SC140 Core Overview
An alternative way to interpret PE>T is as the ratio of uncorrectable encoded blocks to the total number of received
blocks, as the latter tends to infinity. A decoding error happens when an uncorrectable error is not recognized as
such, and the whole block is decoded into another valid code word. The probability Pm of a miscorrection is
bounded by
Pm
≤
--1--
T!
PE
>
T
In typical applications with m = 8, the miscorrection rate Pm is about five orders of magnitude less than PE>T. The
curves in Figure 4, below, depict the probability of uncorrectable error for a block length N fixed to 255 and T
varying from 1 to 8, as a function of the channel bit-error rate.
PE>T
10 0
10 –5
T=1
10 –10
T=2
T=4
T=8
10
–15
10
–8
10 –6
10 –4
10 –2
10 0
Channel Bit-Error Rate
Figure 4. Probability of Uncorrectable Error Versus Bit-Error Rate
Notice that for bit-error rates below 10–2, the curve exhibits a very steep slope. This is characteristic for good
codes. It implies that the chances of encountering an uncorrectable error decrease drastically with only a
moderately improved bit-error rate.
3 SC140 Core Overview
The SC140 core (see Figure 5) is a programmable high-performance DSP core that uses parallelism to execute
multiple instructions in one clock cycle, running currently at 275 MHz and, eventually, at 400 MHz.
Reed Solomon Encoder/Decoder on the StarCore™ SC140/SC1400 Cores, With Extended Examples, Rev. 1
10
Freescale Semiconductor