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Abstract-Many network information theory problems face the similar difficulty of single letterization. We argue that this is due to the lack of a geometric structure on the space of probability distribution. In this paper, we develop such a structure by assuming that the distributions of interest are close to each other. Under this assumption, the K-L divergence is reduced to the squared Euclidean metric in an Euclidean space. Moreover, we construct the notion of coordinate and inner product, which will facilitate solving communication problems. We will also present the application of this approach to the point-to-point channel and the general broadcast channel, which demonstrates how our technique simplifies information theory problems.

Purpose To investigate the clinical efficacy and feasibility of one-stage surgical treatment for upper thoracic spinal tuberculosis by internal fixation, debridement, and combined interbody and posterior fusion via a posterioronly approach. Methods Fourteen patients (eight males, six females) with upper thoracic tuberculosis whose lesions were confined to two adjacent segments were admitted to our hospital. Their ages ranged from 23 to 72 years (average, 50 years). The American Spinal Injury Association (ASIA) impairment scale was used to assess neurological function. ASIA classification showed that preoperatively, one patient was grade A, two patients were grade B, eight patients were grade C, and three patients were grade D. All patients were treated with one-stage surgical treatment by internal fixation, debridement, and combined interbody and posterior fusion via a posterior-only approach. Patients were evaluated preoperatively and postoperatively by measurement of thoracic kyphotic angles using Cobb angle evaluation, determination of erythrocyte sedimentation rate (ESR), evaluation of ASIA impairment scale, and radiological examination. Results Operation time ranged from 70 to 135 min, (average, 110 min). Intraoperative blood loss ranged from 200 to 950 mL (average, 450 mL). All patients were followed up for 22 to 48 months postoperatively (average, 31.5 months). No sinus tract formation, cerebrospinal meningitis, or recurrence of tuberculosis occurred. All patients had significant postoperative improvement in ASIA classification scores. The thoracic kyphotic angles were significantly decreased to 12°-26°postoperatively, and at final follow-up were 13°-28°. The ESR recovered to normal within 6 months postoperatively in all patients. Bone fusion was achieved within 3-8 months (average, 5.5 months). Conclusions One-stage surgical treatment for upper thoracic spinal tuberculosis by internal fixation, debridement, and combined interbody and posterior fusion via a posterior-only approach can be an effective and feasible treatment method.