Information Redundancy

1
Information Redundancy

• Addition of redundant information to data to
  allow fault detection, fault masking, or fault
  tolerance
• Examples error detecting and error correcting
  codes
• A code is a means of representing information
  using a well-defined set of rules
• A code word is a collection of symbols used to
  represent a piece of information based on a
  specific code
• A binary code symbols 0 and 1
• Encoding
• Decoding

2
Information Redundancy

• An error detecting code is a code that allows
  errors introduced into a code word to be
  detected.
• An error correcting code is a code that allows
  errors introduced into a code word to be
  corrected.
• The Hamming distance between any two binary words
  is the number of bit positions in which the two
  words differ.
• The code distance is the minimum Hamming distance
  between any two valid code words.

3
Information Redundancy

• Separable code
• Nonseparable code
• Parity Code
• Odd, even
• Bit-per-word parity
• Bit-per-byte parity
• Bit-per-chip parity
• Bit-per-multiple-chips parity
• Interlaced parity
• Overlapping parity

4
Information Redundancy

• M-of-n codes
• Define code words that are n bits in length and
  contain exactly m 1s
• Separable or nonseparable
• Duplication Codes
• Basic duplication
• Complemented duplication
• Swap and compare

5
Information Redundancy

• Checksums
• A form of separable code
• Useful when block of data are to be transferred
• Types
• Single-precision checksum
• Double precision checksum
• Honeywell checksum
• Residue checksum

6
Information Redundancy

• Overlapping Parity
• Each bit appearing in more than one parity group
• Errors can be detected and located

7
Information Redundancy

• Hamming Error-Correcting Codes
• Used in many memory designs
• Requires 10 - 40 redundancy
• Efficient in terms of time
• Error correction circuits readily available on
  inexpensive chips
• Memory can contribute as much as 60 of faults in
  a system

8
Information Redundancy

• Hamming Error-Correcting Codes
• Example
• Four information bits (d3, d2, d1, d0)
• Parity check bits (c1, c2, c3)
• Groups (d3, d1, d0, c1), (d3, d2, d0, c2), and
  (d3, d2, d1, c3)

9
Information Redundancy
10
Information Redundancy

• Hamming single error correction unit

11
Information Redundancy

• Basic structure of a memory using Hamming single
  error correcting code

12
Information Redundancy

• Hamming code modification to achieve double error
  detection and single error correction

13
Time Redundancy

• Transient Fault detection
• Permanent Fault detection

14
Software Redundancy

• Consistency Checks
• Capability Checks
• N-Version Programming