Answer The Following Questions Briefly - CCA Consider

Answer the Following Questions Very Brieflyais Cca Consider The Fo

1. Briefly answer the following questions:

a. Fault detection by CCA

• i. A jump from the middle of a BFI to the beginning of another BFI: CCA detects this as a fault because it indicates a break in the expected sequence of frame boundaries, violating the continuity of the data stream.
• ii. A jump from end of a BFI to the middle of another valid predecessor BFI: Such a jump disrupts the integrity of the BFI sequence, and CCA detects it via checksum or boundary validation mechanisms that verify the correct ordering and contents of BFIs.
• iii. A jump from end of a BFI to the middle of another invalid predecessor BFI: CCA detects this immediately through checksum mismatch or invalid boundary markers, signifying a fault.

b. Using weighted checksum for fault correction

In a linear array of size 4 with weights 2, 1, 8, and 4, the weighted checksum syndrome is –8. Given the syndrome values, the erroneous element can be identified by matching the syndrome to the weighted sum. Since the syndrome is –8, and the weights are [2, 1, 8, 4], the erroneous element corresponds to the position with weight 8, which is the third element. Correction involves adjusting the third element to restore consistency.

c. N-version programming Vs. Recovery Block Schemes

N-version programming involves developing multiple functionally equivalent versions independently to run in parallel, with a voter selecting the correct output, enhancing fault tolerance through diversity. Recovery Block Schemes (RBS) execute a primary version, and if it fails, a backup or recovery procedure is invoked. While N-version prioritizes redundancy through multiple versions, RBS emphasizes correctness checks and recovery procedures post-failure.

d. The Discrete Reversal Block (DRB) scheme for software fault tolerance

The DRB scheme involves periodically reversing code segments or states to a previously verified safe state to recover from faults. For of its steps:

• Primary node failure: Detect fault, switch to backup node or state.
• Primary alternate on primary node fails: Engage secondary recovery mechanisms or switch to shadow node.
• Primary alternate on shadow node fails: Revert to initial safe state or escalate for manual intervention.

These failures are considered disjoint events, managed through fault detection, isolation, and recovery actions aimed at maintaining system integrity.

e. Reliability growth in software testing and hardware testing limitations

Reliability growth in software testing refers to systematic testing and debugging processes that progressively eliminate faults, thereby increasing software reliability over time. This growth is feasible due to the modifiable nature of software, allowing targeted corrections. In hardware testing, reliability growth is less apparent because hardware components are difficult to modify after manufacturing, making fault mitigation more challenging post-production.

2. Error detection and correction with Parity Check Matrix

a. Expressions for check elements: Assuming the first three columns are check bits, the parity constraints can be expressed as linear combinations of data bits that satisfy the parity conditions, based on the matrix structure.

b. Error correction for [000110]: Given only one error, the syndrome calculation identifies the erroneous bit. The syndrome indicates the position of the error, allowing correction by flipping that bit.

c. Generator matrix: Derived from the parity check matrix, the generator matrix generates the codewords and ensures the code's properties.

3. Generator polynomials for 5-bit cyclic codes

Possible generator polynomials include, for example, x^3 + x + 1 and x^4 + x + 1. All such polynomials are divisors of x^5 + 1, and generate cyclic codes of length 5. Generating codes involves polynomial division and constructing matrices based on these polynomials.

4. Diagnosability and Fault Patterns in a 5-node Loop System

i. The diagnosability of the system is determined by its ability to uniquely identify faults based on test outcomes. With a cycle of tests v1 to v5, the system's diagnosability depends on the design, typically being able to detect and locate single node faults.

ii. Fault patterns for syndrome 11001 involve combinations of node faults that produce this test syndrome during diagnosis, with the pattern corresponding to specific faulty nodes and tests, assuming the syndrome bits represent the outcome of sequential tests.

References

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