Nambirajan Seshadri

List Viterbi decoding algorithms with applications

A list Viterbi decoding algorithm (LVA) produces a rank ordered list of the L globally best candidates after a trellis search. The authors present two such algorithms, (i) a parallel LVA that simultaneously produces the L best candidates and (ii) a serial LVA that iteratively produces the k/sup th/ best candidate based on knowledge of the previously found k-1 best paths. The application of LVA to a concatenated communication system consisting of an inner convolutional code and an outer error detecting code is considered in detail. Analysis as well as simulation results show that significant improvement in error performance is obtained when the inner decoder, which is conventionally based on the Viterbi algorithm (VA), is replaced by the LVA. An improvement of up to 3 dB is obtained for the additive white Gaussian noise (AWGN) channel due to an increase in the minimum Euclidean distance. Ever larger gains are obtained for the Rayleigh fading channel due to an increase in the time diversity. It is also shown that a 10% improvement in throughput is obtained along with significantly reduced probability of a decoding failure for a hybrid FEC/ARQ scheme with the inner code being a rate compatible punctured convolutional (RCPC) code. >

Multilevel codes for unequal error protection

Two combined unequal error protection (UEP) coding and modulation schemes are proposed. The first method multiplexes different coded signal constellations, with each coded constellation providing a different level of error protection. In this method, a codeword specifies the multiplexing rule and the choice of the codeword from a fixed codebook is used to convey additional important information. The decoder determines the multiplexing rule before decoding the rest of the data. The second method is based on partitioning a signal constellation into disjoint subsets in which the most important data sequence is encoded, using most of the available redundancy, to specify a sequence of subsets. The partitioning and code construction is done to maximize the minimum Euclidean distance between two different valid subset sequences. This leads to ways of partitioning the signal constellations into subsets. The less important data selects a sequence of signal points to be transmitted from the subsets. A side benefit of the proposed set partitioning procedure is a reduction in the number of nearest neighbors, sometimes even over the uncoded signal constellation. >

On the use of tentative decisions to cancel intersymbol interference and nonlinear distortion (with application to magnetic recording channels)

We develop a theory of the error rate of receivers that use tentative decisions for adaptive cancellation of intersymbol interference (ISI). We formulate precise conditions under which tentative decisions can be effectively used to cancel linear or nonlinear ISI, and verify the predictions of the theory by Monte Carlo simulations on four typical channels. In the case of magnetic recording channels, we show that the conditions for effective cancellation are satisfied by the precursor interference generated by inductive read heads, resulting in an improvement of the noise margin of 2 dB at the output of a symbol-by-symbol detector or 1 dB at the output of a Viterbi decoder at a bit error rate of 10/sup -9/. This technique has been incorporated in an experimental VLSI partial response maximum-likelihood (PRML) receiver, and the results confirmed by laboratory measurements. We also show that no improvement is obtained when this technique is used to compensate nonlinear distortion, which is another common impairment of magnetic recording channels, and we establish fundamental limits for the improvement achievable by any nonlinear equalization technique in magnetic recording.

Decoding of severely filtered modulation codes using the (M, L) algorithm

The problem of decoding data in the presence of infinite-duration intersymbol interference that is caused by severe channel filtering is considered. Filtered continuous phase modulations (CPM) are the particular object of study. A state-variable approach is used for defining the decoder tree. Maximum likelihood sequence estimation requires exhaustive tree searching, which is restricted by using the (M, L) algorithm since this approach does not require that the channel intersymbol interference be finite. After briefly describing the (M, L) algorithm, the authors motivate the problem of equalization of infinite-impulse-response channels by considering the performance of a discrete-time single-pole channel filtering a binary input sequence. The state variable description of a linear system is used to analyze the filtered modulation. The state of the filtered modulation for a given input modulation is used to define the tree structure of the filtered signal upon which the (M, L) algorithm operates. The minimum signal space distance results for several filtered CPM schemes are then summarized. Extensive simulation results are presented, and comparisons to the optimal performance are made. >

Asymptotic error performance of modulation codes in the presence of severe intersymbol interference

The minimum distance and hence the asymptotic error probability of trellis modulation codes that have been subjected to severe channel filtering are evaluated. A general algorithm is proposed for this purpose and applied to one class of coded modulations. Using a frequency-domain interpretation of the Euclidean distance, it is shown that under extreme channel band limitations, the error event that causes the minimum distance is characterized by a spectral null at DC. Numerical results show that for filtered continuous-phase-modulation codes, decreasing the modulation index or smoothing the frequency pulse does not improve the error performance. For some of these modulations, channel filtering can actually improve the minimum distance. Bandpass and low-pass filtering are contrasted. The numerical results are explained by power spectrum considerations. >