Institute for Systems Research Technical Reports

By means of computer search, several such families are designed so that each family member is at least as good as any comparable code in the literature. (ﲇood here is defined in terms of minimum time diversity and minimum squared product distance, the most important parameters for performance over Rayleigh fading channels.) A protocol to implement these rate-compatible trellis codes in a type-II hybrid ARQ format with only a low-rate feedback channel is described. Upper bounds on the resulting bit error rate are developed and the results are used to select the best adaptive code from several possibilities. Simulation results comparing the proposed scheme with fixed-rate codes of the same throughput show substantial coding gain. Finally, a protocol modification limiting the variability of the code rate over a frame is described; this modification eliminates the need for excessive buffering, with a very small effect on performance

The proposed codes are also simulated under less ideal assumptions. For instance, results for a 1 bit/sec/Hz IQ-TCM code without CSI show a significant gain over conventional coding. Finally, simulations over channels with correlated fading were undertaken; it is concluded that an interleaver span of 4v yields performance close to what is achieved with ideal interleaving.

Also included is an analysis of maximal ratio combining when the diversity branches are correlated; the cutoff rate and a tight upper bound on the pairwise error probability are derived. It is shown that, with double diversity, a branch correlation coefficient as high as 0.5 results in only slight performance degradation.

We begin by quantifying the amount of ﲲesidual redundancy inherent in the LSP's of Federal Standard 1016 CELP. This is done by modeling the LSP's as first and second-order Markov chains. Two models for LSP generation are proposed; the first model characterizes the intra-frame correlation exhibited by the LSP's, while the second model captures both intra-frame and inter-frame correlation. By comparing the entropy rates of the models thus constructed with the CELP rates, it is shown that as many as one-third of the LSP bits in every frame of speech are redundant.

We next consider methods by which this residual redundancy can be exploited by an appropriately designed channel decoder. Before transmission, the LSP's are encoded with a forward error control (FEC) code; we consider both block (Reed- Solomon) codes and convolutional codes. Soft-decision decoders that exploit the residual redundancy in the LSP's are implemented assuming additive white Gaussian noise (AWGN) and independent Rayleigh fading environments. Simulation results employing binary phaseshift keying (BPSK) indicate coding gains of 2 to 5 dB over soft-decision decoders that do not exploit the residual redundancy.

The proposed codes are also simulated over channels with correlated fading; it is concluded that an interleaver span of 4v yields performance close to what is achieved with ideal interleaving.

We begin by quantifying the amount of ﲲesidual redundancy inherent in the LSP's of Federal Standard 1016 CELP. This is done by modeling the LSP's as first-and second-order Markov chains. Two models for LSP generation are proposed; the first model characterizes the intra-frame correlation exhibited by the LSP's, while the second model captures both intra-frame and inter-frame correlation. By comparing the entropy rates of the models thus constructed with the CELP rates, it is shown that as many as one-third of the LSP bits in every frame of speech are redundant.

We next consider methods by which this residual redundancy can be exploited by an appropriately designed channel decoder. Before transmission, the LSP's are encoded with a forward error control (FEC) code; we consider both (Reed-Solomon) codes and convolutional codes. Soft-decision decoders that exploit the residual redundancy in the LSP's are implemented assuming additive white Gaussian noise (AWGN) and independent Rayleigh fading environments. Simulation results employing binary phase-shifting keying (BPSK) indicate coding gains of 2 to 5 dB over soft-decision decoders that do not exploit the residual redundancy.

We investigate the problem of detecting a binary iid non-uniform source transmitted across the Markov channel. Two maximum a posteriori (MAP) formulations are considered: a sequence MAP detection and an instantaneous MAP detection. The two MAP detection problems are implemented using a modified version of the Viterbi decoding algorithm and a recursive algorithm. Necessary and sufficient conditions under which the sequence MAP detector becomes useless as well as simulation results are presented. A comparison between the performance of the proposed system with that of a (substantially more complex) traditional tandem source-channel coding scheme exhibits a better performance for the proposed scheme at relatively high channel bit error rates.

The same detection problem is then analyzed for the case of a binary symmetric Markov source. Analytical and simulation results show the existence of a "mismatch" between the source and the channel. This mismatch is reduced by the use of a rate-one convolutional encoder. Finally, the detection problem is generalized for the case of a binary non-symmetric Markov source.

We First derive a maximum likelihood (ML) decoding algorithm for the channel; it turns out that ML decoding is equivalent to decoding a received vector onto either the closest codeword or the codeword that is farthest away, depending on whether an ﲡpparent epidemic has occurred. We next show that the Poly-contagion channel is an ﲡveraged channel in the sense of Ahlswede (and others) and that its capacity is zero. We then demonstrate that the Poly- contagion channel is a counter-example to the adage, ﲭemory cannot decrease capacity ; the capacity of the Poly-contagion channel is actually less than that of the associated memoryless channel. Finally, we consider a finite-memory version of the Poly-contagion model; this channel is (unlike the original) ergodic with a non-zero capacity that increases with increasing memory.

This paper also views OOC's with unequal auto- and cross-correlation constraints as constant-weight unequal error protection (UEP) codes with two levels of protection. The bounds derived are interpreted from this viewpoint and are compared with previous work on UEP codes.