Re: How much is Alice worth to Bob?

From: Fred the Wonder Worm (ftww_at_maths.usyd.edu.au)
Date: 03/26/04 

Date: 26 Mar 2004 08:26:01 GMT

In article <9e54a9f7.0403252300.7c237597@posting.google.com>,
Guenther von Knakspott <guenther.vonKnakspott@gmx.de> wrote:
>Colin Andrew Percival <cperciva@sfu.ca> wrote in message news:<c3vd7g$s1>
> We can improve, as follows:
>>
>> Strategy 3: Alice takes blocks of 8 bits at a time. She discards the last
>> bit, and decodes the remaining 7 into a block of 4 bits using the distance
>> 3 (7,4) Reed-Solomon code. Bob takes these 4 bits, encodes them into a
>> block of 7 bits using the same code, and guesses the last bit. Minimum
>> correct = 1.5 N, expected correct = 1.656 N.
>
> Hello Percival: Say, are you stating here that Alice can transmit
> every possible 7 bit block using only 4 bits? That is impossible, you
> know. Am I, or are you missing something here?

No, he is saying that Alice can transmit the appropriate 7-bit element
of the distance 3 (7,4) Reed-Solomon code in 4 bits. Since that code
has 16 elements, this is a correct statement.

The point of using this code is that _every_ 7 bit vector is a distance
of at most 3 away from one of the 16 codewords. Thus, by guessing the
bits as directed by the codeword, Bob will get at most three of them
wrong (and thus at least four of them right).

[ And to answer someone else's question, the 8th bit is discarded
because we want to send 4 bits, so we have to consume at least 8 --
we are only allowed to send half the total number of bits. ]

Cheers,
Geoff.

-----------------------------------------------------------------------------
Geoff Bailey (Fred the Wonder Worm) | Programmer by trade --
ftww@maths.usyd.edu.au | Gameplayer by vocation.
-----------------------------------------------------------------------------

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