ON THE GENERALIZED SYMMETRICAL CUTOFF RATE FOR FINITE-STATE CHANNELS

Finite-state discrete-time channels with equiprobable M-ary inputs are considered. The generating function bound, which is ubiquitously appl ied to upper-bound the error probability of uncoded signaling over the se channels, is used here to lower-bound the corresponding generalized symmetric cutoff rate, which lower-bounds the practically achievable rates and error exponents in these channels with symmetric signaling. The bound accounts for general additive metrics. For the special case of the optimal maximum-likelihood metric, the corresponding bound is s hown to be asymptotically tight in the region where the symmetric cuto ff rate approaches its maximum value of log(2) M (bits-per-channel use ). For a finite-state additive white Gaussian noise (AWGN) channel thi s feature is used to relate the minimum Euclidean distance of an uncod ed symmetric system to the corresponding symmetric cutoff rate. The re sults are demonstrated for AWGN channels corrupted by linear and nonli near intersymbol interference. They are also used to assess the effici ency of concatenated coding over the 4-ary AWGN channel where the fini te-state mechanism is defined by simple rate 1/2, four-state Ungerboec k 4-AM trellis code.