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Short unit-memory byte-oriented binary convolutional codes having maximal free distance (Corresp.)

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It is shown that (n_{o},k_{o}) convolutional codes with unit memory always achieve the largest free distance among all codes of the same rate k_{o}/n_{o} and same number 2^{Mk_{o}} of encoder states, where M is the encoder memory. A unit-memory code with maximal free distance is given at each place where this free distance exceeds that of the best code with k_{o} and n_{o} relatively prime, for all Mk_{o} \leq 6 and for R = l/2, 1/3, 1/4, 2/3 . It is shown that the unit-memory codes are byte oriented in such a way as to be attractive for use in concatenated coding systems.

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Information Theory, IEEE Transactions on  (Volume:22 ,  Issue: 3 )