Performance Comparison of MAX-LOG-MAP and LOG-MAP Algorithms

This document presents a comprehensive performance evaluation between the simplified MAX-LOG-MAP algorithm and the conventional LOG-MAP algorithm. The analysis examines two key scenarios: first, using MAX-LOG-MAP_1024 standard interleaving configuration with 1-3 iterations under grid-based testing conditions; second, comparing the simplified MAX-LOG-MAP algorithm against the threshold-based MAX-LOG-MAP variant with 10 iterations and 640-bit interleaving length. The MAX-LOG-MAP algorithm, widely implemented in digital communication systems using MATLAB or C-based turbo decoders, employs logarithmic approximation to reduce computational complexity while maintaining near-optimal error correction capabilities. The algorithm implementation typically involves forward/backward recursion calculations with max* operations approximated by simple max functions. In contrast, the simplified MAX-LOG-MAP variant further optimizes computational efficiency through lookup tables or piecewise linear approximations for Jacobian logarithm operations, achieving significant processing speed improvements with minimal BER performance degradation. Interleaving mechanisms, crucial for mitigating burst errors in wireless communication channels, are implemented through permutation algorithms that rearrange data sequences. The document investigates two interleaving configurations: standard 1024-bit interleaver using row-column permutation techniques, and a 640-length custom interleaver optimized for specific channel conditions. Code implementations typically involve interleaver index generation functions that ensure proper scattering of adjacent bits across the transmission frame. The performance analysis highlights critical trade-offs between computational complexity (measured in operations per decoded bit) and error correction performance (evaluated through bit error rate curves). The simplified MAX-LOG-MAP demonstrates particular advantages in resource-constrained embedded systems where reduced cycle count and memory usage are prioritized, while maintaining acceptable decoding accuracy within 0.1-0.3 dB of the optimal LOG-MAP performance across various SNR conditions. This technical assessment provides valuable insights for communication engineers selecting appropriate decoding algorithms based on system requirements, offering practical implementation guidelines for software-defined radio and 5G NR turbo decoding applications.