Fault-Secure Parity Prediction Arithmetic Operators

MICHAEL NICOLAIDISRICARDO O. DUARTE

TIMA Laboratory

SALVADOR MANICHJOAN FIGUERAS

Polytechnic University of Catalonia

Outline

What is the problem ? Efficient Self-Checking Arithimetic Analysis of fault secureness Single-cell fan-out networks Take some examples Multiple-cell fan-out networks Implementations and experiments Conclusions

What’s The Problem ?

DRAWBACK: Parity prediction may not achieve fault- securene

ss , because single faults propagate o- -utput errors of random multiplicity.

Arithmetic codes can ensure falut secureness for most arithmetic operators.

Problem 1.Arithmetic code checkers are complex circuit 2.Arithmetic code are not compatible with p

arity checking 3.Must implement whole system with A~ code

Efficient self-checking arithimetic

Parity prediction schemes carries a lower overhead and a lower performance penalty than arithmetic coding schemes for small and medium-size operands.

And we are interest in efficient parity prediction implementations.

Method : Include arithemetic operators

Analysis of fault secureness

Definition: In a self-checking design, a circuit is fault secure if its output code detects all errors generated by each modeled fault.

Restriction: Cannot achieve fault secureness because even-multiplicity errors escape detection by parity code.

-Solution : 1.先分析 parity prediction cellular arithmetic operators來看不符合的原因 .

2.一一排解 .

continuous

Analysis of fault secureness

Basic components of cellular arithmetic operators : full- and half- adder cells.

5大主題 : Lemma1. 將不符合 fault-secure的 parity predictor電路給它獨立出來 .

Lemma2. 在不符合 fault-secure的 parity predictor電路中 ,將經由運算得到的 carries,拿來推算其可能產生的parity.

continuous

Analysis of fault secureness

Lemma3. 証明如果上圖的 sum(S)和 carry(C)使用同一個電路則 arithmetic operator將無法 fault secure.

continuous

Analysis of fault secureness

Lemma4. 証明如果一個 cell的 inputs只能生成 sum,carry,跟 redundant carry任兩個 ,則 operator也無法 fault secure.

continuous

Analysis of fault secureness

Lemma5. 証明如果說 C,Cp和 S在 logic有 fault而產生error給 C跟 Cp,則儘管 error會傳給下一個 S,但其仍可符合 fault secureness

Single-cell fan-out networks

Definition: any network in which each cell output enters exactly one input of exactly one cell is a single-cell fan-out networks.

Theorem1 : Parity prediction in a single-cell fan-out network using full- and half- adder cell designed as in Fig.3 achieves fault secureness.

continuous

Single-cell fan-out networks

Theorem2 : The full-adder cell of Fig.4 prserves fault secureness.

Examples

Ripple-carry adders.

Examples

Parity prediction multipliers.

Examples

Improved parity prediction multiplier.

Multiple-cell fan-out networks

A more complex implementation is required if some signals enter an even number of cell inputs.

Fig.9b is one solution. Fig.9c is another

solution with a double-rail checker.

Examples

Nonrestoring-array divider. The array’s basic cell is the controlled add/subtract cell.

Self-Checking nonrestoring-array divider

Divider points

Each carry signal enters the row’s rightmost cell twice.

The divider generates two independent sets of outputs(remainder and quotient).

The leftmost cell’s carry and sum outputs have opposite values,and either can provide the quotient outputs.

The parity of sum outputs is PS=PCp+PN+PD+1 for even number of rows,it becomes PS=PCp+PN+1.

Implementations and experiments

Implementations and experiments

Implementations and experiments

Conclusions

Hardware cost of these fault-secure structures is significant.

For small nad medium size operators,these solution are also more efficient than operators based on arithmetic codes which require complex checkers and code translators for compatibility.