Dual Trellis Construction for High-Rate Punctured Convolutional Codes

Puncturing a low-rate convolutional code to generate a high-rate code has some drawback in terms of hardware implementation. In fact, a Maximum A-Posteriori (MAP) decoder based on the original trellis will then have a decoding throughput close to the decoding throughput of the mother non-punctured code. A solution to overcome this limitation is to perform MAP decoding on the dual trellis of a high-rate equivalent convolutional code. In the literature, dual trellis construction is only reported for specific punctured codes with rate $k/(k+1)$. In this paper, we propose a multi-step method to construct the equivalent dual code defined by the corresponding dual trellis for any punctured code. First, the equivalent nonsystematic generator matrix of the high-rate punctured code is derived. Then, the reciprocal parity-check matrix for the construction of the dual trellis is deduced. As a result, we show that the dual-MAP algorithm applied on the newly constructed dual trellis yields the same performance as the original MAP algorithm while allowing the decoder to achieve a higher throughput. When applied to turbo codes, this method enables highly efficient implementations of high-throughput high-rate turbo decoders.