Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A lower bound on the field size of convolutional codes with a maximum distance profile and an improved construction (2305.08388v2)

Published 15 May 2023 in cs.IT, cs.CC, and math.IT

Abstract: Convolutional codes with a maximum distance profile attain the largest possible column distances for the maximum number of time instants and thus have outstanding error-correcting capability especially for streaming applications. Explicit constructions of such codes are scarce in the literature. In particular, known constructions of convolutional codes with rate k/n and a maximum distance profile require a field of size at least exponential in n for general code parameters. At the same time, the only known lower bound on the field size is the trivial bound that is linear in n. In this paper, we show that a finite field of size $\Omega_L(n{L-1})$ is necessary for constructing convolutional codes with rate k/n and a maximum distance profile of length L. As a direct consequence, this rules out the possibility of constructing convolutional codes with a maximum distance profile of length L >= 3 over a finite field of size $O(n)$. Additionally, we also present an explicit construction of convolutional code with rate k/n and a maximum profile of length L = 1 over a finite field of size $O(n{\min{k,n-k}})$, achieving a smaller field size than known constructions with the same profile length.

Summary

We haven't generated a summary for this paper yet.