The other states of the two flip flops, only two Significantly, theįlip flops could never change directly from 00 to any state except 00 or 10. The stored bits (BA) cannot jump arbitrarily from one state to another.įor example, if the state (BA) of the flip flops is currently 00, it will change to 10 if the Sequential Circuit Analysis Since the bits at B and AĪre defined by a shift register circuit fed from input C, The circuit as an error correction scheme. This observation is key to the performance of The outputs (XY) produced whenever a new bit arrives depend on the new bit (C)Īnd the two previous bits (BA). Since the bits (CBA) represent the most recent three bits to Outputs (XY), as summarized in the table below. Each combination leads to one pair of bits for the In general, a 1/N rate code leads to a proportional lengthĬombinatorial Circuit Analysis - There are eight possible conditions for A coder such as this whichĭoubles the number of bits is called a "rate one half" coder. In common with other error control techniques, convolutional coding involves increasing the length of the original message. Twice as many bits emerge from the circuit asĮnter at point C. Would switch quickly between X and Y to transmit an output bitstreamĪt twice the rate of the input bit stream. (ABC) being the incoming bit and the two previous bits, we define a constraint length K equal to 3.Ĭoding Rate (R=1/2) - For each bit arriving at point C, Ĭonstraint Length (K=3) - Because the output bits (XY) are a function of three bits ![]() TheĬorresponding generating polynomials in decimal are. In this case, the connections defining X and Y can be described as binary values 111 for X=C+B+A and 101 for Y=C+A. ![]() The output bits X and Y are formed by exclusive-OR gates as shown,ĭefined by Connections - The way in which the output bits are generatedĭefines a particular convolutional coding circuit. Through points C and B and A in three clock periods. Circuit Description - The circuit consists of two D-Flip-FlopsĬonnected in series with a common clock (not shown).ĭata arrives at point C and each bit passes
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