, i.e., k-tuples of information bits are first expanded into binary (k+1)-tuples by a rate-S/(S+1) convolutional encoder, where 1≤ S≤k; the (k+l)-tuples are then encoded into binary n-tuples by a memoryless mapper (= block encoder), whose mapping rule is based on set-partitioning of binary n-tuples with respect to Hamming distance. Code searches have been performed for rates k/n in the range 1≤k < n ≤8, and for code memo-ries in the range 2 ≤ v ≤ 10. New codes with larger free Hamming distance than known codes were found for the rates 4/5, 5/6, 6/7, and 7/8.