Interleaved concatenated codes: New perspectives on approaching the Shannon limit

The last few years have witnessed a significant decrease in the gap between the Shannon channel capacity limit and what is practically achievable. Progress has resulted from novel extensions of previously known coding techniques involving interleaved concatenated codes. A considerable body of simulation results is now available, supported by an important but limited theoretical basis. This paper presents a computational technique which further ties simulation results to the known theory and reveals a considerable reduction in the complexity required to approach the Shannon limit.

Training and search methods for speech recognition.

Speech recognition involves three processes: extraction of acoustic indices from the speech signal, estimation of the probability that the observed index string was caused by a hypothesized utterance segment, and determination of the recognized utterance via a search among hypothesized alternatives. This paper is not concerned with the first process. Estimation of the probability of an index string involves a model of index production by any given utterance segment (e.g., a word). Hidden Markov models (HMMs) are used for this purpose [Makhoul, J. & Schwartz, R. (1995) Proc. Natl. Acad. Sci. USA 92, 9956-9963]. Their parameters are state transition probabilities and output probability distributions associated with the transitions. The Baum algorithm that obtains the values of these parameters from speech data via their successive reestimation will be described in this paper. The recognizer wishes to find the most probable utterance that could have caused the observed acoustic index string. That probability is the product of two factors: the probability that the utterance will produce the string and the probability that the speaker will wish to produce the utterance (the language model probability). Even if the vocabulary size is moderate, it is impossible to search for the utterance exhaustively. One practical algorithm is described [Viterbi, A. J. (1967) IEEE Trans. Inf. Theory IT-13, 260-267] that, given the index string, has a high likelihood of finding the most probable utterance.