Exact Burst-Correction Capability of Gilbert Codes
Abstract
Introduction: In order to increase the data exchange rates in data transmission and storage systems, you have to efficiently reduce the noise which comes out during the transmission, storing and processing of the data, using as small redundancy as possible. The coding schemes should consider typical errors, most common in the given communication channel. Most real communications channels are channels with memory, and a typical noise can be described as an error burst. Gilbert codes with simple encoding and decoding procedures have a poor minimal distance, being ineffective for correcting independent errors; nevertheless, they can be used for bursts correction. However, the burst-correcting capability of these codes can be estimated only by bounds which are not always accurate. Purpose: The goal is to obtain exact values for the maximal lengths of error bursts correctable by Gilbert codes depending on their construction parameters. Results: A procedure is developed which allows you to calculate the exact value for the maximal length of a single burst correctable by Gilbert code, depending on the code’s construction parameters. To build this procedure, we analyzed the structure of the parity-check matrix of Gilbert codes and the structure of the bursts which cannot be corrected by parity-check matrix decoding. The novelty of this result is that the procedure allows you to calculate the exact burst-correction capability for any parameters of the Gilbert code. Practical relevance: The obtained accurate values for Gilbert code burst-correction capability can be used for analytical estimation of error probabilities in channels with memory when using Gilbert codes. They also can be taken into account to choose more effective coding schemes in communication and storage systems.Published
2016-02-22
How to Cite
Krouk, E., & Ovchinnikov, A. (2016). Exact Burst-Correction Capability of Gilbert Codes. Information and Control Systems, (1), 80-87. https://doi.org/10.15217/issn1684-8853.2016.1.80
Issue
Section
Information coding and transmission