Abstract
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.
Highlights
The typical turbo code configuration is the parallel concatenation of two systematic recursive constituent convolutional encoders of rate 1/2 connected via an interleaver, resulting in a code of rate 1/3
The codes are optimized in terms of the pairs, where di is the minimum weight of codewords generated by input sequences of weight i and Ni are their multiplicities, and suited to be used as constituent encoders of turbo codes [5]
The reason is that the mapping between information bits and coded bits produced by the minimal trellis corresponds to nonrecursive convolutional encoders, while systematic, recursive mappings are required in turbo coding
Summary
The typical turbo code configuration is the parallel concatenation of two systematic recursive constituent convolutional encoders of rate 1/2 connected via an interleaver, resulting in a code of rate 1/3. An alternative to reduce the decoding complexity is to consider trellis representations for the constituent codes other than the conventional trellis usually adopted. The reason is that the mapping between information bits and coded bits produced by the minimal trellis corresponds to nonrecursive convolutional encoders, while systematic, recursive mappings are required in turbo coding. We introduce the construction of the minimal trellis for a systematic recursive convolutional encoding matrix, the encoding required for the constituent codes of a turbo code. The proposed minimal trellis can be constructed for systematic recursive convolutional encoders of any rate.
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