Soft-Output Guessing Codeword Decoding

We establish that it is possible to extract accurate blockwise and bitwise soft output (SO) from Guessing Codeword Decoding (GCD) with minimal additional computational complexity by considering it through the lens of Guessing Random Additive Noise Decoding (GRAND). Blockwise SO can be used to control decoding misdetection rate, while bitwise SO results in a soft-input soft-output (SISO) decoder that can be used for efficient iterative decoding of long, high redundancy codes.

I. Introduction

For any soft input (SI) forward error correction decoder, it would be highly desirable if it could produce accurate blockwise and bitwise soft output (SO). Blockwise SO, the a posteriori likelihood that the decoding is correct, can be used to inform retransmission requests or to label untrustworthy blocks for an erasure correction code to rectify [1], while bitwise SO can be used for efficient, iterative soft input soft output (SISO) decoding of long, high redundancy codes such as product codes [2], LDPC codes [3], and GLDPC codes [4]. Most error correction decoding algorithms, however, cannot generate accurate SO for reasons articulated in seminal work of Forney [5].