VLSI-SoC: Design and Engineering of Electronics Systems Based on New Computing Paradigms by Nicola Bombieri & Graziano Pravadelli & Masahiro Fujita & Todd Austin & Ricardo Reis

Author:Nicola Bombieri & Graziano Pravadelli & Masahiro Fujita & Todd Austin & Ricardo Reis
Language: eng
Format: epub
ISBN: 9783030234256
Publisher: Springer International Publishing

3.2 Encoding and Decoding Operations

The encoding and decoding operations primarily involve binary matrix multiplications. During the encoding operation, the input data will be multiplied with the generator matrix which will give the encoded data. Similarly, during the decoding operation, the received data will be multiplied with the transpose of parity check matrix to generate the syndromes which helps to locate the error in the received data. Even though the decoding of BCH codes involve multiple steps as presented in Sect. 2, we only require syndrome computation for achieving single-bit error correction.

Suppose A and B are two matrices with dimensions and C be the matrix obtained after multiplication of A and B.

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