ORBGRAND Is Almost Capacity-Achieving
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Decoding via sequentially guessing the error pattern in a received noisy sequence has received attention recently, and the ORBGRAND has been proposed as one such decoding algorithm that is capable of utilizing the soft information embedded in the received noisy sequence. An information theoretic study is conducted for the ORBGRAND, and it is shown that the achievable rate of the ORBGRAND almost coincides with the channel capacity, for an additive white Gaussian noise channel under antipodal input. For finite-length codes, improved guessing schemes motivated by the information theoretic study are proposed that attain lower error rates than the ORBGRAND, especially in the high signal-to-noise ratio regime.
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