Contemporary and future speech telecommunication systems now utilise low bit rate (LBR) speech coding techniques in efforts to eliminate bandwidth expansion as a disadvantage of digital coding and transmission. These speech coders employ model-based approaches in compressing human speech into a number of parameters, using a well-known process known as linear predictive coding (LPC). However, a major side-effect observed in these coders is that errors in the model parameters have noticeable and undesirable consequences on the synthesised speech quality, and unless they are protected from such corruptions, the level of service quality will deteriorate rapidly. Traditionally, forward error correction (FEC) coding is used to remove these errors, but these require substantial redundancy. Therefore, a different perspective of the error control problems and solutions is necessary. In this thesis, emphasis is constantly placed on exploiting the constraints and residual redundancies present in the model parameters. It is also shown that with such source criteria in the LBR speech coders, varying degrees of error protection from channel corruptions are feasible. From these observations, error control requirements and methodologies, using both block- and parameter-orientated aspects, are analysed, devised and implemented. It is evident, that under the unusual circumstances which LBR speech coders have to operate in, the importance and significance of source reliant error control will continue to attract research and commercial interests. The work detailed in this thesis is focused on two LPC-based speech coders. One of the ideas developed for these two coders is an advanced zero redundancy scheme for the LPC parameters which is designed to operate at high channel error rates. Another concept proposed here is the use of source criteria to enhance the decoding capabilities of FEC codes to exceed that of maximum likelihood decoding performance. Lastly, for practical operation of LBR speech coders, lost frame recovery strategies are viewed to be an indispensable part of error control. This topic is scrutinised in this thesis by investigating the behaviour of a specific speech coder under irrecoverable error conditions. In all of the ideas pursued above, the effectiveness of the algorithms formulated here are quantified using both objective and subjective tests. Consequently, the capabilities of the techniques devised in this thesis can be demonstrated, examples of which are: (1) higher speech quality produced under noisy channels, using an improved zero-redundancy algorithm for the LPC filter coefficients; (2) as much as 50% improvement in the residual BER and decoding failures of FEC schemes, through the utilisation of source criteria in LBR speech coders; and (3) acceptable speech quality produced under high frame loss rates (14%), after formulating effective strategies for recovery of speech coder parameters. It is hoped that the material described here provide concepts which can help achieve the ideals of maximum efficiency and quality in LBR speech telecommunications.