Coding Bounds in the Finite-Black-Length Regime: an Application to Spread-Spectrum Systems Design

Recent advances in coding theory have identified compact and tight bounds to the best achievable performance of an encoder/decoder couple in the practical case where codewords have a finite length. Such bounds are able to capture the essence of the physical layer without the need of designing and testing its constituent blocks (e.g., the encoder and decoder), and are thus perfectly suited for system design. In this paper we show how these bounds can be used to infer optimal parameters of a communication system based on a spread-spectrum technique, where the fundamental question is to identify a reasonable balance between the encoding process (i.e., the codeword length) and the length of the spreading sequence. The idea is exemplified in the context of the GNSS data component. However, it has a much wider range of applicability, especially in today's effort towards heterogeneous communications using short-packets where the results in the finite-length-regime play the role once played, in more traditional communication systems, by Shannon's capacity.