For calculating statistical Markov model-like state transition probabilities, a method represents state transition probabilities between a plurality of statistical Markov model-like states and output probabilities associated with a plurality of previous statistical Markov model-like states. The state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states. The output probabilities associated with each of the plurality of states depend on the sequence of previous states.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method comprising: representing, by use of a processor, state transition probabilities between a plurality of statistical Markov model-like states (plurality of states) and output probabilities associated with a plurality of previous statistical Markov model-like states (plurality of previous states), wherein the state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states and the output probabilities associated with each of the plurality of states depend on the sequence of previous states; and calculating a state transition probability for the plurality of states. 2. The method of claim 1, wherein the previous states are represented by a history indicator comprising a real number created by concatenating a number representing each previous state as the most significant digit of the real number. 3. The method of claim 1, wherein the state transition probability is calculated using a transition histogram comprising information from the sequence of previous states. 4. The method of claim 3, wherein the state transition probability is calculated as a parametric approximation of each state transition probability. 5. The method of claim 1, wherein the output probability is calculated using a probability histogram comprising information from the sequence of previous states. 6. The method of claim 5, wherein the output probability is calculated as a parametric approximation of the output probabilities for each state. 7. The method of claim 2, wherein the state transition probability is calculated by minimizing the expression tr(ÃiTDTÃiG)−2tr(DÃiPα,i) subject to constraints that 1TÃiφ(h)≦0 and Ãiφ(h)≧0. 8. The method of claim 7, wherein the sequence of previous states is calculated using a branch metric with a current state, a history leading to the current state, and a next state. 9. A program product comprising a computer readable storage medium that stores code executable by a processor, the executable code comprising code to perform: representing state transition probabilities between a plurality of statistical Markov model-like states (plurality of states) and output probabilities associated with a plurality of previous statistical Markov model-like states (plurality of previous states), wherein the state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states and the output probabilities associated with each of the plurality of states depend on the sequence of previous states; and calculating a state transition probability for the plurality of states. 10. The program product of claim 9, wherein the previous states are represented by a history indicator comprising a real number created by concatenating a number representing each previous state as the most significant digit of the real number. 11. The program product of claim 9, wherein the state transition probability is calculated using a transition histogram comprising information from the sequence of previous states. 12. The program product of claim 11, wherein the state transition probability is calculated as a parametric approximation of each state transition probability. 13. The program product of claim 9, wherein the output probability is calculated using a probability histogram comprising information from the sequence of previous states. 14. The program product of claim 13, wherein the output probability is calculated as a parametric approximation of the output probabilities for each state. 15. The program product of claim 10, wherein the state transition probability is calculated by minimizing the expression tr(ÃiTDTÃiG)−2tr(DÃiPα,i) subject to constraints that 1TÃiφ(h)≦0 and Ãiφ(h)≧0. 16. The program product of claim 15, wherein the sequence of previous states is calculated using a branch metric with a current state, a history leading to the current state, and a next state. 17. An apparatus comprising: a processor; a memory that stores code executable by the processor, the code comprising: code that represents state transition probabilities between a plurality of statistical Markov model-like states (plurality of states) and output probabilities associated with a plurality of previous statistical Markov model-like states (plurality of previous states), wherein the state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states and the output probabilities associated with each of the plurality of states depend on the sequence of previous states; and code that calculates a state transition probability for the plurality of states. 18. The apparatus of claim 17, wherein the previous states are represented by a history indicator comprising a real number created by concatenating a number representing each previous state as the most significant digit of the real number. 19. The apparatus of claim 17, wherein the state transition probability is calculated using a transition histogram comprising information from the sequence of previous states. 20. The apparatus of claim 19, wherein the state transition probability is calculated as a parametric approximation of each state transition probability.