Simplified Syndrome-based Decoding of Punctured Convolutional Codes

This paper introduces a convolutional syndrome former (CSF) which enables reduced complexity decoding of regularly punctured convolutional codes (CCs) of rate r/(r + 1). The CSF is derived by reformulating the parity-check constraints using the punctured dual codewords, and can be implemented either as a parity-check matrix (PCM) or as a multi-binary convolutional (MBC) structure. The former approach significantly reduces the complexity of the decoding process compared to conventional maximum a posteriori (MAP) decoding. Simulation results show that belief propagation (BP) decoding on the CSF achieves comparable performance to conventional MAP decoding, with a penalty of only 0.1 dB. Additionally MAP decoding on the MBC trellis yields identical performance. This enables a decoding complexity reduction ranging from 50% to 90% depending on the code rate. Furthermore, simulation results for turbo decoding shows around 0.3 dB degradation at lower rates and minimal impact (less than 0.15 dB) at higher rates compared to iterative MAP-based decoding.