Pragmatic Formal Verification of Sequential Error Detection and Correction Codes (ECCs) used in Safety-Critical Design

Abstract

Error Detection and Correction Codes (ECCs) are often used in digital designs to protect data integrity. Especially in safety-critical systems such as automotive electronics, ECCs are widely used and the verification of such complex logic becomes more critical considering the ISO 26262 safety standards. Exhaustive verification of ECC using formal methods has been a challenge given the high number of data bits to protect. As an example, for an ECC of 128 data bits with a possibility to detect up to four-bit errors, the combination of bit errors is given by 128C1 + 128C2 + 128C3 + 128C4 = 1.1 * 10^7. This vast analysis space often leads to bounded proof results. Moreover, the complexity and state-space increase further if the ECC has sequential encoding and decoding stages. To overcome such problems and sign-off the design with confidence within reasonable proof time, we present a pragmatic formal verification approach of complex ECC cores with several complexity reduction techniques and know-how that were learnt during the course of verification. We discuss using the linearity of the syndrome generator as a helper assertion, using the abstract model as glue logic to compare the RTL with the sequential version of the circuit, k-induction-based model checking and using mathematical relations captured as properties to simplify the verification in order to get an unbounded proof result within 24 hours of proof runtime.