maxlogMAP

MaxLogMAP is a simplified variant of the log-MAP algorithm used for soft-output decoding of convolutional codes, most notably in turbo decoding systems. It aims to reduce computational complexity by approximating the log-likelihood calculations with a maximum operation, instead of the exact log-sum-exp calculation.

In the standard log-MAP framework, forward and backward metrics (often denoted alpha and beta) are updated through sums of exponentials in the log domain. MaxLogMAP replaces these sums with a maximum, yielding a lower-complexity update that is easier to implement in hardware. This approximation lowers the number of arithmetic operations and can significantly reduce latency and power consumption in iterative decoders. However, the simplification introduces a performance penalty relative to the exact log-MAP, particularly at lower signal-to-noise ratios.

Variants of MaxLogMAP exist to improve robustness. The offset Max-Log-MAP adds a correction term or offset to the maximum value to partially compensate for the approximation error, improving bit-error performance. Other approaches use piecewise-linear or refined approximations, sometimes referred to as refined or approximate max-log implementations, balancing complexity and accuracy.

Applications and significance: MaxLogMAP is widely used in practical turbo decoders for communication standards that employ convolutional codes, where soft outputs are required for iterative decoding. It remains a popular choice when hardware resources are constrained or low latency is essential, provided the performance loss is acceptable for the target application.

See also: log-MAP algorithm, BCJR algorithm, turbo codes, soft-output decoding, max-star operator, offset max-log-MAP.