FEC

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FEC
The Reed-Solomon Method
Project Members Alon Keren Sagi Linsker
Instructor Omer Gurewitz
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FEC The Reed-Solomon Method
Whats Today

• Introduction
• Forward Error Correction (FEC)
• The Reed-Solomon (RS) Method
• Why and why not to use RS
• Whats next.

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FEC The Reed-Solomon Method
Introduction
Started with a 5 pages-long paper published in
1960. Used in hard-disks, CDs, deep-space
communications.
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FEC The Reed-Solomon Method
What is FEC?
Forward Error Correction (FEC) is a system meant
to minimize the amount of digital data lost on
transfer.
Additional methods to diminish error-rates are
ARQ, and Data Carousel, that are sometimes used
together with FEC.
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FEC The Reed-Solomon Method
How does FEC work?
The side transmitting the data actually sends a
greater number of blocks (according to a specific
algorithm).
The receiving side (or sides) may fully
reconstruct the original data, even if some
blocks were lost on transmission, due to noise,
for example.
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FEC The Reed-Solomon Method
How does FEC work? (Cont.)
k symbols
Each symbol contains a predefined No. of bits.
Data block
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FEC The Reed-Solomon Method
How does FEC work? (Cont.)
k symbols
Each symbol contains a predefined No. of bits.
Data block
FEC encoding
n
Data
Redundant
k
l
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FEC The Reed-Solomon Method
How does FEC work? (Cont.)
k symbols
Each symbol contains a predefined No. of bits.
Data block
FEC encoding
n
Data
Redundant
k
l
Noisy channel
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FEC The Reed-Solomon Method
How does FEC work? (Cont.)
k symbols
Each symbol contains a predefined No. of bits.
Data block
FEC encoding
n
Data
Redundant
k
l
k
FEC decoding
Noisy channel
Data block
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FEC The Reed-Solomon Method
Types of FEC codes
Large Blocks (Tornado) Fast Encoding/decoding
time (a kl). Yet, requires small overhead on
reception (5-10 for n2k). K is in order of tens
of thousands, and N is a small multiple of K.
About C10Mb/s encoding/decoding time.
Small Blocks (Reed-Solomon) Slower than Tornado
codes (a kl) , but requires no reception
overhead. Usually, K and n are small (for
example, below 256). About 80/min(k, l)
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FEC The Reed-Solomon Method
What is RS method?
Reed Solomon codes are a subset of BCH codes and
are linear block codes. A Reed-Solomon code is
specified as RS(n,k). RS will correct code as
long as 2s r lt 2t. gt Up to t errors or up to
2t erasures. t half the number of redundancy
symbols s errors in block r erasures in block
(occur when the position of an erred symbol is
known.)
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FEC The Reed-Solomon Method
What is RS method? (Cont.)
Otherwise (if 2s r lt 2t is not upheld)
either

• The decoder will detect that it cannot recover
  the original code word. Or
• The decoder will mis-decode and recover an
  incorrect code word without any indication.
• The probability of each of those cases depends
  on the specific RS code.

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FEC The Reed-Solomon Method
Why Reed-Solomon?
1. Good for handling burst-errors (using symbols
and not bits).
2. Does not require a back-channel (as opposed to
ARQ). Therefore, an excellent solution for
multicast.
3. Can be good for streaming (unlike ARQ, in
which a message can arrive later than expected).
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FEC The Reed-Solomon Method
Why NOT Reed-Solomon?

• Demands large encoding/decoding time for large
  value of k and n.

• Redundant information is added, therefore, larger
  amount of data needs to be transferred.

Both of those disadvantages are obvious when the
channel is almost error-free.
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FEC The Reed-Solomon Method
Whats next

• Continue exploring the Reed-Solomon parameters
  (n, k) trade-offs, and possible uses.
• Possibly, implementing RS for a specific purpose.
• Possibly, comparing RS with ARQ.
• and more

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FEC The Reed-Solomon Method
FIN