The analysis of ORBGRAND achievable rate can be extended to channels with memory or non-uniform input distributions by considering the impact of these factors on the decoding process. In channels with memory, the previous channel outputs influence the current output, leading to dependencies that need to be accounted for in the decoding algorithm. This can be addressed by incorporating memory models into the analysis and adjusting the decoding criteria to handle the memory effects.
For non-uniform input distributions, the probabilities of different symbols occurring vary, affecting the reliability of the received symbols. In such cases, the decoding metric and error pattern generation in ORBGRAND need to be adapted to reflect the varying probabilities of different symbols. Analyzing the achievable rate in channels with non-uniform input distributions involves calculating the GMI under these specific conditions, considering the impact of the distribution on the decoding performance.
By extending the analysis to channels with memory or non-uniform input distributions, a more comprehensive understanding of the performance limits of ORBGRAND in diverse channel scenarios can be obtained, enabling the optimization of the decoding process for a wider range of communication channels.