Reseeding-based Test Set Embedding with Reduced Test Sequences

1
Reseeding-based Test Set Embedding with Reduced
Test Sequences

• E. Kalligeros1, 2, D. Kaseridis1, 2, X.
  Kavousianos3 and D. Nikolos1, 2
• 1Computer Engineering Informatics Dept.,
• University of Patras, Greece
• 2Research Academic Computer Technology Institute,
  Greece
• 3Computer Science Dept., University of Ioannina,
  Greece

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Motivation

• Core-oriented way of designing contemporary
  Systems on Chip (SoCs) is placing a severe burden
  on the Automatic Test Equipment (ATE)
• This designing style leads to larger and denser
  circuits that require greater test data volumes
  and longer test-application times

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Motivation

• IP protected systems (unknown structure) ways of
  test
• Deterministic test set generation TPG for
  precisely reproduction of test set
• Test-pattern compression Compressed vectors
  stored on tester and decompressed on chip with
  small built-in circuit
• Test set embedding Encodes test patterns in
  longer sequences
• Therefore Test-set embedding techniques with
  short test sequences are required

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Outline of the presentation

• Seed-selection algorithm
• Test-sequence reduction scheme
• Evaluation-Comparisons

5
Outline of the presentation

• Seed-selection algorithm
• Test-sequence reduction scheme
• Evaluation-Comparisons

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Seed-selection algorithm

• We consider the classical LFSR-based reseeding
  scheme LFSR of length n and a Vector Counter
• The algorithm receives as input the size L of the
  window that each seed expands to and a set of
  test cubes T
• For determining a new seed the seed-algorithm
  makes uses of the well-known concept of solving
  systems of linear equations (i.e. assuming
  Gauss-Jordan elimination) Koenemann ETC91
• If each bit of the seed of the LFSR were replaced
  by a binary variable then each one of the L
  window states would be a symbolic vector

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Seed-selection algorithm

• The algorithm examines all possible linear
  systems and chooses one to solve
• If no system can be solved for any of the
  remaining test cubes the above procedure stops
  and a new window has been determined
• Since at each step of algorithm, linear systems
  corresponding to more than one test cubes will be
  solvable at more than one positions of the
  window, as set of heuristics is needed for
  selecting the system that will be actually solved

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Seed-selection algorithm

• Five heuristics are utilized
• Three basic of the algorithm proposed in
  Kalligeros et al, ISQED02
• Two new heuristics that significantly refine the
  selection process (improved encoding ability of
  proposed algorithm)

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Seed-selection algorithm

• First criterion
• At each step of the algorithm the system that is
  actually selected to be solved is the one that
  leads to the replacement of the fewest variables
  in the initial window state
• Second criterion
• The cube containing the maximum number of
  defined bits is the first to be selected for each
  new seed
• Third criterion
• Test cube set is split in two different groups
• High priority Cubes that contain many defined
  bits
• Low priority Rest cubes of set T
• At each step of the algorithm, cubes of 1 are
  targeted first and only if no such cube can be
  covered then the cubes of 2 are targeted

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Seed-selection algorithm

• Although the application of the previous
  heuristics leads to good result in terms of
  resulting seed volumes they are not elaborate
  enough
• At each step of the algorithm there are many
  solvable systems that require the same minimum
  number of variables to be replaced
• The choice among them is a random choice that
  does not improve the efficiency of the algorithm.
• For that reason two new criteria are introduced

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Seed-selection algorithm

• Fourth criterion
• From the systems that require the elimination of
  the same minimum number of variables, those
  corresponding to the test cubes with the maximum
  number of defined bits are preferred
• Fifth criterion
• In the case the fourth criterion gives more than
  one cube then the systems corresponding to the
  cube which can be covered at the fewest positions
  within the L-state window are preferred
• The addition of those two criteria improves
  significantly the encoding ability of the
  seed-selection algorithm resulting in 25 smaller
  seed sets on average

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Outline of the presentation

• Seed-selection algorithm
• Test-sequence reduction scheme
• Evaluation-Comparisons

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Test-sequence reduction scheme

• Seed-selection algorithm assumes a L state window
  for every seed
• Only some of these states of each window are
  actually being used for reproducing a test cube
  of T
• If the last state of a window is not a useful one
  then all states from the last useful one to the
  last state of each window are redundant

• As more seeds are selected by the algorithm, more
  variables are replaced and thus fewer cubes are
  encoded in each seed ? more useless states at the
  end of these windows

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Test-sequence reduction scheme

• This problem is much more important in the case
  of test set embedding since the increased number
  of seeds leads to much longer test sequences
• Most efficient way (in terms of test-sequence
  length)
• Maximum reduction approach which stops the
  expansion of each seed after the clock cycle in
  which the last useful state was generated by the
  LFSR ? number of redundant states will be zero
• Problem
• Vector Counter has to be initialized with a
  different value at each reseeding ? Excessive
  test data storage

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Test-sequence reduction scheme

• An intermediate approach has to be followed
• Proposed approach
• Each window is segmented into a number (m) of
  equal-sized groups of LFSR states
• The useful states of the window are included in
  the first k segments and thus the remaining m-k
  segments contain redundant states and can be
  dropped during test generation
• Segment-Vectors Counter Generate the states of
  each group (counts from Segment_Size-1 to 0)

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Test-sequence reduction scheme
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Test-sequence reduction scheme

• With proper selection of Segment_Size, the
  distance between the last useful state and the
  end of last useful segment can be minimized
• The Upper limit of number of eliminated redundant
  states is the one of the Maximum reduction
  approach

A low hardware-overhead solution for generating
the useful segment of each window is required
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Test-sequence reduction scheme

• Rearrangement technique
• Main idea
• Order the seeds according to the number of useful
  segments
• if these volumes for every two successive windows
  differs at most by one ? Only a single extra bit
  per seed is needed for indicating this relation.
• Extra bit0 ? Same number of useful segment
• Extra bit1 ? One segment difference
• Problem
• The difference in the number of useful segment
  between two successive (ordered) seeds may be
  greater than one
• Solution
• Some useless segments should be maintained in
  the window with the smaller number of useful
  segments

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Test-sequence reduction scheme
Example of rearrangement technique
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Test-sequence reduction scheme

• Load Counter
• Down counter that maintains the necessary number
  of segments for each window
• Initially loaded with maximum number of segments
  required among all windows
• The value of the extra bit of each window
  determines the operation of the counter
• Extra bit1 ? Load counter decreases by one
• Extra bit0 ? Load counter stays unchanged

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Test-sequence reduction scheme

• In order to actually control the generation of
  the patterns of a window, two counters are need
• Segment-Vectors Counter Counts from
  Segment_Size-1 to 0 and controls the generation
  of the vectors of a segment
• Segment Counter Counts the requiring number of
  segments in each window and thus initialized with
  the value of Load Counter at the beginning of a
  new window
• These two counters constitute a combined counter
• Segment Counters value is decreased by one every
  time Segment-Vectors Counter signals that
  Segment_Size patterns have been applied to the
  CUT

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Test-sequence reduction scheme

• New window generation
• Next stored seed is loaded into LFSR
• Segment Counter is loaded with current Load
  Counters Value
• Load Counter is triggered (or not) according to
  value of seeds stored extra bit
• Segment-Vectors Counter is enabled

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Test-sequence reduction scheme

• The previous process is repeated until all the
  seeds
• have been expanded to their corresponding
  vector-segments
• Extra hardware overhead of Control Logic
• The combination of Segment and Segment-Vectors
  Counters is equal to the Vector Counter of the
  classical reseeding approach
• Therefore H/W overhead is only the Load Counter

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Outline of the presentation

• Seed-selection algorithm
• Test-sequence reduction scheme
• Evaluation-Comparisons

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Evaluation-Comparisons

• First Important issue Choice of window size L
• Affects both number of final selected seeds and
  the length of the resulting test sequences
• As ? L ? of required seeds ?
• But of required seeds is gradually saturated
  as ? L resulting in larger test sequences with
  small benefits for the of seeds

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Evaluation-Comparisons

• Second Important issue Choice of Segment_Size
• Can be calculated easily by a very-fast brute
  force procedure
• This procedure tests all possible segment_size
  values and chooses the best one with respect to
• Number of allowed redundant segments in seeds
  windows
• Number of redundant vectors in the last useful
  segment of each window
• Running time on Pentium 2.6 GHz workstation was
  less than 2 sec

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Evaluation-Comparisons
Results of proposed technique (?) Reduction of
test-sequence lengths of segmentation-rearrangemen
t technique compared to unreduced sequences of
the seed-selection algorithm (?) Percentage of
test-sequence reduction over those of maximum
reduction technique
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Evaluation-Comparisons
Comparison with Twisted-Ring Counters
approach Resulting Test Sequences (?)
Twisted-Ring with Mintest (?) Twisted-Ring with
Atalanta (?) Proposed technique
Proposed technique
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Evaluation-Comparisons
Comparison with Twisted-Ring Counters
approach Test Data Storage (?) ROM bits of
Twisted-Ring with Mintest (?) ROM bits of
Twisted-Ring with Atalanta (?) ROM bits of
Proposed technique
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Conclusions

• Segmentation-rearrangement techniques achieves on
  average 20,17 reduction in final test-sequence
  lengths having on average 74,76 of the reduction
  of the maximum reduction approach
• The combination of the two proposed techniques
  (seed-selection algorithm segmentation-rearrange
  ment techn.) requires on average 85,39 and
  74,04 fewer test vectors than Twisted-Ring
  Counter for Mintest and Atalanta cases
  respectively
• On average, compared to Twisted-Ring Counters our
  technique requires 27,79 and 39,94 less
  test-data storage for Mintest and Atalanta cases
  respectively