New Sphere-Packing Bounds for Finite-Blocklength Coding Over Additive Noise Channels

Ultra-reliable low-latency communication (uRLLC) is of increasing importance in the evolution of 5G and beyond wireless communication networks. Since the communication latency is bounded by the blocklength of codewords, channel coding theory at finite blocklength is important in the design and analysis of uRLLC systems. Based on the concept of sphere-packing introduced by Shannon in 1959, in this paper, we introduce a new codebook design, namely the volume-uniform random coding codebook, and derive a corresponding achievability result in closed form. Comparing to conventional sphere-packing codebook designs where all codewords are located on the surface of the sphere, the proposed design allows codewords to lie inside the sphere, which provides greater freedom in the codebook. A concise and explicit approximation bound is obtained as (Equation Presented ), where ϵis the decoding error probability, n is the blocklength, P is the signal-to-noise ratio (SNR), and E0 is a simple explicit function of only P. It is shown by both simulation and analysis that the derived bounds are much tighter compared to existing bounds, especially when the blocklength is short, e.g., n 100.