# how symbol and bit error prob. are related.

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#### mehtesham

##### Junior Member level 3 symbol error and bit error

hi
can you determine how symbol and bir error rates are related.and what this relation depends on.

#### mnosrati

##### Junior Member level 1 hi

P_M : symbol error prob.
P_b : bit error prob.
k : number of bit per each symbol

P_M= [2^(k-1)/(2^k-1)]*P_b

" digital communication" by proakis(chapter five)

##### Junior Member level 3 [size=18]if you are using grey code in coding therefore
ser= symbol error rate
ber= bit error rate
k=number of bits per sybol = log (base 2) M
where M is the M ary you are using
therefore ber=ser/k[/size]

#### changfa If gray coding is assumed, the bit error rate is 1/log2(M) of symbol rate where M is the modulation order (for example, M=4 for 4PSK).

However, gray coding is not always applicable to all modulation constellation. In such case, some approxiamate can be found in Proakis's book.

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