Delay-Constrained Capacity and Probabilistic Codes

The Noisy Channel Coding Theorem discovered by C. E. Shannon assumes infinite coding latency. The objective of this work is to identify the maximal achievable (transmit) rates over noisy, delay-constrained channels, referred to as (e, n)-capacity C_eⁿ with e denoting target error probability and n coding latency (viz. block length). We investigate a family of block codes based on a probabilistic construction that approaches delay-constrained capacity closely and provably achieves the Shannon limit over an additive white Gaussian noise (AWGN) channel. We also present an improved construction of a probabilistic code with correlated codewords, enhancing its asymptotic distance by introducing a specific amount of correlation between codewords. Analytical results show that, if the correlation coefficients are chosen uniformly to be -1/(M-1), where M denotes the number of codewords, the corresponding probabilistic code is asymptotically (in the sense of block length) the ``best-d(min)***asy'' code.

Keywords: AWGN, Shannon limit, probabilistic codes, coding latency, (e, n)-capacity.