# Turbo Decoder Design based on an LUT-Normalized Log-MAP Algorithm
###### Abstract  
Turbo codes have been widely used in wireless communication systems due to their good error correction performance. Under time division long term evolution (TD-LTE) of the 3 rd generation partnership project (3 GPP) wireless communication standard, a Log maximum a posteriori (Log-MAP) decoding algorithm with high complexity is usually approximated as a lookup-table Log-MAP (LUT-Log-MAP) algorithm and Max-Log-MAP algorithm, but these two algorithms have high complexity and high bit error rate, respectively. In this paper, we propose a normalized Log-MAP (Nor-Log-MAP) decoding algorithm in which the function max* is approximated by using a fixed normalized factor multiplied by the max function. Combining a Nor-Log-MAP algorithm with a LUT-Log-MAP algorithm creates a new kind of LUT-Nor-Log-MAP algorithm. Compared with the LUT-Log-MAP algorithm, the decoding performance of the LUT-Nor-Log-MAP algorithm is close to that of the LUT-Log-MAP algorithm. Based on the decoding method of the Nor-Log-MAP algorithm, we also put forward a normalization functional unit (NFU) for a soft-input soft-output (SISO) decoder computing unit. The simulation results show that the LUT-Nor-Log-MAP algorithm can save about 2.1% of logic resources compared with the LUT-Log-MAP algorithm. Compared with the Max-Log-MAP algorithm, the LUT-Nor-Log-MAP algorithm shows a gain of 0.25-0.5 dB in decoding performance. Using the Cyclone IV platform, the designed Turbo decoder can achieve a throughput of 36 Mbit/s under a maximum clock frequency of 44 MHz.  
turbo decoder; normalized-Log-MAP algorithm; normalization functional unit; LTE-advanced; cyclone IV 2019 21 814 [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [3  
interleaving address output and reduces storage unit consumption [8; 9]. [PERSON] et al. also proposed a flexible functional unit (FFU) for a soft-input soft-output (SISO) decoder, while a turbo decoder achieves a throughput of 1280 Mbit/s with a clock frequency of 400 MHz under 3 GPP-LTE and LTE-advanced standards [9; 10]. [PERSON] et al. put forward an idea for a hybrid algorithm in 2013, and its decoding performance is better than a Log-MAP algorithm after combining a LUT-Log-MAP algorithm and Linear-Log-MAP algorithm in every state metric calculation [11], although this implementation results in a large consumption of logic resources. In 2017, [PERSON] et al. proposed a calculation method of the function max* that can be applied for reverse calculation in engineering implementation [12].  
In this paper, we propose a Nor-Log-MAP algorithm that uses a fixed normalized factor to approximate the function max*. According to the idea of a hybrid algorithm [11], we also propose a LUT-Nor-Log-MAP algorithm that uses different algorithms in different metric calculation states so as to reduce the number of lookup tables and consumption of logical resources. LUT-Nor-Log-MAP is a new kind of algorithm that combines Nor-Log-MAP with LUT-Log-MAP. The LUT-Log-MAP algorithm is used to calculate forward-state and backward-state metrics, and the Nor-Log-MAP algorithm is used to compute external information and posteriori information. Based on the LUT-Nor-Log-MAP algorithm, we incorporated an FFU and a normalization functional unit (NFU) into the design of the SISO unit.  
The rest of this paper is organized as follows. Section 2 reviews turbo decoding principles and the Log-MAP algorithm. Section 3 presents the Nor-Log-MAP algorithm. Section 4 introduces the LUT-Nor-Log-MAP algorithm and the structure of the SISO unit. Section 5 analyzes the proposed algorithm. Section 6 presents the synthesis results and comparisons. Section 7 concludes the paper.