The Log-domain BCJR algorithm is broadly used in iterative decoding processes. However, the serial nature of the recursive state metric calculations is a limiting factor for throughput increase. A possible solution resorts to high-radix decoding, which involves decoding several successive symbols at once. Despite several studies aiming at reducing its complexity, high-radix processing remains the most computationally intensive part of the decoder when targeting very high throughput. In this work, we propose a reformulation specifically targeting the complexity reduction of the recursive calculation units by either limiting the required number of operations or by selectively removing unnecessary ones. We report a complexity reduction of the add-compare-select units in the order of 50% compared to the recently proposed local-SOVA algorithm. In addition, our results show that several performance/complexity trade-offs can be achieved thanks to the proposed simplified variants. This represents a promising step forward in order to implement efficient very high throughput convolutional decoders.