Second-Order Performance of Early Decoding with Shell Codes in Gaussian Broadcast Channels

We investigate early decoding in a Gaussian broadcast channel with heterogeneous blocklength constraints when shell codes are used. By shell codes, we refer to non-i.i.d. codes that fulfill the power constraint with equality. Early decoding is a technique where one user can perform successive interference cancellation with an interference codeword that is not yet fully received. By decoding the interfering shell codeword earlier, it loses the shell property, making the statistical error analysis more challenging. We address this by using composite shell codes in combination with change of measure techniques and the Berry-Esseen Theorem for functions. We derive a bound on the minimum number of symbols that is required to successfully early decode the interference and we characterize the rate region when shell codewords are used. Numerical results show a latency reduction that is at least doubled compared to the state of the art as well as a much broader range of feasible input powers, leading to a significantly improved rate region compared to previous results on early decoding.

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