Altera Reed-Solomon II MegaCore Function - Manual (Page 19)

Figure 3-3: Codeword Decoding
1 238
Decoded Codeword
239 ... 237 240 ... 255 RS II Decoder
Encoded Codeword plus noise
... ...
The received encoded codeword may differ from the original codeword due to the noise in the channel.
The decoder detects errors using several polynomials to locate the error location and the error value.
When the decoder obtains the error location and value, the decoder corrects the errors in a codeword, and
sends the codeword to the output. As the number of errors increases, the decoder gets to a stage where it
can no longer correct but only detect errors, at which point the decoder asserts the
out_error
signal.
Table 3-1: Decoder Detection and Correction
Lists how the decoder corrects and detects errors (e) depending on the number of check symbols (R).
Number of Errors Description
e ≤R/2 Decoder detects and corrects errors.
R/2 ≤ e ≤R Decoder asserts error signal and can only detect
errors.
e >R Unpredictable results.
For small numbers of check symbols, out_error is not always reliable. RS codewords have at least d
different symbols: d = R + 1 A received packet containing e errors can be either the transmitted codeword
t1 with e errors, or another valid codeword t2 with d–e errors (if t2 exists). When e> R/2, the received
packet looks more like t2 than t1 (because d – e < e) so, the decoder outputs t2 and does not assert
out_error
. The probability that t2 exists is inferior or equal to the inverse of factorial of R/2. It decreases
exponentially as R increases, but is nonetheless significant for small numbers of check symbols.
Figure 3-4: Decoder Timing—One Channel
shows the timing diagram of the RS II decoder with one channel.
clk_clk
reset_reset_n
in_valid
in_startofpacket
in_endofpacket
in_data[7:0]
in_ready
out_valid
out_startofpacket
out_endofpacket
out_data[7:0]
out_ready
out_error
0 1 2 3 4 5 6 105 216 193 137 138 139 140 141 245 246 247 248 249 250 251 252 253 254 245 246 247 248 249 250 251 252
0 X 1 2 3 4 5 6 105 216 193 137 138 139 140 141 1
status_error_value[7:0] 0 0 0 0 0
status_num_error_symbol[3:0] 0 0 0 8
status_num_error_bit[6:0] 0 0 0 0
UG-01090
2015.05.01
Decoder 3-3
Reed-Solomon II IP Core Functional Description Altera Corporation
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