Buffer overflow in variable length coding of fixed rate sources

In this paper, we develop and analyze an easily instrumentable scheme for variable length encoding of discrete memoryless fixed-rate sources in which buffer overflows result in codeword erasures at locations that are perfectly specified to the user. Thus, no loss of synchronism ever occurs. We find optimal (i.e., minimizing the probability of buffer overflow) code-wold length requirements under the Kraft inequality constraint, relative to various constant transmission rates
R
, and show that these do not result in the minimal average code-word length. The corresponding bounds on the probability of buffer overflow provide a linkup between source coding and Rényi's generalized source entropy. We show, further, that codes having optimal word lengths can be constructed by the method of Elias, and we develop corresponding sequentially instrumented encoders and decoders. We show that the complexity of these encoders and decoders grows only linearly with the encoded message block length
k
, provided the size
d
of the coder alphabet is a power of
2
, and otherwise grows no worse than quadratically with
k
.