In addition to a codeword, error correction decoders that provide blockwise soft output (SO) return an estimate of the likelihood that the decoding is correct. Following Forney, such estimates have traditionally only been possible for list decoders with the approximate soft output being the likelihood that a decoding is correct given it is assumed to be in the list. Recently, it has been established that Guessing Random Additive Noise Decoding (GRAND), Guessing Codeword Decoding (GCD), Ordered Statistics Decoding (OSD), and Successive Cancellation List (SCL) decoding can provide accurate soft output without the need for list decoding. Central to the improvement is the evaluation of an estimate of the likelihood that the correct decoding has not been found. We explore how binary linear codebook constraints can be leveraged to further enhance SO precision. We evaluate performance by adapting a forecasting statistic called the Brier Score. Results indicate that the SO generated by the approach is essentially as accurate as the maximum a posteriori estimate.

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