Revisiting the Max-Log-Map Algorithm With SOVA Update Rules: New Simplifications for High-Radix SISO Decoders

Abstract

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.

A Low-Complexity Dual Trellis Decoding Algorithm for High-Rate Convolutional Codes

“…As shown in Table I, despite a minor increase in the number of adders, the dual MLM algorithm uses significantly less LUTs than the dual ML algorithm. More specifically, due to the max-log approximation, the use of function f (∆) is no longer needed in (13) and the use of function g(∆) is also limited, thanks to the local SOVA. As the coding rate increases, the percentage of LUTs saved in the dual MLM decoder also increases.…”

“…The complexity of the dual LM decoder can be lowered by limiting the use of LUTs to compute (13) and (14). These LUTs are mainly used to derive the soft outputs according to (6) in the SOUs.…”

“…This variability requires the hardware implementation to be able to handle all possible sizes for S + j and S − j , which comes at a cost in complexity. However, this problem can be easily solved by resorting to a recently proposed method, namely the local soft-output Viterbi algorithm (local SOVA) [13], to compute W lj ,s , W lj ,m and ∆ j in (25) and (26).…”

“…The algorithm presented in this section is a variant of the original one recently proposed in [13]. First, we present the algorithm for the general case and, then, its application to the computation of (26) is derived.…”

“…In addition, as presented in [13], the practical implementation of the local SOVA can be carried out in a dichotomous fashion using elementary operations, called Merge, that each processes two paths and are organized in layers. In Algorithm 1, two paths P 2p−1 and P 2p at layer l−1 are merged into a resulting path P p at layer l. The overall local SOVA decoder can therefore be implemented as a tree structure composed of elementary Merge operators.…”