This paper proposes a new soft-input soft-output decoding algorithm particularly suited for low-complexity highradix turbo decoding, called local soft-output Viterbi algorithm (local SOVA). The local SOVA uses the forward and backward state metric recursions just as the conventional Max-Log MAP (MLM) algorithm does, and produces soft outputs using the SOVA update rules. The proposed local SOVA exhibits a lower computational complexity than the MLM algorithm when employed for high-radix decoding in order to increase throughput, while having the same error correction performance even when used in a turbo decoding process. Furthermore, with some simplifications, it offers various trade-offs between error correction performance and computational complexity. Actually, employing the local SOVA algorithm for radix-8 decoding of the LTE turbo code reduces the complexity by 33% without any performance degradation and by 36% with a slight penalty of only 0.05 dB. Moreover, the local SOVA algorithm opens the door for the practical implementation of turbo decoders for radix-16 and higher.

Decoding using the dual trellis is considered as a potential technique to increase the throughput of soft-input soft-output decoders for high coding rate convolutional codes. However, the dual Log-MAP algorithm suffers from a high decoding complexity. More specifically, the source of complexity comes from the soft-output unit, which has to handle a high number of extrinsic values in parallel. In this paper, we present a new low-complexity sub-optimal decoding algorithm using the dual trellis, namely the dual Max-Log-MAP algorithm, suited for high coding rate convolutional codes. A complexity analysis and simulation results are provided to compare the dual Max-Log-MAP and the dual Log-MAP algorithms. Despite a minor loss of about 0.2 dB in performance, the dual Max-Log-MAP algorithm significantly reduces the decoder complexity and makes it a first-choice algorithm for high-throughput high-rate decoding of convolutional and turbo codes. Index Terms-Convolutional codes, high coding rate, dual trellis, high-throughput decoder, low-complexity decoder, turbo 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.