Synthesis-by-analysis of BCH Codes

TL;DR

This paper introduces a blind synthesis method for BCH codes that identifies generator polynomials and block lengths through GCD calculations and correlation analysis, enabling parameter extraction without prior knowledge.

Contribution

It presents a novel GCD-based technique for synthesizing BCH code parameters blindly, improving understanding and analysis of these codes.

Findings

High correlation values indicate correct block length and generator polynomial.

Method accurately extracts code parameters such as minimum distance and error correction capability.

Technique effectively identifies BCH code structures without prior code information.

Abstract

In this paper we propose a technique to blindly synthesize the generator polynomial of BCH codes. The proposed technique involves finding Greatest Common Divisor (GCD) among different codewords and block lengths. Based on this combinatorial GCD calculation, correlation values are found. For a valid block length, the iterative GCD calculation results either into generator polynomial or some of its higher order multiples. These higher order polynomials are factorized under modulo-2 operation, and one of the resulting factors is always the generator polynomial which further increases the correlation value. The resulting correlation plot for different polynomials shows very high values for correct block length and valid generator polynomial. Knowing the valid block length and generator polynomial, all other parameters including number of parity-check digits (n-k), minimum distance dmin and error correcting capability t are readily exposed.