paragraph change

Author: ChainlessCoder

content/posts/information_chaining_part_1.md

@@ -162,7 +162,7 @@ We want high reliability without excessive redundancy. A connection-oriented pro
 
 If we can estimate the percentage of packets likely to be lost during transmission, say, due to noise, congestion, or interference we can use **erasure coding** for reliable, one-way transmission. In coding theory, an erasure code is a type of *forward error correction* (FEC) code. FEC schemes allow the receiver to detect and correct errors, or, in the case of erasures, to reconstruct missing data, without requiring retransmission. This property is invaluable for storing data across unreliable networks or transmitting it through noisy channels. For example, if a sender transmits several data packets to a receiver, the goal of an erasure code is to enable the receiver to reconstruct the original message even if some packets are lost in transit (i.e., "erased").
 
-Erasure codes work by transforming an original message of $n$ symbols into a longer message of $z$ symbols. The $n$ original symbols are called *source symbols*, while the additional ones are *encoded symbols*. Even if some encoded symbols are lost, the receiver can reconstruct the original message using a subset of the $z$ encoded symbols. The number of encoded symbols required to recover the original message depends on the erasure code's *code rate*, defined as $\frac{n}{z}$. Or in other words, it represents the portion of the data that is not redundant. For every $n$ source symbols, $z$ encoded symbols are created, $z-n$ of which are redundant. An *optimal erasure code* allows full reconstruction from any $n$ of the $z$ encoded symbols.
+Erasure codes work by transforming an original message of $n$ symbols into a longer message of $m$ symbols. The $n$ original symbols are called *source symbols*, while the $m$ transformed $ones are *encoded symbols*. Even if some encoded symbols are lost, the receiver can reconstruct the original message using a subset of the $m$ encoded symbols. The number of encoded symbols required to recover the original message depends on the erasure code's *code rate*, defined as $\frac{n}{m}$. Or in other words, it represents the portion of the data that is not redundant. An *optimal erasure code* allows full reconstruction from any $n$ of the $m$ encoded symbols. I’m intentionally reusing the symbol $m$ here. Previously it referred to the Bloom filter size; now I use it for the number of encoded symbols. That’s not an accident: in our scheme, the filter is the encoding, so its bits are the encoded symbols.
 
 
 ## Designing a Bloom filter–based erasure encoder