Efficient Computation of Viterbi Decoder Reliability With an Application to Variable-Length Coding

Abstract

This paper compares the accuracy and complexity of Raghavan and Baum’s Reliability Output Viterbi Algorithm (ROVA), Polyanskiy’s accumulated information density (AID), and Fricke and Hoeher’s lower complexity approximation of ROVA. It turns out that AID is far less accurate than ROVA in practice. This paper proposes codeword information density (CID), which modifies AID to improve its accuracy and leads to a lower-complexity implementation of ROVA. The paper includes an analytical expression for the random variable describing the correct decoding probability computed by ROVA and uses this expression to characterize how the probabilities of correct decoding, undetected error, and negative acknowledgement behave as a function of the selected threshold for reliable decoding. This paper examines both the complexity and the simulation time of ROVA, CID, AID, and the Fricke and Hoeher approximation to ROVA. This paper also derives an expression for the union bound on the frame error rate for zero-terminated trellis codes with punctured symbols and uses it to optimize the order of symbol transmission in an incremental retransmission scheme. This paper concludes by comparing the performance of an incremental retransmission scheme using ROVA as a stopping condition to one that uses a CRC as a stopping condition.