The application of a combined test-error-correcting procedure is studied to improve the mean time to failure (MTTF) for degrading memory systems with defects. The degradation is characterized by the probability p that within a unit of time a memory cell changes from the operational state to the permanent defect state. Bounds are given on the MTTF and it is shown that, for memories with N words of k information bits, coding gives an improvement in MTTF proportional to (k/n) N(d/sub min//sup -2/)/(d/sub min//sup -1/), where d/sub min/ and (k/n) are the minimum distance and the efficiency of the code used, respectively. Thus the time gain for a simple minimum-distance-3 is proportional to N/sup -1/. A memory word test is combined with a simple defect-matching code. This yields reliable operation with one defect in a word of length k+2 at a code efficiency k/(k+2).>

It is shown that the set of nonachievable rates for the collision channel without feedback is convex, as had been conjectured by Massey.

A study is made of the Cover-Leung capacity region for two specific noiseless two-userM-ary input multiple-access channels with complete feedback. It is shown that the symmetric rate point of the Cover-Leung capacity region is on the total cooperation line for large enough values of M. Thus feedback allows communication at the same rates as if both users had complete joint knowledge of intended messages.

Maximum likelihood (ML) decoding of short constraint length convolutional codes became feasible with the invention of the Viterbi decoder. Several authors have since upper bounded the performance of ML decoders. A method to calculate the event error probability of an ML decoder for convolutional codes is described.

A state-space approach to the syndrome decoding of binary ratek/nconvolutional codes is described. State-space symmetries of a certain class of codes can be exploited to obtain a reduction in the exponent of growth of the decoder hardware. Aside from these savings it is felt that the state-space formalism developed has some unique intrinsic value.

An explicit method is given to evaluate Viterbi's union bounds on both the first event error probability and the bit error probability of binary convolutional codes on a binary symmetric channel. These bounds are evaluated for the rate1/2code with generators1 + D + D^{2}and1 + D^{2}. Comparison is made with the bounds and experimental results of van de Meeberg.

No abstract.

The error probability for a class of binary recursive feedback strategies is evaluated. An exact analysis is given for both a nonsequential and a sequential decision strategy. We obtain the interesting result that even for the nonsequential receiver the error probability vanishes exponentially fast at channel capacity. A similar result had been previously obtained by Horstein for the sequential receiver, but was believed to be a consequence of the sequential nature of his decision strategy. For rates below capacity our feedback strategies have two error exponents, i.e., a lower error exponentE^- (R)and an upper error exponentE^+ (R). The lower error exponentE^- (R)exhibits an anomalous behavior in thatE^- (R)increases monotonically fromE^- (0) = 0toE^- (C) = E(C)as the rateRincreases from 0 to capacity.