High-rate systematic recursive convolutional encoders: minimal trellis and code search

Abstract

We consider high-rate systematic recursive convolutional encoders to be adopted as constituent encoders in turbo schemes. Douillard and Berrou showed that, despite its complexity, the construction of high-rate turbo codes by means of high-rate constituent encoders is advantageous over the construction based on puncturing rate-1/2 constituent encoders. To reduce the decoding complexity of high-rate codes, we introduce the construction of the minimal trellis for a systematic recursive convolutional encoding matrix. A code search is conducted and examples are provided which indicate that a more finely grained decoding complexity-error performance trade-off is obtained.