Logarithmic Non-uniform Quantization for List Decoding of Polar Codes

The quantization of intermediate log-likelihood ratios (LLRs) is a concern in the hardware implementation of the LLR-based tree search algorithms such as successive cancellation list (SCL) and sequential (SCS) decoding for polar codes (particularly for large block-lengths), where comparability of tree paths requires precision for path metrics that the uniform quantization demands a large memory space due to the wide dynamic range. As the consequence of low accuracy in uniform quantization (with large step size) for small LLR values, the error correction performance degrades. In this work, we present a logarithmic non-uniform quantization (based on lookup table, logarithm functions, and piecewise linear functions) which can provide an error correction performance close to floating-point precision for a wide range of code-lengths.